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

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    Mathematics A3 for Electrical Engineers

    A tantárgy neve magyarul / Name of the subject in Hungarian: Matematika A3 villamosmérnököknek

    Last updated: 2012. november 23.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Course ID Semester Assessment Credit Tantárgyfélév
    TE90AX09   2/1/0/v 4  
    3. Course coordinator and department Dr. Simon András,
    6. Pre-requisites
    Kötelező:
    TárgyEredmény( "BMETE90AX02" , "jegy" , _ ) >= 2
    VAGY TárgyEredmény( "BMETE90AX03" , "jegy" , _ ) >= 2
    VAGY TárgyEredmény( "BMETE901918" , "jegy" , _ ) >= 2
    VAGY TárgyEredmény( "BMETE90AX26" , "jegy" , _ ) >= 2

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

    A kötelező előtanulmányi rendek grafikus formában itt láthatók.

    7. Objectives, learning outcomes and obtained knowledge The objective is to provide the students with the required theoretical background in differential geometry, complex calculus, and differential equations for further studies in electrical engineering.

     

    Obtained skills and expertise:

     

    Theoretical knowledge and problem solving competence in the treated fields of mathematics.

     

    8. Synopsis Differential geometry of curves and surfaces. Tangent and normal vector, curvature. Length of curves. Tangent plane, surface measure. Scalar and vector fields. Differentiation of vector fields, divergence and curl. Line and surface integrals. Potential theory. Conservative fields, potential. Independence of line integrals of the path. Theorems of Gauss and Stokes, the Green formulae. Examples and applications. Complex functions. Elementary functions, limit and continuity. Differentiation of complex functions, Cauchy-Riemann equations, harmonic functions. Complex line integrals. The fundamental theorem of function theory. Regular functions, independence of line integrals of the path. Cauchy's formulae, Liouville's theorem. Complex power series. Analytic functions, Taylor expansion. Classification of singularities, meromorphic functions, Laurent series. Residual calculation of selected integrals. Laplace transform. Definition and elementary rules. The Laplace transform of derivatives. Transforms of elementary functions. The inversion formula. Transfer function. Classification of differential equations. Existence and uniqueness of solutions. The homogeneous linear equation of first order. Problems leading to ordinary differential equations. Electrical networks, reduction of higher order equations and systems to first order systems. The linear equation of second order. Harmonic oscillators. Damped and forced oscillations. Variation of constants, the inhomogeneous equation. General solution via convolution, the method of Laplace transform. Nonlinear differential equations. Autonomous equations, separation of variables. Nonlinear vibrations, solution by expansion. Numerical solution. Linear differential equations. Solving linear systems with constant coefficients in the case of different eigenvalues. The inhomogeneous problem, Laplace transform. Stability.

     

    13. References, textbooks and resources

    John H. Mathews and Russell W. Howell: Complex Analysis for Mathematics and Engineering, 5th edition, ISBN: 0-7637-3748-8, Jones and Bartlett Pub. Inc., Sudbury, MA, 2006

    Joseph Bak: Complex Analysis, 2nd edition, Springer, 2997

    Meyberg K., Vachena P.: Höhere Mathematik 1-2, Springer, 2003, 2004

    W.E. Boyce, Richard C. DiPrima: Elementary Differential Equations and Boundary Value Problems , 8th Edition, Wiley, 2004

    14. Required learning hours and assignment
    Kontakt óra
    Félévközi készülés órákra
    Felkészülés zárthelyire
    Házi feladat elkészítése
    Kijelölt írásos tananyag elsajátítása
    Vizsgafelkészülés
    Összesen