Partial Differential Equations 1

Partial Differential Equations 1
Methods of analysis for hyperbolic, elliptic, and parabolic equations, including characteristic manifolds, distributions, Green's functions, maximum principles and Fourier analysis.
MATH
547
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesMath 334, 342; or equivalents.
 RecommendedMath 352.
 TaughtFall Contact Department, Winter Contact Department, Spring Contact Department, Summer Contact Department
 ProgramsContaining MATH 547
Course Outcomes

Learning Outcomes

Students should understand the topics listed in the minimal learning outcomes on the Math 547 Wiki page. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, and ability to make direct application of those results to related problems, including calculations.

Overview

General Cauchy problem

Method of characteristics for first-order equations

Quasilinear systems of conservation laws on a line

Classification of general second-order equations

Canonical forms for semilinear second-order equations

Hyperbolic equations

Elliptic equations

Parabolic equations