Course Contents I: (Wi3150TU) Introduction. Types of second order equations. Initial and initial boundary value problems. Fourier series. Quasilinear, 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: (Wi3151TU) Boundary value problems. Delta functions and distributions. Greens 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).
Study Goals 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.
