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.

__Classes:__MWF 9:00am-9:50am, NDSU South Engineering Rm 120__Office hours:__MWF 11:00am-12:00am (Minard 408E22)- Syllabus
__Textbook:__P. Olver, Introduction to Partial Differential Equations, Springer, 2014. Amazon. Springer.

- 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*)

- 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)

- 01. What are PDE?
- 02. Linear transport equation
- 03. Solving first order linear PDE
- 04. Glimpse of the nonlinear world. Hopf's equation
- 05. Wave equation. Derivation
- 06. Wave equation. d'Alembert's formula
- 07. Duhamel's principle
- 08. Half infinite string
- 09. Heat or diffusion equation
- 10. Motivation for Fourier series
- 11. Fourier series
- 12. Fourier method for the heat equation
- 13. Sturm-Liouville problem
- 14. Fourier method for the wave equation
- 15. Fourier method for the Laplace equations
- 16. Delta-function
- 17. Green's functions for one dimensional problems
- 18. Green's functions for the Poisson equation
- 19. Fourier transform
- 20. Application of Fourier transform to PDE
- 21. Telegrapher's equation
- 22. The method of separation of variables revisited
- 23. Bessel's functions
- 24. The heat and wave equations in polar coordinates
- 25. Solving the wave equation in 2D and 3D space

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