PH211 - Physical Mathematics I

Course description

This course is the first half of a one year introduction to physical mathematics. It aims to help you gain a physical understanding of the mathematics used in physics.

Syllabus and lecture notes

Please download the Physical Mathematics I style file to the same directory as the LaTeX files. This and other files will be revised frequently, so please make sure you have the most recent version.

LaTeX
1. Download LaTeX
  - Download Basic MiKTeX. Note that you can install LaTeX packages when needed using the MiKTeX Package Manager.
  - Download Ghostscript and GSview
2. Choose a LaTeX editor
  - Any text editor
  - Texmaker
  - TeXnicCenter
  - TeXworks (included in MiKTeX)
  - WinShell
  - Many others
3. LaTeX guides
4. LaTeX packages and extensions
  - TikZ and PGF - a package for creating graphics
    - Graphics with TikZ
  - Beamer - a package for creating talks
    - Beamer by Example
  - Hyperref - a package for creating hypertext links
  - Asymptote - a powerful vector graphics language
  - XeTeX - Unicode TeX
5. Links
6. Examples
Complex variables
1. Holomorphic functions (tex file)
  1. Complex functions
  2. Holomorphic functions
  3. Analytic functions
  4. Analytic continuation
  5. Singularities
2. Holomorphic integration (tex file)
  1. Holomorphic integrals
  2. Contour integration
3. Gamma function (tex file)
  1. Definition and holomorphic structure
  2. Saddle point approximation
  3. Asymptotic series
Hilbert spaces
1. Hilbert spaces (tex file)
  1. Vector spaces
  2. Hermitian conjugation and covectors
  3. Subspaces
2. Linear operators (tex file)
  1. Hermitian conjugate, inverse and commutator
  2. Hermitian, unitary and projection operators
  3. Eigenspaces
3. Bases and components (tex file)
  1. Discrete bases
  2. Continuous bases
  3. Delta function
  4. Eigenspace bases
4. Integral and differential operators (tex file)
  1. Integral operators
  2. Differential operators
  3. Hermitian differential operators
  4. Eigenfunctions
5. Operator equations (tex file)
  1. Hermitian operator equations
  2. Green's functions
  3. Inhomogeneous differential equations
  4. Poisson's equation
6. Laplace operator (tex file)
  1. Hermitian boundary conditions
  2. Eigenfunctions in one dimension
  3. Eigenfunctions in two dimensions
  4. Eigenfunctions in three dimensions

Problems

You may collaborate with one or two other students of similar ability, provided that you first get permission from the teaching assistants, and may submit a single joint homework with the names of all collaborators on it. There will be two deadlines for each homework. The teaching assistants will give comments on your first submission to help you improve it for your second submission. Your grade will be based on a combination of your first and second submissions.

Please download the Physical Mathematics I style file to the same directory as your LaTeX files. Answers should be submitted, as both a tex file and a pdf file, to me and both teaching assistants by email.

Talk

You should give a 10 minute talk, on a mathematical topic of your choice, using the LaTeX Beamer package. Topic requests should be emailed to me and will be listed here on a first come first served basis. After your topic is approved, prepare your talk and submit it (including pdf, tex and any other files such as figure or style files) to both me and the teaching assistants for comments. You will then present your talk during the Physical Mathematics I Conference 2011. Submit the final version of your talk to me before the exam for evaluation and to be posted here. Grades will depend on the visual and oral presentation, and the originality and interest of the content.

Physical Mathematics I Conference 2011 - December 9th to 13th - Creative 311/310/206

Exam

The exam will be open book and open time (up to 24 hours). It will start at 1pm on Thursday 22nd December in Creative 311.

PH211 - Physical Mathematics I - Fall 2011