Calculus B 3

Course guarantor:

Andrii Anikushyn

Lecturer:

Andrii Anikushyn

Tutor:

Andrii Anikushyn

Supervisor:

Department of Mathematics

Synopsis:

1. Functional sequences and series - convergence range, criteria of uniform convergence, continuity, limit, differentiation and integration of functional series, power series, Series Expansion, Taylor´s theorem.

2. Ordinary differential equations - equations of first order (method of integration factor, equation of Bernoulli, separation of variables, homogeneous equation and exact equation) and equations of higher order (fundamental system, reduction of order, variation of parameters, equations with constant coefficients and special right-hand side, Euler differential equation).

3. Metric spaces - metric, norm, scalar product, neighborhood, interior and exterior points, boundary point, isolated and non-isolated point, boundary of set, completeness of space, Hilbert spaces. Orthogonal polynomials. Complete orthogonal systems.

4. Fourier series - expansion of functions into Fourier series, trigonometric Fourier series and their convergence.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

100 points will be awarded for the whole course. 40 for the final exam, and 60 can be earned during the term itself.

Those 60 are: 20 for the hometasks, 20 for midterm-1 and 20 for midterm-2.

In order to get a Credit/Zápočet one needs to earn at least 40 out of 60 points during the term.

It is allowed to miss not more than 5 exercises classes.

Study Objective:

Study materials:

Key references:

[1] M. L. Bittinger, D. J. Ellenbogen, S. J. Surgent: Calculus and Its Applications (11th Ed.), Pearson, 2015

[2] R. A. Adams, Calculus: A Complete Course, 1999

[3] J. E. Marsden, A. Tromba: Vector Calculus, W.H. Freeman, New York, 2013.

Recommneded references:

[4] J. Stewart: Multivariable Calculus, 8th Edition, Brooks Cole, 2015.

Media and tools: MATLAB

Note:

Time-table for winter semester 2026/2027:

Time-table is not available yet

Time-table for summer semester 2026/2027:

Time-table is not available yet

The course is a part of the following study plans:

• Physical Engineering - Computational physics (PS)
• Quantum Technologies (compulsory course in the program)
• Nuclear and Particle Physics (compulsory course in the program)
• Physical Engineering - Plasma Physics and Thermonuclear Fusion (PS)
• Physical Engineering - Solid State Engineering (PS)
• Physical Engineering - Laser Technology and Photonics (PS)