CCU Course Syllabus
Research Methods (I)研究方法(一)
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 First-Order Linear Equations, Nonlinear Differential Equations and Stability, Boundary Value Problems and Sturm-Liouville Theory

L3: Transport equation, Laplace’s equation, Heat equation, Wave equation, Separation of variables, Similarity solutions, Transform Methods
Document of syllabusSyllabus-111.1 Research Methods (I).pdf
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