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, Monte Carlo Integration
- Part 9 – Hilbert Spaces, Orthogonal polynomials, Fourier Series, Fourier Transforms
Funny Stuff (mostly from xkcd):
