Universität des Saarlandes
FR Mathematik
Arbeitsgruppe Prof. S. Rjasanow

Institut für angewandte Mathematik

PDEs and Boundary-Value Problems

Lecture
  1. On Mondays, 10-12 and on Fridays, 8-10 in HS001, Building E1.3, Begin 23.10.15
  2. Lecturer: PD Dr. Darya Apushkinskaya ,
    Office hours: Mondays 09:00-10:00 or by appointment (during semester break only by appointment)
  3. Tutor: Jón Arnar Tómasson jonarnar90@gmail.com
Target Group

The course is suitable for students specialising in applied mathematics, physics, computer science,
visual computing, bioinformatics. The course language is English.

Assignments
Date Assignments Due Date
23.10.15 Sheet 1 02.11.15
09.11.15 Sheet 216.11.15
16.11.15Sheet 3 30.11.15
30.11.15 Sheet 414.12.15
14.12.15Sheet 511.01.16
19.01.16Sheet 6 25.01.16
01.02.16 Sheet 708.02.16
09.02.16Exam (Writing Part) 17.04.16
Script

The script in terms of transparencies will be available for download in the table below.

Date Topic
23.10.15 Lecture 1. Introduction to PDEs.
26.10.15 Lecture 2. Introduction to BVPs.
30.10.15 Lecture 3. Parabolic (Diffusion) Type
Problems. Boundary Conditions for
Parabolic-Type Problems.
02.11.15 Lecture 4. Boundary Conditions
for Parabolic-Type Problems.
Derivation of the Heat Equation.
09.11.15 Lecture 5. Separation of Variables
13.11.15 Lecture 6. Transforming Nonhomogeneous BCs into Homogeneous Ones. More Complicatited Problems and Separation of Variables
16.11.15 Lecture 7. Eigenfunction Expansion Method. Sine and Cosine Integral Transforms
23.11.15 Lecture 8. Exponential Fourier Transform. Laplace Transform
30.11.15 Lecture 9. Solving IBVP with Maple (Fourier Transform)
30.11.15 Lecture 10. Duhamel's Principle. Convection Term in Diffusion Problem
07.12.15 Lecture 11. Fundamental Solution of the Heat Equation
11.12.15 Lecture 12. Properties of Solutions of the Heat Equation. The One-Dimensional Wave Equation
14.12.15 Lecture 13. The D'Alembert Solution of the Wave Equation
04.01.16 Lecture 14. Semi-Infinite String. Boundary Conditions Associated with the Wave Equation.
08.01.16 Lecture 15. The Finite Vibrating String (Standing Wave). The Vibrating Beam (Fourth-Order-PDE)
11.01.16 Lecture 16. The Vibrating Drumhead (Wave Equation in Polar Coordinates). Dimensionless Problem.
19.01.16 Lecture 17. The Wave Equations in Three and Two Dimensions (Free Space).
22.01.16 Lecture 18. Boundary Conditions Associated with the Laplace Equation. Interior Dirichlet Problem for a Circle.
25.01.16 Lecture 19. The Dirichle Problem in an Annulus. Exterior Dirichlet Problem for a Circle. Spherical Harmonics.
01.02.16 Lecture 20. Fundamental Solution of the Laplace Equation. Green's Functions for a Half-Space and for a Ball. Numerical Solutions (Elliptic Problems).
05.02.16Lecture 21. An Explicit Finite-Difference Method. An Implicit Finite-Difference Method (Crank-Nicolson Method). Introduction in Monte-Carlo Method.
Literature
  • L.C. Evans, Partial Differential Equations, Graduate Stud. Math., 19, Amer. Math. Soc.,
    Providence, Rhode Island, 1998.
  • M.A. Pinsky, Partial-Differential Equations and Boundary-Value Problems with Applications,
    Reprint of the third (1998) edition, Pure and Applied Undergraduate Texts, 15, Amer. Math.
    Soc., Providence, Rhode Island, 2011.
  • S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications,
    INC. New York, 1993.
News

On Monday 08.02.16 there is no lecture due to Rosenmontag.

Registration
lehre/vorlesung/pdebvp1516.txt · Zuletzt geändert: 2016/09/15 11:51 von agrja
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