MATH3078 Partial Differential Equations Intro Notes | Assignment Help | Syllabus
University: University Of Sydney
The goal of this course is to teach some basic ideas in partial differential equations (PDEs) theory as they apply to Physics, Chemistry, Biology, and Mathematical Finance. Although the emphasis is on linear equations, several significant examples of nonlinear equations and associated phenomena are included. We start with first-order PDEs and the technique of characteristics after an introductory talk. Nonlinear transport equations and shock waves are also addressed here. The theory of elliptic equations is next taught, with a focus on eigenvalue issues and how they may be used to solve parabolic and hyperbolic initial boundary-value problems. The maximum principle and Harnack’s inequality, as well as the theory of Green’s functions, will be addressed.
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