Calculus B 3

Relations:

It is not possible to register for the course 01ANB3 if the student is concurrently registered for or has already completed the course 01ANA3 (mutually exclusive courses).

The course 01ANB3 can be graded only after the course 01MAN2 has been successfully completed.

It is not possible to register for the course 01ANB3 and for the course 01ANA3 in the same semester.

It is not possible to register for the course 01ANB3 if the student is concurrently registered for or has previously completed the course 01ANA3 (mutually exclusive courses).

It is not possible to register for the course 01ANB3 if the student is concurrently registered for or has previously completed the course 01DIFR (mutually exclusive courses).

Course guarantor:

Milan Krbálek

Lecturer:

Milan Krbálek

Tutor:

Maksym Dreval, Lukáš Heriban, Václav Klika, Milan Krbálek

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. Quadratic functions and quadrics.

4. 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.

5. Differential calculus for functions of several variables - limit, continuity, partial and directional derivative, gradient, total derivatives and tangent plane.

6. Taylor series for functions of several variables.

7. Fundamentals in vector analysis, Jacobi matrix.

Requirements:

Credit is awarded based on the number of points a student has earned for various activities during the semester. 120 points can be earned for three credit papers, 25 points for five mini-tests, and 10 points for significant activity in lectures and seminars. 4 absences from seminars are allowed without point reductions, but 3 points are deducted for each absence above the allowed limit. Credit is awarded for 70 points or more. If a student earns 40 points or more (but less than 70), he/she must complete a remedial written paper with at least half the number of points to earn credit. A student who earns less than 40 points loses the right to credit.

A detailed description of the credit criteria is here: https://www.krbalek.cz/For_students/Files_to_load/Harmo_MAB3.pdf

Syllabus of lectures:

Syllabus of tutorials:

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.

Note:

Further information:

https://www.krbalek.cz/For_students/mab3/mab3.html

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Aplikace informatiky v přírodních vědách (compulsory course in the program)
• Aplikované matematicko-stochastické metody (compulsory course in the program)
• Jaderné inženýrství - Aplikovaná fyzika ionizujícího záření (PS)
• Fyzikální inženýrství - Fyzikální inženýrství materiálů (PS)
• Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (PS)
• Fyzikální inženýrství - Inženýrství pevných látek (PS)
• Jaderná a částicová fyzika (compulsory course in the program)
• Jaderné inženýrství - Jaderné reaktory (PS)
• Fyzikální inženýrství - Laserová technika a fotonika (PS)
• Kvantové technologie (compulsory course in the program)
• jaderné inženýrství - Radioaktivita v životním prostředí (PS)
• Vyřazování jaderných zařízení z provozu (compulsory course in the program)
• Physical Engineering - Physical Engineering od Materials (PS)