Course detail

Mathematical Analysis II

FSI-SA2Acad. year: 2015/2016

The course “Mathematical Analysis II” is a follow-up to the introductory course “Mathematical Analysis I”. It deals with the differential and integral calculus of functions in one several variables. Students acquire theoretical knowledge in several variables functions necessary for solving of difficult problems in mathematics, physics and technical disciplines.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

doc. Ing. Luděk Nechvátal, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Calculus count methods for applications in technical disciplines.

Prerequisites

The differential and integral calculus of functions in one real variable.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit is conditional on attendance. Examination: oral

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Students will be made familiar with fundaments of differential and integral calculus in n real variables. They will be able to apply it in various engineering tasks.

Specification of controlled education, way of implementation and compensation for absences

Seminars: required
Lectures: recommended

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

V. Jarník: Diferenciální počet II, Academia, 1984. (CS)
V. Jarník: Integrální počet II, Academia, 1984. (CS)
D. M. Bressoud: Second Year Calculus, Springer, 2001. (EN)
J. Škrášek, Z. Tichý: Základy aplikované matematiky I a II, SNTL Praha, 1989. (CS)

Recommended reading

J. Karásek: Matematika II, skripta FSI VUT, 2002. (CS)

Classification of course in study plans

  • Programme B3A-P Bachelor's

    branch B-MAI , 1. year of study, summer semester, compulsory
    branch B-FIN , 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

1. Functions in several variables. Basic concepts.
2. Partial derivations. The gradient.
3. Total differentials. Taylor polynomials.
4. Local extremes.
5. Relative and absolute extremes.
6. Functions defined implicitly.
7. Double and triple integral.
8. Applications of double and triple integrals.
9. Curves and their orientations.
10. Line integrals and its applications. Green's theorem.
11. The potential, the nabla and delta operators, divergence and curl of a vector field.
12. Surfaces and their orientability.
13. Surface integrals and its applications. Gauss-Ostrogradskii's theorem and Stokes' theorem.

Exercise

33 hours, compulsory

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.
doc. Mgr. Zdeněk Opluštil, Ph.D.

Syllabus

Seminars related to the lectures in the previous week.

Computer-assisted exercise

6 hours, compulsory

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

Seminars in a computer lab have the programme MAPLE as a computer support. Obligatory topics to go through: Plotting of the graph of a function of more variables (given by explicit, implicit or parametric equations), extrema of functions of more variables.