Course detail

Mathematical Analysis 2

FIT-IMA2Acad. year: 2019/2020

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.

Learning outcomes of the course unit

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

Prerequisites

The IMA1 course.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2013.
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.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Written tests during semester (maximum 30 points).
Exam prerequisites:
At least 10 points from the tests during the semester.

Language of instruction

Czech, English

Work placements

Not applicable.

Aims

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.

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

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

Classification of course in study plans

  • Programme BIT Bachelor's, 2. year of study, winter semester, 4 credits, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 2. year of study, winter semester, 4 credits, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

  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.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

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

eLearning

eLearning: opened course