MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2020
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Wed 9:40–11:10 D415, Z. Dušek
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
Lecture
Seminar
Exercise
Tutorial
Consultation
lecture exercise
Teaching Methods
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test1414
Preparation for Seminars, Exercises, Tutorial1015
Preparation for the Final Test1313
Attendance on Seminars/Exercises/Tutorial/Excursion138
Participation in the final test22
Total:5252
Assessment Methods and Assesment Rate
Test – final 70 %
seminar activity 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2019
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Mon 13:05–14:35 A7, Z. Dušek
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Exercise
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2018
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Tue 13:05–14:35 B2, Z. Dušek
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Exercise
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2018
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
Ing. Jaroslav Staněk, DiS.
Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/CCV: Tue 6. 3. 11:25–12:55 D515, Tue 20. 3. 11:25–12:55 D515, Tue 3. 4. 11:25–12:55 D515, Tue 17. 4. 11:25–12:55 D515, J. Vysoká
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 90 student(s).
Current registration and enrolment status: enrolled: 0/90, only registered: 0/90
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2017
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S02: Wed 13:05–14:35 B4, Z. Dušek
MAT_3/TS01: Tue 8:00–9:30 A219, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 90 student(s).
Current registration and enrolment status: enrolled: 0/90, only registered: 0/90
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2016
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Michaela Vargová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S02: Wed 14:50–16:20 D617, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 60 student(s).
Current registration and enrolment status: enrolled: 0/60, only registered: 0/60
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Grading of the course: First Test/Seminar Work/ … : maximum 30% (0-30 points), Final Test: maximum 70% (0-70 points). Successful graduates of the course have to get totally at least 70 points: A 100 – 90, B 89,99 – 84, C 83,99 – 77, D 76,99 – 73, E 72,99 – 70, FX 69,99 – 30, F 29,99 - 0. Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
Summer 2016
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
doc. Ing. Zuzana Rowland, MBA, PhD.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/CAP_prez: Wed 13. 4. 13:50–16:20 A2, J. Vysoká
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2015
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Thu 14:50–16:20 D616, D. Smetanová
MAT_3/S02: Thu 14:50–16:20 B5, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2015
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Michaela Vargová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
doc. Ing. Zuzana Rowland, MBA, PhD.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/CAP: Mon 20. 4. 12:10–13:35 A6, 13:45–15:15 A6, 15:30–17:00 A6, M. Vargová, J. Vysoká, CCV - zkrácený kurz v rámci CŽV
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2014
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Tue 11:25–12:55 E7, J. Vysoká
MAT_3/S02: Tue 14:50–16:20 D515, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 80 student(s).
Current registration and enrolment status: enrolled: 0/80, only registered: 0/80
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2014
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jana Vysoká, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/CAP: Tue 8. 4. 9:00–12:45 D303L, J. Vysoká, výuka ve zkráceném kurzu v rámci CŽV
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2013
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jana Vysoká, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Wed 14:45–16:15 D616, J. Vysoká
MAT_3/S02: Thu 8:15–9:45 D515, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2013
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jana Vysoká, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/ccv: Tue 23. 4. 11:35–14:40 B3, J. Vysoká, výuka v rámci CŽV
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Exam – oral 5 %
Test – final 95 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2012
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jana Vysoká, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Thu 9:55–11:25 B5, J. Vysoká
MAT_3/S02: Tue 13:10–14:40 B5, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Exam – oral 5 %
Test – final 95 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2012
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jana Vysoká, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Tue 14:45–16:15 D416, J. Vysoká
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Exam – oral 5 %
Test – final 95 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2011
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Petr Chládek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_3/S01: Fri 8:15–9:45 A4, J. Vysoká
MAT_3/S02: Fri 9:55–11:25 A4, J. Vysoká
Prerequisites
( MTT_1 Mathematics for technicians I || MTE Mathematics for economists || MA_ST_II Matematika SM II || MTT_2 Mathematics II (Civil engineering) || MAT_2 Mathematics_2 ) && FORMA(P)
Mathematics I, II.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The goal is to add the parts of mathematics concerning the courses Mathematics 1 and Mathematics 2. Emphasis will be placed on the application tasks. The subject is devoted to the solution of ordinary differential equations and systems and introduction to integral calculus of two and three variables.
Syllabus
  • The ordinary linear differential equations of the first and higher order with constant coefficients. The characteristic equation, variation of parameters, estimation method. The principle of superposition. Systems of differential equations. Functions of several variables. Polar, circular, spherical coordinates. Double and triple integral, Fubini's theorem. Solving application problems.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Exam – oral 5 %
Test – final 95 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, summer 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2011
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Stuchlý, CSc.
Timetable
each odd Tuesday 17:10–18:40 B5, each odd Tuesday 18:45–20:15 B5
Prerequisites
MTT_1 Mathematics for technicians I || MTE Mathematics for economists || MA_ST_II Matematika SM II || MTT_2 Mathematics II (Civil engineering)
Mathematics I, II.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The goal is to add the parts of mathematics concerning the courses Mathematics 1 and Mathematics 2. Emphasis will be placed on the application tasks. The subject is devoted to the solution of ordinary differential equations and systems and introduction to integral calculus of two and three variables.
Syllabus
  • The ordinary linear differential equations of the first and higher order with constant coefficients. The characteristic equation, variation of parameters, estimation method. The principle of superposition. Systems of differential equations. Functions of several variables. Polar, circular, spherical coordinates. Double and triple integral, Fubini's theorem. Solving application problems. Curve integral. Green's theorem. Application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Exam – oral 5 %
Test – final 95 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
The course is also listed under the following terms Winter 2010, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
Winter 2010
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Stuchlý, CSc.
Department of Civil Engineering – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites (in Czech)
MTT_1 Mathematics for technicians I || MTE Mathematics for economists || MA_ST_II Matematika SM II || MTT_2 Mathematics II (Civil engineering)
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The goal is to add lots of mathematics content courses related to Mathematics I and Mathematics II. Emphasis will be placed on the application tasks. The subject is the solution of ordinary differential equations, as well as an introduction to integral calculus.
Syllabus
  • 1.Continuation of ordinary differential equation 1 Procedure type ^ y / = f (y / x). 2. Differential equation 1 Procedure type ^ y / f = (((a_1 x + b_1 y + c_1 ))/(( a_2 x + b_2 y + c_2))) 3. Differential equation 1 Procedure type ^ y / + a (x). y = b (x) 4. Introduction to differential equations of second Procedure type ^(//)= y f (y, s ^ /) and y ^(//)= f (xy ^ /) 5. Homogeneous linear differential equations with constant coefficients 6. Inhomogeneous linear differential equations with constant coefficients  , variation of constants 7. Double integral in the rectangular area 8. Double integral in general concluded 9. Substitution method for double integrals 10. Geometric and physical applications of double integrals 11. Definition of triple integrals 12. Substitution method for integrals 13. Geometric and physical applications of triple integrals
Literature
    required literature
  • NAVRÁTIL, M. Diferenciální a integrální počet funkcí dvou a více proměnných. Vydavatelství Mendelovy zemědělské a lesnické univerzity Brno, ISBN 978-8071579038.
  • REKTORYS, K. Přehled užité matematiky. Praha : Prometheus, 2000. 7. vydání. ISBN 80-7196-181-72
  • ZINDULKA, O. Matematika 3. Česká technika - nakladatelství ČVUT, 2007, 1. vydání, ISBN 978-80-01-03678-5.
Forms of Teaching
Seminar
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Exam – oral 5 %
Test – final 95 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 50 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test.
Language of instruction
Czech
Further Comments
The course is taught: every week.
The course is also listed under the following terms summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2024

The course is not taught in winter 2024

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
FORMA(P)
The student masters the range of MAT_z, MAT_2z courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_z and MAT_2z courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
    not specified
  • STRANG, G., Calculus, online https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf
Forms of Teaching
Seminar
Tutorial
Consultation
Teaching Block - tutorial
lecture exercise
Teaching Methods
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial2129
Preparation for the Final Test1313
Attendance on Seminars/Exercises/Tutorial/Excursion168
Participation in the final test22
Total:5252
Assessment Methods and Assesment Rate
Project – semestral 100 %
Exam conditions
The student gains the credit on the base of the attendance and the result of a semester project, completed tasks. Final classification: A minimum of 70% for the project must be obtained in order to be gained credit.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2023

The course is not taught in winter 2023

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
Lecture
Seminar
Exercise
Tutorial
Consultation
lecture exercise
Teaching Methods
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test1414
Preparation for Seminars, Exercises, Tutorial1015
Preparation for the Final Test1313
Attendance on Seminars/Exercises/Tutorial/Excursion138
Participation in the final test22
Total:5252
Assessment Methods and Assesment Rate
Test – final 70 %
seminar activity 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2022

The course is not taught in winter 2022

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
Lecture
Seminar
Exercise
Tutorial
Consultation
lecture exercise
Teaching Methods
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test1414
Preparation for Seminars, Exercises, Tutorial1015
Preparation for the Final Test1313
Attendance on Seminars/Exercises/Tutorial/Excursion138
Participation in the final test22
Total:5252
Assessment Methods and Assesment Rate
Test – final 70 %
seminar activity 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
winter 2021

The course is not taught in winter 2021

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
FORMA(P)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
Lecture
Seminar
Exercise
Tutorial
Consultation
lecture exercise
Teaching Methods
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test1414
Preparation for Seminars, Exercises, Tutorial1015
Preparation for the Final Test1313
Attendance on Seminars/Exercises/Tutorial/Excursion138
Participation in the final test22
Total:5252
Assessment Methods and Assesment Rate
Test – final 70 %
seminar activity 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2021

The course is not taught in summer 2021

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Prerequisites
OBOR(uznavani)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 90 student(s).
Current registration and enrolment status: enrolled: 0/90, only registered: 0/90
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2020

The course is not taught in summer 2020

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Guaranteed by
Ing. Lukáš Polanecký
Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables.
Learning outcomes
At the end of the course, the student is be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student is be able to orientate in the basic terminology of functions of several variables. He/she is be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
Seminar
Exercise
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2019

The course is not taught in summer 2019

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Prerequisites
OBOR(uznavani)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 90 student(s).
Current registration and enrolment status: enrolled: 0/90, only registered: 0/90
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.

MAT_3 Mathematics III

Institute of Technology and Business in České Budějovice
summer 2017

The course is not taught in summer 2017

Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Guaranteed by
doc. Ing. Zuzana Rowland, MBA, PhD.
Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
OBOR(CAP)
The student masters the range of MAT_1, MAT_2 courses (the bases of differential calculus - derivation of a function, process and properties of a function, bases of integral calculus - direct integration, substitution method, integration by parts, integration of rational functions, special substitution methods, application of definite integral, basic methods in solving of differential equations of first and second order).
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to complement mathematical parts related to the knowlege gained in MAT_1 and MAT_2 courses. The emphasis is placed on the application tasks. The course contains the bases of differential calculus of functions with several variables, using the theory of ordinary differential equations to solve simple problems in practice. The course also includes solving of systems of differential equations, introduction to integral calculus of functions of several variables. At the end of the course, the student will be able to solve easy tasks using models containing differential equation of first and second order, systems of differential equations. The student will be able to orientate in the basic terminology of functions of several variables. He/she will be able to apply the calculation of multiply integrals in practice.
Syllabus
  • ­1.Definition of function of several variables, domain of a function, a graph. 2.Partial derivatives and their geometric meaning. 3.Rules for calculation of derivatives, derivatives higher order derivatives. 4.Gradient of a function, directional derivatives. 5.Local extremes, Hessian matrix. 6.Bound extremes of functions of several variables. ­7.Systems of differential equations. 8.Mathematical models (using differential equations). ­­9.Polar, cyclic, spherical coordinates. ­10.Double integral, Fubini theorem. ­11.Substitution method for double integrals. 12.Triple integral, Fubini theorem. ­13.Double and triple integrals - solving of application tasks.
Literature
    required literature
  • Zindulka, O.: Matematika 3, Česká technika - nakladatelství ČVUT, 2007, 1. vydání, 155 stran, ISBN 978-80-01-03678-5
    recommended literature
  • Bubeník, F., Matematika 2, Česká technika - nakladatelství ČVUT, 2006, 1. vydání, ISBN 80-01-03535-2
  • Bubeník, F., Zindulka, O., Matematika 1, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03309-0
Forms of Teaching
přednáškové cvičení (in Czech)
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Critical Thinking
Individual Work– Individual or Individualized Activity
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial16 
Preparation for the Final Test10 
Attendance on Seminars/Exercises/Tutorial/Excursion26 
Total:520
Assessment Methods and Assesment Rate
Test – final 70 %
aktivita na semináři (in Czech) 30 %
Exam conditions
The student gains the credit on the base of the attendance and the result of the final written test. The student has to attend 70% of seminars. The final test consists of four examples with a total of 70 points. It is necessary to reach 30 points to gain the credit. Students have the possibility of a reparative test. First Test/Seminar Work/ … : maximum 30% (0-30 points) Final Test: maximum 70% (0-70 points) Successful graduates of the course have to get totally at least 70 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
The course is also listed under the following terms Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, winter 2019, winter 2020.
  • Enrolment Statistics (recent)