**Introduction to Vector Space** |

Lecture 01 - Introduction to Vector Space |

Lecture 02 - Introduction to Vector Space (cont.) |

**Onto, Into, One to One function, Completeness Space** |

Lecture 03 - Onto, Into, One to One Function |

**Vectors** |

Lecture 04 - Vectors |

Lecture 05 - Vectors (cont.) |

**Contraction Mapping** |

Lecture 06 - Contraction Mapping |

Lecture 07 - Contraction Mapping (cont.) |

**Matrix, Determinants and Properties** |

Lecture 08 - Matrix, Determinant |

**Eigenvalue Problem** |

Lecture 09 - Eigenvalue Problem in Discrete Domain |

Lecture 10 - Eigenvalue Problem in Discrete Domain (cont.) |

Lecture 11 - Eigenvalue Problem in Discrete Domain (cont.) |

Lecture 12 - Eigenvalue Problem in Discrete Domain (cont.) |

**Applications of Eigenvalue Problems** |

Lecture 13 - Stability Analysis |

Lecture 14 - Stability Analysis (cont.) |

Lecture 15 - Stability Analysis (cont.) |

Lecture 16 - More Examples |

**Partial Differential Equations** |

Lecture 17 - Partial Differential Equations |

Lecture 18 - Partial Differential Equations (cont.) |

Lecture 19 - Eigenvalue Problem in Continuous Domain |

**Special Ordinary Differential Equations and Adjoint Operators** |

Lecture 20 - Special Ordinary Differential Equations |

Lecture 21 - Adjoint Operators |

Lecture 22 - Theorems of Eigenvalues and Eigenfunctions |

**Solution of Linear, Homogeneous PDEs by Separation of Variables** |

Lecture 23 - Solution of PDE: Separation of Variables Method |

Lecture 24 - Solution of Parabolic PDE: Separation of Variables Method |

Lecture 25 - Solution of Parabolic PDE: Separation of Variables Method (cont.) |

Lecture 26 - Solution of Higher Dimensional PDEs |

Lecture 27 - Solution of Higher Dimensional PDEs (cont.) |

Lecture 28 - Four Dimensional Parabolic PDE |

Lecture 29 - Solution of Elliptic and Hyperbolic PDE |

Lecture 30 - Solution of Elliptic and Hyperbolic PDE (cont.) |

Lecture 31 - PDE in Cylindrical and Spherical Coordinates |

**Solution of Nonhomogeneous PDEs by Green's Function** |

Lecture 32 - Solution of Nonhomogeneous PDE |

Lecture 33 - Solution of Nonhomogeneous PDE (cont.) |

Lecture 34 - Solution of Nonhomogeneous Parabolic PDE |

Lecture 35 - Solution of Nonhomogeneous Elliptic PDE |

Lecture 36 - Solution of Nonhomogeneous Elliptic PDE (cont.) |

**Solution of PDEs by Similarity Solution Method** |

Lecture 37 - Similarity Solution |

Lecture 38 - Similarity Solution (cont.) |

**Solution of PDEs by Integral Method** |

Lecture 39 - Integral Method |

**Solution of PDEs by Laplace Transformation** |

Lecture 40 - Laplace Transform |

**Solution of PDEs by Fourier Transformation** |

Lecture 41 - Fourier Transform |