| 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 |