VŠTE:MAT_3 Mathematics III - Course Information

MAT_3 Mathematics III

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

Activities	Number of Hours of Study Workload
	Daily Study	Combined Study
Preparation for Seminars, Exercises, Tutorial	16
Preparation for the Final Test	10
Attendance on Seminars/Exercises/Tutorial/Excursion	26
Total:	52	0

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

• Enrolment Statistics (winter 2013, recent)
  
• Permalink: https://is.vstecb.cz/course/vste/winter2013/MAT_3