Fachrichtung 6.1 Mathematik

PDE and Boundary-Value Problems - Winter Term 2014/15

• Lecture.

  1. On Mondays, 12-14 and on Thursdays, 08-10 in HS003 in Building E1 3, Begin: 23.10.14

  2. Lecturer: PD Dr. Darya Apushkinskaya, Building E2 4, Room 433, Tel.: 302-2956,
     Office hours: Mondays 10:30-11:30 or by appointment (during semester break only by appointment)

  3. Tutor: Adam Hanka

• Assignments.
  

  
  
  

  Date	Assignments
  27.10.14	Assignment 1
  10.11.14	Assignment 2
  24.11.14	Assignment 3
  08.12.14	Assignment 4
  05.01.15	Assignment 5
  19.01.15	Assignment 6
  02.02.15	Assignment 7
  25.02.15	Exam (Part W)

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

  Date	Transparencies
  23.10.14	Lecture 1. Introduction to PDEs.
  27.10.14	Lecture 2. Introduction to BVPs.
  30.10.14	Lecture 3. Parabolic (Diffusion) Type Problems. Boundary Conditions for Parabolic-Type Problems.
  10.11.14	Lecture 4. Boundary Conditions for Parabolic-Type Problems. Derivation of the Heat-Equation.
  13.11.14.	Lecture 5. Separation of Variables.
  17.11.14	Lecture 6. Transforming Nonhomogeneous BCs into Homogeneous Ones. Solving More Complicated Problems by Separation of Variables. Eigenfunction Expansion Method.
  24.11.14	Lecture 7. Sine and Cosine Integral Transforms. Fourier Transform.
  27.11.14	Lecture 8. The Fourier Transform and its Application to PDEs. The Laplace Transform.
  01.12.14	Lecture 9. Part 1. Solving IBVP with Maple (Fourier Transform).
  01.12.14	Lecture 9. Part 2. Solving IBVP with Maple (Fourier Transform).
  08.12.14	Lecture 10. Duhamel's Principle. The Convection Term in the Diffusion Problems.
  11.12.14	Lecture 11. Fundamental Solution of the Heat Equation.
  15.12.14	Lecture 12. The One-Dimensional Wave Equation. The D'Alembert Solution of the Wave Equation.
  05.01.15	Lecture 13. The modified D'Alembert Solution of the Wave Equation. Boundary Conditions Associated with the Wave Equation.
  08.01.15	Lecture 14. The Finite Vibrating String (Standing Waves). The Vibrating Beam (Fourth-Order PDE).
  12.01.15	Lecture 15. Dimensionless problem. The Wave Equations in Three and Two Dimensions (Free Space). The Finite Fourier Transforms (Sine and Cosine Transforms).
  19.01.15	Lecture 16. The Vibrating Drumhead (Wave Equation in Polar Coordinates). Boundary Conditions Associated with the Laplace Equation.
  22.01.15	Lecture 17. Interior and Exterior Dirichlet Problems for a Circle. The Dirichlet Problem in an Annulus.
  28.01.15	Lecture 18. Spherical Harmonics. Fundamental Solution of the Laplace Equation.
  05.02.15	Lecture 19. Green's Functions for a Half-Space and for a Ball.
  05.02.15	Lecture 20. An Explicit Finite-Difference Method. An Implicit Finite-Difference Method (Crank-Nicolson Method).
  27.02.15	Lecture 21. Monte-Carlo Solutions of PDEs.

  
  

• News.
  Attention!!! There is no lecture on 03.11.14. Next lecture will be given on 10.11.14!!!