Partial Differential Equations

**This information is for the 2019/20 session.**

**Teacher responsible**

Prof Amol Sasane

**Availability**

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available with permission as an outside option to students on other programmes where regulations permit and to General Course students.

**Pre-requisites**

Students must have completed Further Mathematical Methods (MA212) and Real Analysis (MA203).

**Course content**

The aim of the course is the study of partial differential equations. The focus will be on first order quasilinear equations, and second order linear equations. The method of characteristics for solving first order quasilinear equations will be discussed. The three main types of linear second order partial differential equations will be considered: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation). Techniques for solving these for various initial and boundary value problems on bounded and unbounded domains, using eigenfunction expansions (separation of variables, and elementary Fourier series), and integral transform methods (Fourier and Laplace transforms) will be treated. Elementary distributional calculus and the notion of weak solutions will also be considered. Applications and examples, such as the solution technique for Black-Scholes option pricing, will be discussed throughout the course.

**Teaching**

22 hours of lectures and 10 hours of classes in the LT.

**Formative coursework**

Students will be expected to produce 10 problem sets in the LT.

Written answers to set problems will be expected on a weekly basis.

**Indicative reading**

- S.J. Farlow.
*Partial Differential Equations for Scientists and Engineers.*Dover, 1993. - J.D. Logan.
*Applied Partial Differential Equations.*Second Edition. Springer, 2004. - W. Strauss.
*Partial Differential Equations. An Introduction.*Second Edition. John Wiley, 2008.

Lecture notes will be provided.

**Assessment**

Exam (100%, duration: 2 hours) in the summer exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: 7

Average class size 2018/19: 7

Capped 2018/19: No

Value: Half Unit

**Personal development skills**

- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills