MAT-30806 Applied Partial Differential Equations

Course

Credits 6.00

Language of instruction:

English

Assumed knowledge on:

MAT-14903, MAT-15003 and MAT-23306

Contents:

This course discusses partial differential equations in an applied context; modelling, mathematical analysis, mathematical method, implementation, solution and interpretation of the results. Topics are:
- convection-diffusion, wave and Laplace equation;
-separation of variables; Fourier and Bessel series, Legendre polynomials;
-integral transformations; Fourier and Laplace transformation;
-finite difference methods for ordinary differential equations; Euler, Trapezoidal rule. Stability;
-finite difference methods for partial differential equations; explicit methods, Crank Nicolson.

Learning outcomes:

After this course the student is expected to:
- have working knowledge of basic concepts, methods and techniques used in solving partial differential equations;
- be able to apply mathematical knowledge, insights and methods to solve basic problems in the technological sciences using a systematic approach;
- be able to critically reflect upon the results;
- be able to interpret the results in terms of the applied problem that was modelled mathematically;
- be able to use mathematical software in elaborating and implementing mathematical models;
- be able to present and discuss the mathematical analysis of an applied problem both orally and in written form.

Activities:

The student is expected to prepare the material to be discussed at the course, do exercises, and actively partake in the discussions. Moreover computer exercises must be worked out on a PC and submitted to apply the acquired skills and knowledge, and a project thesis must be written. The projects are case studies that, as much as possible, are closely related to the students' own field of expertise.

Examination:

Attendance at the practical is mandatory. Final examination is based upon the practical exercises, the project thesis and its discussion. Students work in pairs, but are judged individually.

Literature:

Lecture notes ' Applied Partial Differential Equations' (WUR Shop).