Computational Introduction to Partial Differential Equations

12 units · Undergraduate

Fall: 12 units A Partial Differential Equation (PDE for short) is a differential equation involving derivatives with respect to more than one variable. These arise in numerous applications from various disciplines. Most PDEs do not have explicit solutions, and hence computational methods are essential for understanding the underlying phenomena. This course will serve as a first introduction to PDEs and their numerical approximation, and will focus on a variety of mathematical models. It will cover both analytical methods, numerical methods (e.g. finite differences) and the use of a computer to approximate and visualize solutions. The mathematical ideas behind phenomena observed in nature will be studied at the theoretical level and in numerical simulations (e.g. speed of wave propagation, and/or shocks in traffic flow). Topics will include: Derivation of PDEs from physical principles, analytical and computational tools for the transport equation and the Poisson equation, Fourier analysis, analytical and numerical techniques for the solution of parabolic equations and if time permits, the wave equation. (Three 50 minute lectures, one 80 minute recitation) Prerequisites: ( 21-241 or 21-242 or 21-240 ) and ( 21-268 or 21-269 or 21-259 ) and ( 21-261 or 33-231 or 21-630 or 21-260 ) and ( 15-110 or 15-112 or 02-120 ) Course Website: https://www.cmu.edu/math/undergrad/math-course-information.html