**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 |