Course Description and Grading BreakdownA partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. They are used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, or elasticity. In this course, we will discuss three important PDEs in detail: the Laplace equation, the heat equation and the wave equation. We will learn various techniques for finding explicit solutions of these PDEs. We will introduce distributions and discuss the notion of a 'fundamental solution'. We will also introduce Sobolev spaces, investigate their properties and use them to solve general second order elliptic equations. The course will be offered Pass-Fail. Course webpage: www.its.caltech.edu/~sparikh/ma142.html Course Meeting Time and LocationTuesday and Thursday 9:00 - 10:25 am 103 Downs Laboratory of Physics (DWN) Course Instructor Contact Information and Office Hours210-2 Math Building (Building 15) Course Schedule and Textbook
Course PoliciesLate work - Assignments
Midterm and Final ExamCollaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |