Fachrichtung 6.1 Mathematik

PDE and Boundary-Value Problems - WS 2012/13

• Lecture.

  1. On Wednesdays, 10-12 and on Fridays, 8-10 in HS IV in Building E2 4, Begin: 17.10.12

  2. Lecturer: Dr. Darya Apushkinskaya, Building E2 4, Room 433, Tel.: 302-2956,
     

• Assignments.
  

  
  
  

  Date	Assignments
  19.10.	Assignment 1
  09.11.	Assignment 2
  23.11.	Exercise 2. Part 1
  23.11.	Exercise 2. Part 2
  23.11.	Assignment 3
  07.12.	Assignment 4
  21.12.	Assignment 5
  21.01.	Assignment 6
  22.02.	Exam (Part W)

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

  Date	Transparencies
  17.10.	Lecture 1. Introduction to PDEs.
  19.10.	Lecture 2. Introduction to BVPs. Diffusion-Type Problems (Parabolic Equations).
  31.10.	Lecture 3. Boundary Conditions for Parabolic-Type Problems. Derivation of the Heat Equation .
  07.11.	Lecture 4. Separation of Variables. Transforming Nonhomogeneous BCs into Homogeneous Ones.
  14.11.	Lecture 5. Solving More Complicated Problems by Separation of Variables. Eigenfunction Expansion Method.
  16.11.	Lecture 6. Sine and Cosine Transforms. The Fourier Transfrom and Its Application to PDEs.
  21.11.	Lecture 7. The Laplace Transfrom. Duhamel's Principle. The Convection Term in the Diffusion Problems.
  28.11.	Lecture 8. Fundamental Solution of the Heat Equation. The One Dimensional Wave Equation.
  30.11.	Lecture 9. The D'Alembert Solution of the Wave Equation.
  05.12.	Lecture 10. Boundary Conditions Associated with the Wave Equation. The Finite Vibrating String (Standing Waves).
  12.12.	Lecture 11. The Vibrating Beam (Fourth-Order PDE). Dimensionless Problems. The Wave Equations in Three Dimensions (Free Space).
  14.12.	Lecture 12. The Wave Equations in Two Dimensions (Free Space). The Finite Fourier Transforms (Sine and Cosine Transforms).
  19.12.	Lecture 13. The Vibrating Drumhead (Wave Equation in Polar Coordinates). Boundary Conditions Associated with the Laplace Equation.
  11.01.	Lecture 15. The Dirichlet Problem in an Annulus. Spherical Harmonics.
  16.01.	Lecture 16. Fundamental Solution of the Laplace Equation. Green's Function.
  23.01.	Lecture 17. Green's Functions for a Half-Space and for a Ball. Numerical Solutions (Elliptic Problems).
  25.01.	Lecture 18. An Explicit Finite-Difference Method. An Implicit Finite-Difference Method (Crank-Nicolson Method).
  30.01.	Lecture 19. Monte-Carlo Solutions of PDEs.

  
  

• News.