杏吧论坛

Simon, Robert

This course is available on the BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. 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 Real Analysis (MA203).

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) and their relation to the classification of conic sections. 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. How to change between polar and Cartesian coordinates will be presented, especially for the solution of Laplacian and Poisson equations. Elementary distributional calculus and the notion of weak solutions will also be considered. Applications and examples will be discussed throughout the course.

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Autumn Term.

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

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 spring exam period.