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Applied Mathematics III - NCHF073

Title:	Aplikovaná matematika III
Guaranteed by:	Department of Condensed Matter Physics (32-KFKL)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time

Guarantor:	RNDr. Viktor Holubec, Ph.D. RNDr. Artem Ryabov, Ph.D.
Teacher(s):	Mgr. Václav Březina, Ph.D. Julian David Giraldo Barreto RNDr. Viktor Holubec, Ph.D. Enrique Puga Cital

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

The third semester of the four-semester course on Applied Mathematics. Vector calculus. Fourier series and Fourier transformation. Eigenvalues and eigenvectors of matrices.

Last update: Houfek Karel, doc. RNDr., Ph.D. (14.05.2023)

Course completion requirements -

The course credit is awarded at practicals after passing three brief (60 min.) tests, one from each major topic in the syllabus: 1) Line and surface integrals, 2) Fourier series and transform, 3) Eigenvalues and eigenvectors. Passing each test means gaining at least 50% of points from it.

After getting course credit at practicals, students can attend final exams. These exams consist of written and oral parts and take place during the examination period. The written part (60 min.) comprises solving 2 practical examples from topics 1) —3). The oral part (60 min.) is a discussion of theoretical concepts (definitions and theorems from lectures) related to the examples in the written part.

Last update: Holubec Viktor, RNDr., Ph.D. (25.06.2024)

Literature -

M. Corral, Vector Calculus, LibreTexts Mathematics.

G. Strang, Introduction to Linear Algebra, Fifth Edition (2016).

R. T. Seeley, An Introduction to Fourier Series and Integrals, Dover Publications 2014.

Lecture notes and materials for practical exercises.

Last update: Holubec Viktor, RNDr., Ph.D. (25.06.2024)

Requirements to the exam -

The requirements for the exam correspond to the course syllabus to the extent that was given in the lectures and exercises.

For more details, see Moodle https://dl1.cuni.cz/course/view.php?id=16748.

Last update: Holubec Viktor, RNDr., Ph.D. (02.10.2024)

Syllabus -

Line integral of scalar and vector field, vector potential, field with zero curl.

Surface integral of scalar and vector field, Gauss-Green's theorem, Stokes‘ theorem. Integral form of divergence and curl.

Fourier series, Bessel’s inequality, Parseval’s identity. Differentiation and integration of Fourier series.

Fourier transformation of functions, Fourier inversion theorem, applications.

Eigenvalues and eigenvectors of matrices, characteristic polynomial.

Jordan normal form, basis of the eigenspace.

Last update: Houfek Karel, doc. RNDr., Ph.D. (02.05.2023)