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 2023:

Classes: MWF 10:00am-10:50am, NDSU AGHILL CTR Building, Rm 126
Office hours: MWF 11:00am-11:50am (or by appointment)
Syllabus
Textbook (optional): P. Olver, Introduction to Partial Differential Equations, Springer, 2014. Amazon. Springer.

Other useful sources:

Partial Differential Equations for Scientists and Engineers by Farlow (a non-rigorous undergraduate texbook with excellent intuitive explanations)
Partial Differential Equations: An Introduction by Strauss (a quite terse and detailed undegraduate textbook)
Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Haberman (a very detailed undergraduate textbook with a wide array of worked out examples)
Partial Differential Equations in Action by Salsa (a graduate level text-book that should be accesible to interested undergaduate)
Partial Differential Equations by Evans (a de-facto standard graduate textbook. Part I is very much recommended for an advanced undergaduate)
Lectures on Partial Differential Equations by Arnold (a non-ordodox set of lectures with minumum computational details, see Preface)
Methods of Mathematical Physics, Vol. I and Vol. II by Courant and Hilbert (a compedium written by two outstanding mathematicians which contains many details difficult to find anywhere else. The state of art of the PDE area by 1940)

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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