# Trinity College Dublin

## Notes.

Note 1: Conservative fields: pdf, short pdf, ps, short ps or tarred source.
Note 2: Uniqueness of solutions to the Laplace equation, an example application of the Gauss theorem: pdf, ps or LaTeX source.
Note 3: Fourier Series Example: pdf, short pdf, ps or tarred source.
Note 4: Bessel's Equation: pdf, ps or LaTeX source. This has now been incorporated into 231.III.5.
Note 5: Christmas Quiz 2008: I don't always remember to type out the christmas quiz, this year I did: pdf, ps or LaTeX source.

## Lecture Notes from Chris Ford.

These are notes from Chris Ford who taught the course in 2003/4 and 2004/5.

Vector potentials: pdf, ps or tex (not latex) source.
Ordinary differential equations: pdf, short pdf, ps or tex (not latex) source.

## Lecture Notes from John Kearney.

These are notes from John Kearney who took the course in 2005/6 and has been very kind in sending me notes to post here.

Part 3: pdf, ps, short pdf, or latex source.
Part 4: pdf, ps, short pdf, or latex source.

## Lecture Notes.

These notes are in draft form, there are mistakes and things may not be explained in the best way. I hope that they are nonetheless useful. To people in the class I am offering a bounty of 50c for typos, excluding the use of US rather than local spelling and excluding punctuation around equations, 2 euro for other mistakes and between 1 euro and 5 euro for accepted suggested improvements. I am also happy to negotiate for LaTeX notes that are complimentary to what is here. I have not done diagrams yet and so there are scans of hand-drawn diagrams available

Part I.1: Vector calculus, the scalar field, integrating in two-dimensions. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.I.1.1-3 231.I.4-6 and 231.I.7-8

Part I.2: Three-dimensions. Vector fields, grad and div. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.I.2.1-4.

Part I.3: Curl. Vector identities. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.I.3.1.

Part I.4: Line integrals, conservative fields. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.I.4.1-2 231.I.4.3-5

Part I.5: Surface integrals, Stokes' Theorem and Green's Theorem. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.I.5.1-2 231.I.5.3-6 231.I.5.7-8 231.I.5.9 231.I.5.10-11

Part I.6: Gauss's Theorem, vector potentials, line and surface integrals of scalars. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.I.6.1-4 231.I.6.5.

Part II.1: Fourier series, complex series, Parseval's theorem. pdf, short pdf, ps, short ps or LaTeX source.

Part II.2: Fourier integrals. pdf, short pdf, ps, short ps or LaTeX source.

Part II.3: Distributions. pdf, short pdf, ps, short ps or LaTeX source.

Part II.4: Distributions and Fourier integrals. pdf, short pdf, ps, short ps or LaTeX source.

Part III.1: Ordinary differential equations: linear first order, second order homogenous. pdf, short pdf, ps, short ps or LaTeX source.

Part III.2: Ordinary differential equations: second order inhomogenous. pdf, short pdf, ps, short ps or LaTeX source.

Part III.3: Ordinary differential equations: Wronskian, Euler's equation. pdf, short pdf, ps, short ps or LaTeX source.

Part III.4: Series solutions, Hermite equation. pdf, short pdf, ps, short ps or LaTeX source.

Part III.5: Froebenius method, Bessel equation and Fuchs theorem. pdf, short pdf, ps, short ps or LaTeX source.

Part III.6: Hermitian operators. pdf, short pdf, ps, short ps or LaTeX source.

Part IV.1: Partial differential equations: introduction and uniqeness and mean value theorems for the Laplace equation. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.IV.1.1-4. This is an uncorrected proof.

Part IV.2: Partial differential equations: seperation of variables. pdf, short pdf, ps, short ps or LaTeX source. Pictures: 231.IV.2.1-4. This is an incomplete and uncorrected proof.

## File conversion note

I am sometimes asked how I make various parts of my on-line teaching notes, for example, people ask how to make the short pdf documents etc. I don't think I do any of these things the best way, in particular, I never manage to pipe as much as I feel I should. Anyway, here is a short list:

• Making pdf To make pdf from dvi files first convert to ps
dvips foo -o
and then convert that to pdf
ps2pdf -sPAPERSIZE=a4 foo.ps foo.pdf
• Short pdf This is the two column format and it actually done using the postscript file
psnup -2 foo.ps foo.c2.ps
• Plots Plots, unfortunately, are usually done in xmaple. The trick here is to get rid of the page number, so make the plot and print it to foo.ps, now
sed s/"(Page 1)"/"()"/g < foo.ps > foo..ps
deletes the page number, next convert to eps
ps2epsi foo..ps foo.eps
and then delete foo.ps and foo..ps.
• Complicated diagrams such as the phase diagrams in my engineering notes are usually done by importing ps from xmaple into xfig and using that to annotate. Sometimes diagrams are drawn in LaTeX because that way the fonts match.