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
|Boundary Value Problems of Mathematical Physics
|Not offered in 2023 (On campus)
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- BSc(Hons), PGDipSci, MSc, MAppSc
Associate Professor Colin Fox (firstname.lastname@example.org)
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- Learning Outcomes
- By the end of the module students are expected to be able to:
- Perform simple manipulations using distributional calculus, in particular find distributional solutions to some simple differential equations
- Know the defining properties of classical, weak and distributional solutions to differential equations
- Know the defining properties of fundamental solutions and Green's functions
- Find Green's functions for linear ordinary differential boundary value problems, including initial-value problems
- Find the adjoint operator and adjoint boundary value problem associated with a linear partial differential boundary value problem
- Derive Green's theorem for arbitrary second-order linear partial differential equations with (classical) boundary conditions
- Use fundamental solutions or Green's functions within Green's theorem to write an integral solution to a linear boundary value problem
- Derive the boundary integral equation for second-order elliptic boundary value problems
- State the steps required for a rudimentary boundary element method
- Code up a boundary element method in MatLab or Python that solves an elliptic problem