Universität des Saarlandes
FR Mathematik
Arbeitsgruppe Prof. S. Rjasanow

Institut für angewandte Mathematik

PDEs and Boundary-Value Problems


Attention! Exceptional case: Due to organisational problems the first lecture on 26.10.16 would take place in Room 0.08, Building E1.7 from 2-4 p.m.

The all other lectures would take place due to standard timetable.

First tutorial: 04.11.2016

There is no lecture on 02.11.2016. Next lecture takes place on Wednesday 09.11.2016, 10-12 in HS003, Building E1.3.

Due to IT-Gipfel there is no lecture on 16.11.2016. Next lecture takes place on Wednesday 23.11.16, 10-12 in HS003, Building E1.3. Assignment sheets can be submitted to Mohsen Mansouryar in Room 210 (2nd Floor, Computer Graphics Department), Building E1.4 (MPI-INF).

  1. On Wednesdays, 10-12 in HS003, Building E1.3 and on Fridays, 8-10 in HS001, Building E1.3; Begin 26.10.2016.
  2. Lecturer: PD Dr. Darya Apushkinskaya ,
    Office hours: Wednesdays 09:00-10:00 or by appointment (during semester break only by appointment)
  3. Tutor: Mohsen Mansouryar s8momans@stud.uni-saarland.de
Target Group

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

Date Assignments Due Date
10.11.16pde16-17-blatt2.pdf 16.11.16
06.01.17 pde16-17-blatt5.pdf11.01.17
03.02.17pde16-17-blatt7.pdf 08.02.17

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

Date Topic Transparencies
29.10.16 Lecture 1. Introduction to PDEspde16-17-lecture-1.pdf
29.10.16 Lecture 2. Introduction to BVPspde16-17-lecture-2.pdf
10.11.16 Lecture 3. Parabolic (Diffusion) Type Problems. Boundary Conditions for Parabolic-Type Problems pde16-17-lecture-3.pdf
11.11.16 Lecture 4. Boundary Conditions for Parabolic-Type Problems. Derivation of the Heat Equation pde16-17-lecture-4.pdf
23.11.16 Lecture 5. Separation of Variables pde16-17-lecture-5.pdf
25.11.16 Lecture 6. Transformation of Nonhomogeneous BCs into Homogeneous Ones. More complicated Problems and Separation of Variablespde16-17-lecture-6.pdf
30.11.16 Lecture 7. Eigenfunction Expansion Method. Sine and Cosine Integral Transformspde16-17-lecture-7.pdf
07.12.16 Lecture 8. Exponential Fourier Transform. Laplace Transform pde16-17-lecture-8.pdf
09.12.16 Lecture 9. Solving IBVP with Maple (Fourier Transform)pde16-17-lecture9.pdf
06.01.17 Lecture 10. Duhamel's Principle. Convection Term in Diffusion Problem pde16-17-lecture-10.pdf
06.01.17 Lecture 11. Fundamental Solution of the Heat Equation. Properties of Solutions of the Heat Equation pde16-17-lecture-11.pdf
06.01.17 Lecture 12. The One-Dimensional Wave Equation. The D'Alembert Solution of the Wave Equation pde16-17-lecture-12.pdf
18.01.17 Lecture 13. Semi-Infinite String. Boundary Conditions Associated with the Wave Equationpde16-17-lecture-13.pdf
18.01.17 Lecture 14. The Finite Vibrating String (Standing Wave). The Vibrating Beam (Fourth-Order-PDE) pde16-17-lecture-14.pdf
20.01.17 Lecture 15. The Vibrating Drumhead (Wave Equation in Polar Coordinates). Dimensionless Problem pde16-17-lecture-15.pdf
25.01.17 Lecture 16. The Wave Equations in Three and Two Dimensions (Free Space). Finite Fourier Transform pde16-17-lecture-16.pdf
01.02.17 Lecture 17. Boundary Conditions Associated with the Laplace Equation. Interior Dirichlet Problem for a Circlepde16-17-lecture-17.pdf
03.02.17 Lecture 18. The Dirichle Problem in an Annulus. Exterior Dirichlet Problem for a Circle. Spherical Harmonicspde16-17-lecture-18.pdf
08.02.17 Lecture 19. Fundamental Solution of the Laplace Equation. Green's Functions for a Half-Space and for a Ball pde16-17-lecture-19.pdf
15.02.17 Lecture 20. Numerical Solutions (Elliptic Problems). An Explicit Finite-Difference Method. An Implicit Finite-Difference Method (Crank-Nicolson Method)pde16-17-lecture-20.pdf
17.02.17 Lecture 21. Introduction in Monte-Carlo Methodpde16-17-lecture-21.pdf
  • 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.
lehre/vorlesung/pdebvp1617.txt · Zuletzt geändert: 2017/03/10 18:55 von agrja
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