PH211 - Physical Mathematics I

Syllabus and lecture notes

Please download the Physical Mathematics I style file to the same directory as the LaTeX files.

1. 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
      • The Not So Short Introduction to LaTeX2e
      • LaTeX Tutorials: A primer
      • LaTeX2e for Authors
      • LaTeX: Structured documents for TeX
   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
      • Asymptote and LaTeX: An integration guide
      • XeTeX - Unicode TeX
   5. Links
      • Comprehensive TeX Archive Network
      • LaTeX project site
      • TeX Users Group
      • Korean TeX Users Group
   6. Examples
      • homework.tex, homework.pdf
      • pgf.tex, data and images, pgf.pdf
      • beamer.tex, beamer.pdf
2. 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
3. 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. Eigenbases
   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