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Lecturer(s)
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Course content
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1. Integration for functions of several variables: curve and surface integrals. 2. Ordinary differential equation: existence and uniqueness of an initial value problem, numerical methods. 3. Linear and non-linear dynamical systems, classification of stationary points, stability, Poincare-Bendixon Theorem, bifurcation and chaos. 4. Banach and Hilbert spaces, operators and functionals, dual and reflexivity, weak convergence and compactness. 5. Exact combinatorial optimization methods, duality in linear programming, the simplex method, pros and cons of exact methods. 6. Heuristics in combinatorial optimization, examples, deterministic and stochastic approach, basic algorithms, pros and cons. 7. Mathematical physics: elliptic, parabolic and hyperbolic equations, motivation and problem formulation, representing formulas, numerical methods. 8. Fourier analysis: Fourier series and Fourier transformation and its application.
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Learning activities and teaching methods
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Work with Text (with Book, Textbook)
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Learning outcomes
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Realize contexture of basic conceptions and statements concerning mathematical and functional analysis, differential equations, equations of mathematical physics, dynamic systems and combinatorial optimization.
Synthesis Realize contexture of basic conceptions and statements concerning contents of this subject.
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Prerequisites
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The student has to meet all prerequisites given for the bachalor tudy course Applied Mathematics and all the conditions of Study and Examination Regulations of the Palacký University in Olomouc.
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Assessment methods and criteria
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Oral exam
the student has to understand the subject
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Recommended literature
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Franců, J. (2003). Parciální diferenciální rovnice. Brno. Brno.
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Kalas, J., Ráb, M. (2012). Obyčejné diferenciální rovnice. Brno.
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Kopáček, J. (2007). Matematická analýza nejen pro fyziky (III). Praha.
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Kutz, N. (2013). Data Driven Modeling & Scientific Computation.
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Papadimitriou, Ch. H., Steiglitz, K. (1998). Combinatorial Optimization: Algorithms and Complexity.
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Rachůnková, I., Fišer, J. (2014). Dynamické systémy 1. Olomouc.
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Zeidler, E. (1995). Applied Functional Analysis, Main Principles and Their Applications.
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