I: (Wi3150TU) Introduction. Types of second order equations. Initial and initial boundary value problems. Fourier series. Quasi-linear, first order partial differential equations. Waves and reflections of waves. Separation of variables. Sturm-Liouville problems. Parabolic, elliptic and hyperbolic equations. Maximum principle. Diffusion and heat transport problems. Lectures (3 ECTS).

II: (Wi4150TU) Boundary value problems. Delta functions and distributions. Green’s function for heat, wave and Laplace equations. Fourier and Laplace transform methods. Waves in R2 and in R3. Vibrations of membranes. Bessel functions. Shock waves. Lectures and Maple practical work (3 ECTS).

Many mathematical—physical problems can be formulated using partial differential equations. Therefore it is important to be able to both interpret and solve this type of equations. At the end of the course the student:

1- is able to formulate various physical problems (wave—equation, heat—equation, transport—equations) in terms of partial differential equations.

2- has knowledge and understanding of various mathematical techniques which are necessary to solve these problems (Fourier—series, method of separation of variables, Sturm-Liouville problems, Greens’ functions, Fourier- and Laplace transformations) and is able to apply these techniques to (simple) problems.

3- is able to interpret the solutions obtained and is able to place them in (a physical) context.

**Literature**

R.Haberman, Applied Partial Differential Equations, Fourth edition, Pearson Prentice Hall, New Jersey, 2004, ISBN 0-13-065243-1

**Course code TUD**

WI3150 en WI4150

- Prerequisites*

Analyse 3

**Assessment**

Takehome exam and oral exam *Contact hours *

4 hour lectures per week **Relation with Spring PDE-course**

These two courses WI3150 en WI4150 together are equal to the Spring course “Partiele Differentiaalvergelijkingen” (TUD, WI2607) **Please note**

This course is admissible as an elective for a Leiden bachelor’s degree and sometimes admissible for a Leiden master’s degree. In case of the latter, please contact the study advisor dr. M. Lubke beforehand. **Links**

Blackboard TU Delft