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The fourth semester of the four-semester course on Applied Mathematics. Hilbert spaces. Complex analysis.
Introduction to partial differential equations and theory of distribution.
Last update: Houfek Karel, doc. RNDr., Ph.D. (14.05.2023)
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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%). Last update: Mikšová Kateřina, Mgr. (09.02.2022)
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T. Needham, Visual Complex Analysis, Oxford Univeristy Press, 1999. Lecture notes, materials for practical exercises. Last update: Houfek Karel, doc. RNDr., Ph.D. (14.05.2023)
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The requirements for the exam correspond to the course syllabus to the extent that was given in the lectures and exercises. Last update: Houfek Karel, doc. RNDr., Ph.D. (02.05.2023)
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Hilbert spaces: 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. Last update: Houfek Karel, doc. RNDr., Ph.D. (17.05.2024)
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