# ELEC443 Boundary Value Problems of Mathematical Physics

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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.

Paper title Boundary Value Problems of Mathematical Physics ELEC443 Electronics 0.0833 10 points Not offered in 2021 (On campus) \$673.90 \$2,981.97
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.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
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

### Not offered in 2021

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

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.

Paper title Boundary Value Problems of Mathematical Physics ELEC443 Electronics 0.0833 10 points Not offered in 2022 (On campus) Tuition Fees for 2022 have not yet been set Tuition Fees for international students are elsewhere on this website.
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.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
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

### Not offered in 2022

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None