Course Introduction  This course is concerned with the basic theories of vector analysis, phase plane analysis, 4 fundamental linear partial diﬀerential equation(PDE) and other ways to represent solutions. We will give 3 lectures on Chapter 16 in Stewart’s book, Chapter 7,9 and 11 in Boyce’s Book, and Chapter 2 and 4 in Evan’s book, respectively. There are main topics that we will cover throughout the course:
L1: Vector Fields, Line Integrals, The Fundamental Theorem for Line Integrals, Green’s Theorem, Curl and Divergence, Parametric Surfaces and Their Areas, Surface Integrals, Stokes’ Theorem, The Divergence Theorem
L2: Systems of FirstOrder Linear Equations, Nonlinear Diﬀerential Equations and Stability, Boundary Value Problems and SturmLiouville Theory
L3: Transport equation, Laplace’s equation, Heat equation, Wave equation, Separation of variables, Similarity solutions, Transform Methods
