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).
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
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.
  • ­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.
    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 exercise
Teaching Methods
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
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
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
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.
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