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.
  • Enrolment Statistics (summer 2014, recent)
  • Permalink: https://is.vstecb.cz/course/vste/summer2014/MAT_3