Faculty of Information Technology, BUT

Course details

Mathematical Analysis 2

IMA2 Acad. year 2019/2020 Winter semester 4 credits

Course is not open in this year
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Series. The Fourier an wavelet transforms. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.

Guarantor

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)

Deputy Guarantor

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

26 hrs lectures, 26 hrs exercises

Assessment points

70 exam, 30 half-term test

Department

Lecturer

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)
Vítovec Jiří, Mgr., Ph.D. (DMAT FEEC BUT)

Instructor

Rebenda Josef, Mgr., Ph.D. (CEITEC BUT)
Vítovec Jiří, Mgr., Ph.D. (DMAT FEEC BUT)

Subject specific learning outcomes and competences

The ability to understand the basic problems of higher calculus and use derivatives, integrals and differential equations for solving specific problems.

Learning objectives

The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems.

Why is the course taught

The IMA2 course follows on the IMA1 course and complements the necessary knowledge of the concepts of calculus needed to understand and master advanced technical and physical subjects.

Prerequisites

Prerequisite kwnowledge and skills

The IMA1 course.

Study literature

  • Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2013. (in Czech).

Fundamental literature

  • Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966.
  • Edwards, C. H., Penney, D. E., Calculus with Analytic Geometry, Prentice Hall, 1993.
  • Fong, Y., Wang, Y., Calculus, Springer, 2000.
  • Ross, K. A., Elementary analysis: The Theory of Calculus, Springer, 2000.
  • Small, D. B., Hosack, J. M., Calculus (An Integrated Approach), Mc Graw-Hill Publ. Comp., 1990.
  • Thomas, G. B., Finney, R. L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.
  • Zill, D. G., A First Course in Differential Equations, PWS-Kent Publ. Comp., 1992.

Syllabus of lectures

  1. Number series.
  2. Power series.
  3. Fourier series.
  4. Fourier transform, discrete Fourier transform.
  5. Wavelets, wavelet transform.
  6. Functions of several variables (particularly in 2 and 3 dimensions), limit and continuity.
  7. Differential calculus of functions of several variables I: partial derivatives, Hess matrix, Schwarz theorem.
  8. Differential calculus of functions of more variables II: local extrema, Sylvester criterion.
  9. Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
  10. Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
  11. Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
  12. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equations.
  13. Numerical solution of differential equations of the first order.

Syllabus of numerical exercises

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

Progress assessment

Written tests during semester (maximum 30 points).

Controlled instruction

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

Exam prerequisites

At least 10 points from the tests during the semester.

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Compulsory
  • Programme IT-BC-3, field BIT, 2nd year of study, Compulsory
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