Partial Differential Equations Math 483/683
Partial differential equations (PDE) are the main tool of applied mathematics that
are used to model various processes in physics, engineering, economics, natural and
social sciences. The purpose of the course is to learn the basics of the theory of linear PDE and
master the elementary tools (Fourier series, integral transforms, Green's functions) to solve three most important linear partial differential equations: the heat, wave, and Laplace equations. The students
will be exposed to both theoretical and applied points of view.
Spring 2020:
- Classes: MWF 10:00am-10:50am, NDSU Minard Hall Rm 306
- Office hours: MWF 9:00am-9:50am (Minard 408E22)
- Syllabus
- Textbook: P. Olver, Introduction to Partial Differential Equations, Springer, 2014.
Amazon.
Springer.
Other useful sources:
I plan (tentatively) to include the following topics:
- Introduction. What are the PDE? (Chapter 1)
- Linear waves. (Sections 2.1, 2.2, 2.4)
- Fourier series. (Chapter 3)
- Separation of variables. (Chapter 4)
- Delta-function and the Green's functions (Chapter 6)
- Fourier transform. Fundamental solution to the heat equation (Sections 7.1,7.2,7.3,8.1)
- Planar heat and wave equations. Bessel's equation (Chapter 11)
Lecture notes:
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