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
