Fachrichtung 6.1 Mathematik

PDE and Boundary-Value Problems - Winter Term 2013/14

• Lecture.

  1. On Wednesdays, 10-12 and on Fridays, 12-14 in HS001 in Building E1 3, Begin: 16.10.13

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

  3. Tutor: Hosna Sattar

• Assignments.
  

  
  
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  Date	Assignments
  23.10.	Assignment 1
  07.11.	Assignment 2
  22.11.	Assignment 3
  04.12.	Assignment 4
  17.12.	Assignment 5
  16.01.	Assignment 6
  23.01.	Assignment 7
  01.02.	Exam (Part W)

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

  Date	Transparencies
  16.10.	Lecture 1. Introduction to PDEs.
  21.10.	Lecture 2. Introduction to BVPs.
  23.10.	Lecture 3. Parabolic (Diffusion) Type Problems. Boundary Conditions for Parabolic-Type Problems.
  28.10.	Lecture 4. Boundary Conditions for Parabolic-Type Problems. Derivation of the Heat-Equation.
  30.10.	Lecture 5. Separation of Variables.
  06.11.	Lecture 6. Transforming Nonhomogeneous BCs into Homogeneous Ones. Solving More Complicated Problems by Separation of Variables.
  22.11.	Lecture 7. Eigenfunction Expansion Method. Sine and Cosine Integral Transforms.
  22.11.	Lecture 8. Sine and Cosine Integral Transforms. The Fourier Transform and its Application to PDEs.
  22.11.	Lecture 9. Part 1. Solving IBVP with Maple (Fourier Transform).
  22.11.	Lecture 9. Part 2. Solving IBVP with Maple (Fourier Transform).
  29.11.	Lecture 10. The Laplace Transform.
  03.12.	Lecture 11. Duhamel's Principle. The Convection Term in the Diffusion Problems. Fundamental Solution of the Heat Equation.
  04.12.	Lecture 12. Fundamental Solution of the Heat Equation (cont.). The One-Dimensional Wave Equation.
  11.12.	Lecture 13. The D'Alembert Solution of the Wave Equation.
  19.12.	Lecture 14. Boundary Conditions Associated with the Wave Equation.
  11.12.	Lecture 15. The Finite Vibrating String (Standing Waves). The Vibrating Beam (Fourth-Order PDE).
  08.01.	Lecture 16. Dimensionless problem. The Wave Equations in Three and Two Dimensions (Free Space).
  10.01.	Lecture 17. The Finite Fourier Transforms (Sine and Cosine Transforms). The Vibrating Drumhead (Wave Equation in Polar Coordinates)-Part 1.
  15.01.	Lecture 18. The Vibrating Drumhead (Wave Equation in Polar Coordinates)-Part 2. Boundary Conditions Associated with the Laplace Equation.
  23.01.	Lecture 19. Interior Dirichlet Problem for a Circle.
  29.01.	Lecture 20. The Dirichlet Problem in an Annulus. Spherical Harmonics-Part 1.
  29.01.	Lecture 21. Spherical Harmonics- Part 2. Fundamental Solution of the Laplace Equation.
  01.02.	Lecture 22. Green's Functions for a Half-Space and for a Ball.

  
  

• News.