Analysis III D-MAVT D-MATL
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Beginn der Vorlesung: Donnerstag, 25.9.2014
Beginn der Übungen: Donnerstag, 25.9.2014
Übungsseite
Prüfungseinsicht
Am Dienstag, 22.9. von 16-17 Uhr im HG G 19.2.
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 Transforms
- Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform
- Partial 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 on Rectangle
- Laplacian in Polar Coordinates: Laplace Equation on Disk, Dirichlet/Neumann boundary conditions, Poisson-Formula, Maximum Principle on Disk
Hauptliteratur
- E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9. Auflage, 2011
Ergänzende Literatur
- 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, 2005
- N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieuere, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997.
- P. Henrici, R. Jeltsch, Komplexe Analysis für Ingenieure, Band 1 & 2, Birkhäuser Verlag, 1998.
- R. Haberman, Elementary applied partial differential equations, 3rd edition, Prentice Hall, 1998.
- M. D. Greenberg, Advanced engineering mathematics, Prentice Hall, 1998.
- J. Ockendon, S. Howison, A. Lacey, A. Movchan, Applied Partial Differential Equations, Oxford University Press, 1999.
- E. C. Zachmanoglou, D. W. Thoe, Introduction to Partial Differential Equations with Applications, Dover.
Klausur
Erlaubte Hilfsmittel: 20 Seiten (=10 Blätter A4) handgeschriebene oder mit LaTeX verfasste Zusammenfassung. Wörterbuch für Fremdsprachige. Üblicher wissenschaftlicher Taschenrechner. Keine weiteren Hilfsmittel.