Lecture Notes for Math Methods

Lecture Notes are posted approximately twice a month (when we complete a large block of material):

  • Part 1 – Complex Numbers, Euler’s Relation, Functions of Complex Variables
  • Part 2 – Multivariable Calculus, Laplacians, Total, exact, and inexact differentials, Maxima and minima, Taylor’s formula in several variables, Lagrange multipliers, Multi-dimensional integration
  • Part 3 – Differential Equations, damped oscillations
  • Part 4 – Linear Algebra, Vector Calculus, Divergence, Curl, non-Cartesian coordinates, Determinants, Matrices, Inverses, Rotation matrices, Orthogonal matrices
  • Part 5 – Singular matrices, solving linear systems, the Trace, complex vectors, Unitary transformations, Hilbert spaces
  • Part 6 – Eigenvalues and Eigenvectors, applications to kinetics and molecular vibrations
  • Part 7 – Probability & Statistics, Continuous distributions, Treatment of experimental errors, Central Limit Theorem, Propagation of Errors, Linear Regression
  • Part 8 – Permutations & Combinatorics, Entropy, Extensivity
  • Part 9 – Hilbert Spaces, Orthogonal polynomials, Fourier Series, Fourier Transforms

Funny Stuff (mostly from xkcd):