Dr Amol Sasane

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics 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.

Students must have completed Further Mathematical Methods (MA212) and Introduction to Abstract Mathematics (MA103).

The aim of the course is to study the three main types of partial differential equations: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation), and the techniques of solving these for various initial and boundary value problems on bounded and unbounded domains, using eigenfunction expansions (separation of variables, and elementary Fourier series), integral transform methods (Fourier and Laplace transforms). Applications and examples, such as the solution technique for Black-Scholes option pricing, will be discussed throughout the course.

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

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

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

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

Lecture notes will be provided.

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