| Error Analysis, Probability and Distributions |
| Lecture 01 - Errors, Precision of Measurement, Accuracy, Significant Figures |
| Lecture 02 - Probability, Probability Distributions, Binomial and Poisson Distributions |
| Lecture 03 - Gaussian Distribution, Integrals, Averages |
| Lecture 04 - Estimation of Parameters, Errors, Least Square Fit |
| Lecture 05 - Practice Problems 1 |
| Vectors, Vector Spaces and Vector Functions |
| Lecture 06 - Vectors and Scalars, Vector Space, Vector Products |
| Lecture 07 - Linear Independence, Basis, Dimensionality |
| Lecture 08 - Vector Functions, Scalar and Vector Fields, Vector Differentiation |
| Lecture 09 - Vector Differentiation: Gradient, Divergence, Curl |
| Lecture 10 - Practice Problems 2 |
| Vector Integration, Matrices, Determinants, Linear Systems, Cramer's Rule |
| Lecture 11 - Line Integrals and Potential Theory |
| Lecture 12 - Surface and Volume Integrals |
| Lecture 13 - Matrices, Matrix Operations and Determinants |
| Lecture 14 - Cramer's Rule |
| Lecture 15 - Practice Problems 3 |
| Matrix Rank, Inverse, Eigenvalues, Eigenvectors, Special Matrices, Normal Modes |
| Lecture 16 - Rank of Matrix, Inverse of a Matrix |
| Lecture 17 - Eigenvalues and Eigenvectors for a Matrix |
| Lecture 18 - Special Matrices: Symmetric, Orthogonal, Hermitian, Unitary |
| Lecture 19 - Spectral Decomposition: Normal Modes, Sparse Matrices, Ill-conditioned Systems |
| Lecture 20 - Practice Problems 4 |
| First Order Ordinary Differential Equations |
| Lecture 21 - Differential Equations, Order, 1st Order ODEs, Separation of Variables |
| Lecture 22 - Exact Differentials |
| Lecture 23 - Integrating Factors |
| Lecture 24 - System of 1st Order ODES, Matrix Method |
| Lecture 25 - Practice Problems 5 |
| Second Order ODEs, Homogeneous/Nonhomogeneous Equations |
| Lecture 26 - Types of 2nd Order ODEs, Nature of Solutions |
| Lecture 27 - Homogeneous 2nd Order ODEs, Solution using Basis Functions |
| Lecture 28 - Homogeneous and Nonhomogeneous Equations |
| Lecture 29 - Nonhomogeneous Equations - Variation of Parameters |
| Lecture 30 - Practice Problems 6 |
| Power Series Method for Solving 2nd Order ODEs |
| Lecture 31 - Power Series Method for Solving Legendre Differential Equation |
| Lecture 32 - Properties of Legendre Differential Equation |
| Lecture 33 - Associated Legendre Polynomials, Spherical Harmonics |
| Lecture 34 - Hermite Polynomials, Solutions of Quantum Harmonic Oscillator |
| Lecture 35 - Practice Problems 7 |
| Modified Power Series Method, Frobenius Method |
| Lecture 36 - Conditions for Power Series Solution |
| Lecture 37 - Frobenius Method, Bessel Functions |
| Lecture 38 - Prosperities of Bessel Functions, Circular Boundary Problems |
| Lecture 39 - Laguerre Polynomials, Solution to Radial Part of H-atom |
| Lecture 40 - Practice Problems 8 |