Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Advanced Mathematics for Electrical Engineers A

    A tantárgy neve magyarul / Name of the subject in Hungarian: Felsőbb matematika villamosmérnököknek A

    Last updated: 2012. november 24.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Course ID Semester Assessment Credit Tantárgyfélév
    TE90MX30 1 4/2/0/v 6 1/1
    3. Course coordinator and department Dr. Rónyai Lajos,
    6. Pre-requisites
    Kötelező:
    NEM ( TárgyEredmény( "BMETE90MX54" , "jegy" , _ ) >= 2
    VAGY
    TárgyEredmény("BMETE90MX54", "FELVETEL", AktualisFelev()) > 0
    VAGY
    TárgyEredmény( "BMETE90MX55" , "jegy" , _ ) >= 2
    VAGY
    TárgyEredmény("BMETE90MX55", "FELVETEL", AktualisFelev()) > 0)

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rendek grafikus formában itt láthatók.

    8. Synopsis Advanced Linear Algebra: Overview of basic notions of linear algebra, linear space, dimension, linear map, rank, determinant, eigenvalue and eigenvector, characteristic polynomial. The Jordan normal form, functions of matrices, systems of linear differential equations, applications. Euclidean spaces, special matrices. Moore-Penrose inverse and its application to solving matrix equations. Singular value decomposition (SVD), polar decomposition, QR-decomposition. Eigenvalues, singular values, matrix norms, Gershgorin circles, inequalities for the spectral values. Convexity, convex optimization, duality, ellipsoid method, linear matrix inequalities.
    Nonnegative matrices, Frobenius-Perron theorem, stochastic matrices. Some important applications of linear algebra.
    Stochastics: Review of basic probability theory: random variables, distribution, expectation, covariance matrix, important types of distributions. Generating and characteristic functions and their applications: limit theorems and large deviations (Bernstein inequality, Chernoff bound, Kramer's theorem). Basics of mathematical statistics: samples, estimates, hypotheses, important tests, regressions. Basics of stochastic processes: Markov chains and Markov processes. Markov chains with finite state space: irreducibility, periodicity, linear
    algebraic tools, stationary measures, ergodicity, reversibility, MCMC. Chains with countable state space: transience, recurrence. Application to birth and death processes and random walks. Basics of continuous time Markov chains: Poisson process, semigroups. Weakly stationary processes: spectral theory, Gauss processes, interpolation, prediction and filtering.
    14. Required learning hours and assignment
    Kontakt óra
    Félévközi készülés órákra
    Felkészülés zárthelyire
    Házi feladat elkészítése
    Kijelölt írásos tananyag elsajátítása
    Vizsgafelkészülés
    Összesen