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Course, academic year 2023/2024
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Applied Mathematics IV - NCHF074
Title: Aplikovaná matematika IV
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 5
Hours per week, examination: summer 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. Jan Kuriplach, CSc.
doc. RNDr. Karel Houfek, Ph.D.
Annotation -
Last update: doc. RNDr. Karel Houfek, Ph.D. (14.05.2023)
The fourth semester of the four-semester course on Applied Mathematics. Hilbert spaces. Complex analysis. Introduction to partial differential equations and theory of distribution.
Course completion requirements -
Last update: Mgr. Kateřina Mikšová (09.02.2022)

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. (14.05.2023)

T. Needham, Visual Complex Analysis, Oxford Univeristy Press, 1999.

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: Mgr. Kateřina Mikšová (09.02.2022)

Hilbert space, Hilbert space and Fourier series. Orthogonal polynomial systems. Operators on Hilbert space.

Complex analysis, Cauchy’s theorem, Cauchy’s integral formula, Residue theorem and its applications

Introduction to partial differential equations. Heat equation, wave equation, Laplace’s and Poisson’s equation.

Introduction to the theory of distributions.

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