# Techniques of Applied Mathematics

## Trinity revisions (2012-2013)

These should be sent out a day or two before the consults. You will have about 100 minutes to complete them (likely less if we talk), so do your best to have them solid and up-to-speed on the day-of.

### Week 1: Problem sets 1-3

• Week 1: Problem sets 1-3 and solution
• 80 minutes/5 questions = 16 minutes per question

Typo on Q2 solution: should be $y = \int G(x,\xi) f(\xi)/(\xi+3) \, \de{\xi} + x^2/4$ (courtesy of A. David)

### Week 2: Problem sets 4-6

• Week 2: Problem sets 4-6
• 80 minutes/5 questions = 16 minutes per question (hopelessly optimistic)

Typo on Q1: should be $(1+\alpha)y$ (courtesy of T. Simpkins)

Typo on Q2a: should be $y(2\pi)$ and not $2(2\pi)$ (courtesy of T. Simpkins)

For a nice summary of the Frobenius series result, see this. The excerpt is from Mathematical Methods and Boundary Value Problems by Sam Melkonian.

Post revision notes: There was much confusion about how adjoint boundary conditions were defined. Here is a writeup on defining adjoints.

### Week 3: Problem sets 6 and 2008 exam

• Week 3: Problem set 6 and 2008 exam
• About 30 minutes per question.

Odd classes

Even classes

## Summary of exam questions from 2006-2012

You can get a pdf version here or click the image for a larger version.