PARTIAL DIFFERENTIAL EQUATIONS

Prerequisites & course information

Requisites: Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the basic theorems regarding solutions to the transport, Laplace, heat, and wave equations. Audience: Graduate 2. Use the above theorems to analyze solutions to first and second order linear partial differential equations of the above types, with novel initial data or boundary values. Audience: Graduate 3. Apply basic tools for studying first order nonlinear partial differential equations to analyze conservation laws and equations of Hamilton-Jacobi type. Audience: Graduate 4. Recall and state the definitions and basic theorems of Sobolev spaces. Audience: Graduate 5. Analyze novel second order elliptic equations by establishing existence, regularity, and maximum principles of solutions, given initial or boundary data with various properties. Audience: Graduate Learning Outcomes: 1. Recall and state the basic theorems regarding solutions to the transport, Laplace, heat, and wave equations. Audience: Graduate 2. Use the above theorems to analyze solutions to first and second order linear partial differential equations of the above types, with novel initial data or boundary values. Audience: Graduate 3. Apply basic tools for studying first order nonlinear partial differential equations to analyze conservation laws and equations of Hamilton-Jacobi type. Audience: Graduate 4. Recall and state the definitions and basic theorems of Sobolev spaces. Audience: Graduate 5. Analyze novel second order elliptic equations by establishing existence, regularity, and maximum principles of solutions, given initial or boundary data with various properties. Audience: Graduate