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.
Recommended optional programme components
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
Assesment methods and criteria linked to learning outcomes
Written tests during semester (maximum 30 points).
At least 10 points from the tests during the semester.
Language of instruction
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.
Type of course unit
26 hours, optionally
Teacher / Lecturer
- Number series.
- Power series.
- Fourier series.
- Fourier transform, discrete Fourier transform.
- Wavelets, wavelet transform.
- Functions of several variables (particularly in 2 and 3 dimensions), limit and continuity.
- Differential calculus of functions of several variables I: partial derivatives, Hess matrix, Schwarz theorem.
- Differential calculus of functions of more variables II: local extrema, Sylvester criterion.
- Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
- Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
- Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
- Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equations.
- Numerical solution of differential equations of the first order.
26 hours, compulsory
Teacher / Lecturer
Problems discussed at numerical classes are chosen so as to complement suitably the lectures.
eLearning: opened course