Lecture 1 - Errors, precision and accuracy

Lecture 2 - Probability and distributions

Lecture 3 - Gaussian distribution and integrals

Lecture 4 - Gaussian distribution, integrals, averages

Lecture 5 - Practice problems 1

Lecture 6 - Vectors and Vector Spaces

Lecture 7 - Linear Independence

Lecture 8 - Scalar and vector fields

Lecture 9 - Gradient, divergence and curl

Lecture 10 - Practice problems 2

Lecture 11 - Line integrals, Potential Theory

Lecture 12 - Surface and Volume Integrals

Lecture 13 - Matrices

Lecture 14 - Linear Systems, Cramer's Rule

Lecture 15 - Practice Problems 3

Lecture 16 - Rank and Inverse of a Matrix

Lecture 17 - Eigenvalues and Eigenvectors

Lecture 18 - Special matrices

Lecture 19 - Spectral decomposition and Normal modes

Lecture 20 - Practice Problems 4

Lecture 21 - Differential equations, Order

Lecture 22 - Exact and Inexact differentials

Lecture 23 - Integrating Factors

Lecture 24 - System of 1st order ODEs, matrix methods

Lecture 25 - Practice Problems 5

Lecture 26 - Types of 2nd order ODEs, nature of solutions

Lecture 27 - Homogeneous 2nd order ODEs

Lecture 28 - Homogeneous and nonhomogeneous equations

Lecture 29 - Nonhomogeneous equations Variation of parameters

Lecture 30 - Practice Problems 6

Lecture 31 - Power series method for solving Legendre DE

Lecture 32 - Properties of Legendre Polynomials

Lecture 33 - Associated Legendre Polynomials, Spherical Harmonics

Lecture 34 - Hermite Polynomials, Solution of Quantum Harmonic Oscillator

Lecture 35 - Practice Problems 7

Lecture 36 - Conditions for power series solution

Lecture 37 - Frobenius Method, Bessel Functions

Lecture 38 - Properties of Bessel Functions, circular boundary problems

Lecture 39 - Leguerre Polynomials, solution to radial part of H-atom

Lecture 40 - Practice Problems 8