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Course, academic year 2023/2024
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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
Teaching methods: full-time
Guarantor: RNDr. Viktor Holubec, Ph.D.
RNDr. Artem Ryabov, Ph.D.
Annotation -
Last update: doc. RNDr. Karel Houfek, Ph.D. (14.05.2023)
The third semester of the four-semester course on Applied Mathematics. Vector calculus. Fourier series and Fourier transformation. Eigenvalues and eigenvectors of matrices.
Course completion requirements -
Last update: Mgr. Kateřina Mikšová (14.02.2022)

Final examination (written and oral) takes place during the examination period and students must first obtain the credit for practical exercises. Credit for exercises is based on the solution of take-home problems (34%) and two tests (midterm and final, each 33%).

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

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

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

Lecture notes, materials for practical exercises.

Requirements to the exam -
Last update: doc. RNDr. Karel Houfek, Ph.D. (02.05.2023)

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

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

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.

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