The documents on this page were developed for various courses at NTU. They are released under the Creative Commons Attribution-ShareAlike 4.0 International License Creative
	Commons License.

Complex Methods for the Sciences

An introductory course in mathematical methods for science and engineering students. Topics covered include complex analysis, contour integration, Fourier analysis, and Green's function methods. Mathematical methods are illustrated with examples drawn from physics, with a focus on oscillations and waves. These notes are also available in the form of Jupyter notebooks on Github (GPLv3).

  1. Mathematical Functions [pdf]
  2. Derivatives [pdf]
  3. Integrals [pdf]
  4. Complex numbers [pdf]
  5. Complex oscillations [pdf]
  6. Complex waves [pdf]
  7. Complex derivatives [pdf]
  8. Branch points and branch cuts [pdf]
  9. Contour integration [pdf]
  10. Fourier series and Fourier transforms [pdf]
  11. Green's functions [pdf]
  12. Solutions [pdf]

Physics Laboratory

A course on experimental physics for second-year undergraduates.

  1. Error Analysis [pdf]
  2. Writing a Good Lab Report [pdf]

Graduate Quantum Mechanics

An advanced course on quantum mechanics, covering scattering and resonances, multi-particle quantum mechanics, and the basics of quantum field theory. Python source files for the numerical examples are available on Github (GPLv3).

  1. Scattering [pdf]
  2. Resonances [pdf]
  3. Quantum Entanglement [pdf]
  4. Identical Particles [pdf]
  5. Quantum Electrodynamics [pdf]
  6. Appendices:
    1. Circular Waves [pdf]
    2. The Transfer Matrix Method [pdf]
    3. Entropy [pdf]
    4. Numerical Tensor Products [pdf]
    5. Coherent States [pdf]
    6. Anyons [pdf]

Computational Physics

An introductory course in computational physics for upper-level undergraduates. Topics covered include numerical linear algebra, eigenvalue problems, sparse matrix problems, numerical integration and initial-value problems, Fourier transforms, and Monte Carlo simulations. Programming examples are based on Scientific Python.

  1. Scipy tutorial (part 1)
  2. Scipy tutorial (part 2)
  3. Numbers, arrays, and scaling
  4. Numerical linear algebra
  5. Gaussian elimination
  6. Eigenvalue problems
  7. Finite-difference equations
  8. Sparse matrices
  9. Numerical integration
  10. Numerical integration of ODEs
  11. Discrete Fourier transforms
  12. Markov chains
  13. The Markov chain Monte Carlo method