Lecture 1 - Vectors, Vector Operations and Linear Independence

Lecture 2 - Vector Operations, Generalization of Vectors

Lecture 3 - Vector Differentiation, Vector Transformations

Lecture 4 - Vector Integration, Line, Surface and Volume Integrals

Lecture 5 - Practice Problems

Lecture 6 - Matrix as a vector transformation, linear system

Lecture 7 - Special Matrices: Symmetric, Orthogonal, Complex

Lecture 8 - Rotational Matrices, Eigenvalues and Eigenvectors

Lecture 9 - Determinants, Matrix Inverse

Lecture 10 - Practice Problems

Lecture 11 - Step Function, Delta Function

Lecture 12 - Gamma Function, Error Function

Lecture 13 - Spherical Polar Coordinates

Lecture 14 - Cylindrical Polar Coordinates, Integrals

Lecture 15 - Recap of Module 3, Practice Problems

Lecture 16 - ODEs and PDEs, First order ODEs, system of 1st order ODEs

Lecture 17 - First order ODEs, exact integrals, integrating factors

Lecture 18 - System of first order ODEs, Linear first order ODEs

Lecture 19 - General solution of a system of linear first order ODEs with constant coefficients

Lecture 20 - Recap of Module 4, Practice problems

Lecture 21 - Homogeneous 2nd Order ODE, Basis Functions

Lecture 22 - Nonhomogeneous 2nd Order ODE

Lecture 23 - Power Series Method of Solving ODEs

Lecture 24 - Frobenius Method / Power Series Method

Lecture 25 - Time-independent Schrodinger Equation for H-atom

Lecture 26 - Maxima and Minima, Taylor Series

Lecture 27 - Taylor Series for functions of several variables

Lecture 28 - Critical Points of Functions

Lecture 29 - Lagranges Method of Undetermined Multipliers

Lecture 30 - Recap of Module 6, Practice Problems

Lecture 31 - Nonlinear Differential Equations

Lecture 32 - Phase Plane of A Pendulum

Lecture 33 - Stability of Critical Points

Lecture 34 - Population Dynamics Models

Lecture 35 - Recap of Module 7, Practice Problems

Lecture 36 - Fourier Series, Fourier Expansion of Periodic Functions

Lecture 37 - (Part A): Fourier Expansions and Differential Equations

Lecture 38 - (Part B): Fourier Expansions and Differential Equations

Lecture 39 - Orthogonal Eigenfunctions, Sturm-Liouville Theory

Lecture 40 - Recap of Module 8, Practice Problems

Lecture 41 - Fourier Transforms

Lecture 42 - Properties of Fourier Transforms

Lecture 43 - Fourier Transforms and Partial Differential Equations

Lecture 44 - Laplace Transforms

Lecture 45 - Recap of Module 9, Practice Problems

Lecture 46 - Partial Differential Equations, Boundary Conditions

Lecture 47 - Separation of Variables

Lecture 48 - (Part A): Two-dimensional Wave Equation, Bessel Functions

Lecture 49 - (Part B): Two-dimensional Wave Equation, Bessel Functions

Lecture 50 - Recap of Module 10, Practice Problems

Lecture 51 - Discrete and Continuous Random Variables

Lecture 52 - Probability Distribution Functions

Lecture 53 - Poisson Distribution, Gaussain Distribution

Lecture 54 - Error Estimates, Least Square Fit, Correlation Functions

Lecture 55 - Recap of Module 11, Practice Problems