In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
For more details, see the Wikipedia page and the term on MathWorld.
Here is the syllabus of the course Math3606.
MATH2205 Multivariate Calculus
MATH3405 Ordinary Differential Equations
| Chapter | Schedule | Assignments | Solutions |
|---|---|---|---|
| Ch1: Introduction | Week 1 | Assignment One | Reference Solutions |
| Ch2: Parabolic Equations | Week 2-4 | Assignment Two | Reference Solutions |
| Ch3: Elliptic Equations | Week 5-8 | Assignment Three | Reference Solutions |
| Ch4: Hyperbolic Equations | Week 9-11 | Assignment Four | Reference Solutions |
| Ch5: First Order PDEs | Week 12 | No Assignments | |
| Ch6: Integral Transforms | Week 12-13 | No Assignments |
| Partial Differential Equations: An Introduction | Walter A. Strauss | Wiley (2nd ed.) | 2007 |
| Partial differential equations: theory and technique | George F. Carrier, Carl E. Pearson | Academic Press (2nd ed.) | 1988 |
| Applied Partial Differential Equations | Richard Haberman | Pearson (5th ed.) | 2013 |
| Partial Differential Equations | Fritz John | Springer-Verlag (4th ed.) | 1982 |
| MITOpenCoureseWave | Introduction to Partial Differential Equations | Jared Speck | 2011 |
| APM346 | Partial Differential Equations | University of Toronto | 2012 |
| WikiBooks | Partial Differential Equations | ||
| Scholarpedia | Partial differential equation | Andrei D. Polyanin et al. |