PH211 - Physical Mathematics I - Fall 2010

Course
PH211 - Physical Mathematics I
Instructor
Ewan Stewart
Webpage
http://cosmology.kaist.ac.kr/pm1/
Time
1:00 - 2:30pm, Tuesdays and Thursdays
Place
Teaching assistants
Problem classes
Evaluation
class participation, problems, talk, exam

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.

  1. LaTeX
    1. Download LaTeX
    2. Choose a LaTeX editor
    3. LaTeX guides
    4. LaTeX packages and extensions
    5. Links
    6. Examples
  2. Complex variables
    1. Holomorphic functions
      1. Complex functions
      2. Holomorphic functions
      3. Analytic functions
      4. Analytic continuation
      5. Singularities
    2. Holomorphic integration
      1. Holomorphic integrals
      2. Contour integration
    3. Gamma function
      1. Gamma function
      2. Saddle point approximation
      3. Asymptotic series
  3. Hilbert spaces
    1. Hilbert spaces
      1. Vector spaces
      2. Hermitian conjugation and covectors
      3. Subspaces
    2. Linear operators
      1. Hermitian conjugate, inverse and commutator
      2. Hermitian, unitary and projection operators
      3. Eigenspaces
    3. Bases and components
      1. Discrete bases
      2. Continuous bases
      3. Delta function
      4. Eigenvectors as basis vectors
    4. Integral and differential operators
      1. Integral operators
      2. Differential operators
      3. Hermitian differential operators
      4. Eigenfunctions
    5. Laplace operator
      1. Hermitian boundary conditions
      2. Eigenfunctions in one dimension
      3. Eigenfunctions in two dimensions
      4. Eigenfunctions in three dimensions
      5. Hydrogen atom
    6. Operator equations
      1. Hermitian operator equations
      2. Green's functions
      3. Inhomogeneous differential equations
      4. Poisson's equation

Problems

You may collaborate with one or two other students of similar ability, provided that you first get permission from the teaching assistant, 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 assistant 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.

Answers should be submitted by email, as both a tex file and a pdf file, to both me and the teaching assistant, until you receive a pass grade for your LaTeX. Thereafter, you may submit handwritten answers to the teaching assistant. Please download the Physical Mathematics I style file to the same directory as the LaTeX files.

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 the tex and pdf files to both me and the teaching assistants for comments. You will then present your talk during the Physical Mathematics I Conference 2010. 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.

Some talks from previous years:

Fall 2006
Fall 2007
Fall 2008
Fall 2009

Exam

The exam will be open book and open time (up to 24 hours).

Recommended links

Recommended books