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