| Unit name | Applied Partial Differential Equations 2 |
|---|---|
| Unit code | MATH20402 |
| Credit points | 20 |
| Level of study | I/5 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Slastikov |
| Open unit status | Not open |
| Pre-requisites |
MATH 20900 Calculus 2 (MATH 11009 Mechancs 1 is preferable, but not required) |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
To provide the student with the necessary mathematical tools in order to model a wide variety of different physical problems, ranging from waves on strings, the propagation of signals, the diffusion of heat in solids and chemicals in solution, traffic flow and the vibrations of membranes and surfaces.
General Description of the Unit
Partial differential equations (PDEs) are differential equations involving partial derivatives of functions of several variables. They are essential for understanding many physical processes including the behaviour of ocean waves, the flow of rivers, the diffusion of pollutants, aerodynamics, the operation of musical instruments, atomic physics, and many other branches of science. This unit will give an introduction to simple PDEs and how they arise in physical problems; it will develop techniques for solving them and understanding the behaviour of the solutions.
The unit will develop students' understanding of first year multivariable calculus and linear algebra. It will introduce Fourier series, the Fourier integral, the delta function and other methods for solving linear and nonlinear PDEs, (such as the method of characteristics) and will show how eigenvalues play a central role in applied mathematics. The course emphasises techniques and broad understanding rather than proofs.
Relation to Other Units
This unit will be a prerequisite for Mathematical Methods, Fluid Dynamics, Quantum Mechanics and other applied mathematics units. It gives applications of the vector calculus, complex variable methods and other material in Calculus 2 (or from 2014/15: Multivariable Calculus and Methods of Complex Functions), and includes material (Sturm-Liouville theory) relevant to Ordinary Differential Equations 2, though that course is not a prerequisite.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
At the end of the course the student should should be able to:
Transferable Skills:
Three lectures and one problems class per week. Regular problem sheets will be distributed which will test the students' understanding of the material through a variety of problems ranging from elementary to difficult. Set questions will be marked promptly and returned with comments. Full solutions of all problems will be distributed.Problems classes will go through examples that compliment both the lectures and the worksheets.
100% Examination
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
