Calculus B 4

Relations:

The course 01ANB4 can be graded only after the courses as required for the group 01ANX3 have been graded.

It is not possible to register for the course 01ANB4 if the student is concurrently registered for or has already completed the course 01ANA4 (mutually exclusive courses).

It is not possible to register for the course 01ANB4 and for the course 01ANA4 in the same semester.

It is not possible to register for the course 01ANB4 and for the course 01DIFR in the same semester.

It is not possible to register for the course 01ANB4 if the student is concurrently registered for or has previously completed the course 01ANA4 (mutually exclusive courses).

Course guarantor:

Milan Krbálek

Lecturer:

Miroslav Kolář, Jiří Mikyška

Tutor:

Lukáš Heriban, Martin Jex, Miroslav Kolář, Martin Kovanda, Jiří Mikyška, Maneesh Narayanan, Jakub Waclawek

Supervisor:

Department of Mathematics

Synopsis:

[1] Implicitly defined functions.

[2] Regular mapping, transformation of coordinates, non-cartesian coordinate systems.

[3] Local, constrained, and global extrema of functions of several independend variables.

[4] Basics of the measure theory, and construction of the Lebesgue measure.

[5] Integral calculus of functions of several independent variables - Riemann and Lebesgue integrals, basic properties, theorem of Fubini, substitution theorem, theorems of Levi and Lebesgue. Limit, continuity and differentiability of parametric integrals.

[6] Line and surface integrals. Integral theorems.

Requirements:

The condition for obtaining the credit is to achieve at least 50 points, which can be obtained in the following way:

1. By writing 2 large credit tests, each worth 40 points, i.e. max. 80 points.

2. By writing 5 mini-tests worth of 4 points each during the exercise, additional 20 points can be obtained.

3. Up to 10 more points can be obtained from the instructor for the activity during the exercises (among N students in the group, the instructor can award up to N points, max. 10 points per student).

4. Attendance is monitored during the exercises, 3 absences are allowed. For further absences, points are deducted, namely, 1 point is deducted for the first absence, 2 points for the second, 3 points for the third...

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] Lynn H. Loomis, Shlomo Z. Sternberg: Advanced Calculus (Revised Ed.), World Scientific Publishing Company, 2014

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

[3] M. Moskowitz and F. Paliogiannis: Functions of Several Real Variables, WSPC, 2011

Recommended references:

[4] S. L. Salas, E. Hille, G. J. Etger: Calculus (One and More variables), Wiley, 9th edition, 2002

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

Note:

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)