The aim of this unit is to introduce some fundamental concepts of the theory of partial differential equations (PDEs) arising in Physics, Chemistry, Biology and Mathematical Finance. The focus is mainly on linear equations but some important examples of nonlinear equations and related phenomena re introduced as well. After an introductory lecture, we proceed with first-order PDEs and the method of characteristics. Here, we also nonlinear transport equations and shock waves are discussed. Then the theory of the elliptic equations is presented with an emphasis on eigenvalue problems and their application to solve parabolic and hyperbolic initial boundary-value problems. The Maximum principle and Harnack's inequality will be discussed and the theory of Green's functions.
|Academic unit||Mathematics and Statistics Academic Operations|
|6cp from (MATH2X21 or MATH2X65 or MATH2067) and 6cp from (MATH2X22 or MATH2X61)|
|MATH3978 or MATH4078|
|[MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22]|
At the completion of this unit, you should be able to:
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