ELEC443 Boundary Value Problems of Mathematical Physics

Overview

Solution methods for boundary-value problems that frequently arise in mathematical physics. Analytic solutions using Green's functions and distribution theory. Computed solutions using the boundary element method.

About this paper

Limited to

BSc(Hons), PGDipSci, MSc, MAppSc

Contact

Associate Professor Colin Fox (colin.fox@otago.ac.nz)

Teaching staff

To be advised when next offered

Textbooks

Textbooks are not required for this paper.

Graduate Attributes Emphasised

Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
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Learning Outcomes

By the end of the module students are expected to be able to:

1. Perform simple manipulations using distributional calculus, in particular find distributional solutions to some simple differential equations
2. Know the defining properties of classical, weak and distributional solutions to differential equations
3. Know the defining properties of fundamental solutions and Green's functions
4. Find Green's functions for linear ordinary differential boundary value problems, including initial-value problems
5. Find the adjoint operator and adjoint boundary value problem associated with a linear partial differential boundary value problem
6. Derive Green's theorem for arbitrary second-order linear partial differential equations with (classical) boundary conditions
7. Use fundamental solutions or Green's functions within Green's theorem to write an integral solution to a linear boundary value problem
8. Derive the boundary integral equation for second-order elliptic boundary value problems
9. State the steps required for a rudimentary boundary element method
10. Code up a boundary element method in MatLab or Python that solves an elliptic problem

Timetable