# 401-0363-10L  Analysis III

 Semester Herbstsemester 2020 Dozierende F. Da Lio Periodizität jährlich wiederkehrende Veranstaltung Lehrsprache Englisch

 Kurzbeschreibung Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. Lernziel Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations. Inhalt Laplace Transforms:- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs- Unit Step Function, t-Shifting- Short Impulses, Dirac's Delta Function, Partial Fractions- Convolution, Integral Equations- Differentiation and Integration of TransformsFourier Series, Integrals and Transforms:- Fourier Series- Functions of Any Period p=2L- Even and Odd Functions, Half-Range Expansions- Forced Oscillations- Approximation by Trigonometric Polynomials- Fourier Integral- Fourier Cosine and Sine TransformPartial Differential Equations:- Basic Concepts- Modeling: Vibrating String, Wave Equation- Solution by separation of variables; use of Fourier series- D'Alembert Solution of Wave Equation, Characteristics- Heat Equation: Solution by Fourier Series- Heat Equation: Solutions by Fourier Integrals and Transforms- Modeling Membrane: Two Dimensional Wave Equation- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series- Solution of PDEs by Laplace Transform Skript Lecture notes by Prof. Dr. Alessandra Iozzi:Link Literatur E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY.G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005For reference/complement of the Analysis I/II courses:Christian Blatter: Ingenieur-Analysis Link