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.
3x 1 hour lectures; 1x1 hour laboratory /wk
Final exam (70%), 2 assignments (15%+15%). To pass the course, students must achieve at least 50% on the final exam.
[MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22]
12 credit points of MATH2XXX units of studyProhibitions
MATH3978 or MATH4078