The course is intended for all PhD students. The course extends and deepens the student's knowledge and skills in the following areas of mathematics: - Linear algebra: solutions of systems of linear equations, direct and iteration methods. Invertion of matrices. Calculation of eigenvalues and eigenvectors. Multilinear forms and tensors. - Diferential and integral calculus of functions of one and several variables. Extremes, implicit functions. Integration of functions of several variables. - Vector analysis: surface and curvilinear integral, divergence, gradient, curl, Gauss-Green and Stokes theorems. - Fourier analysis: Fourier series and Fourier transform of functions and distributions. Convolution and its applications. - Ordinary differential equations and systems, existence, uniqueness, solution methods. Linear differential equations and systems. - Partial differential equations: equations of first order, Laplace and Poisson equation, heat equation, wave equation. Fundamental solutions, boundary and initial problems. - Eventually further selected topics related to the specialization of the student; on basis of the agreement with the student's supervisor and approval in the individual plan of the student.
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