401-0363-10L  Analysis III

SemesterHerbstsemester 2016
DozierendeM. Soner
Periodizitätjährlich wiederkehrende Veranstaltung

KurzbeschreibungIntroduction 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.
LernzielMathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.

The first lecture is on Thursday, September 29 13-15 in HG F 7 and video transmitted into HG F 5.

The exercises Sheet are here: Link

The coordinator is Claudio Sibilia (see Link)

The first exercise session is on Thursday, September 22 or resp. Friday, September 23. If you would like feedback on your work, please give it to your course assistent or leave it in the box of your course assistant in HG F 27. The due Date is one week later the assignment.

Office hour (Praesenz): Thursday 16-17, NO E 39.
InhaltLaplace 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
- Forced Oscillations
- 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
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform

Download the syllabus: Link
SkriptAlessandra Iozzi's Lecture notes: Link

Errata: Link
LiteraturE. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9. Auflage, 2011

C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.

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

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis (Download PDF)