Lecture 1 - Introduction to Matrix Algebra - I

Lecture 2 - Introduction to Matrix Algebra - II

Lecture 3 - System of Linear Equations

Lecture 4 - Determinant of a Matrix

Lecture 5 - Determinant of a Matrix (Continued...)

Lecture 6 - Gauss Elimination

Lecture 7 - Gauss Elimination (Continued...)

Lecture 8 - LU Decomposition

Lecture 9 - Gauss-Jordon Method

Lecture 10 - Representation of Physical Systems as Matrix Equations

Lecture 11 - Tridiagonal Matrix Algorithm

Lecture 12 - Equations with Singular Matrices

Lecture 13 - Introduction to Vector Space

Lecture 14 - Vector Subspace

Lecture 15 - Column Space and Nullspace of a Matrix

Lecture 16 - Finding Null Space of a Matrix

Lecture 17 - Solving Ax=b when A is Singular

Lecture 18 - Linear Independence and Spanning of a Subspace

Lecture 19 - Basis and Dimension of a Vector Space

Lecture 20 - Four Fundamental Subspaces of a Matrix

Lecture 21 - Left and right inverse of a matrix

Lecture 22 - Orthogonality between the subspaces

Lecture 23 - Best estimate

Lecture 24 - Projection operation and linear transformation

Lecture 25 - Creating orthogonal basis vectors

Lecture 26 - Gram-Schmidt and modified Gram-Schmidt algorithms

Lecture 27 - Comparing GS and modified GS

Lecture 28 - Introduction to eigenvalues and eigenvectors

Lecture 29 - Eigenvlues and eigenvectors for real symmetric matrix

Lecture 30 - Positive definiteness of a matrix

Lecture 31 - Positive definiteness of a matrix (Continued...)

Lecture 32 - Basic Iterative Methods: Jacobi and Gauss-Siedel

Lecture 33 - Basic Iterative Methods: Matrix Representation

Lecture 34 - Convergence Rate and Convergence Factor for Iterative Methods

Lecture 35 - Numerical Experiments on Convergence

Lecture 36 - Steepest Descent Method: Finding Minima of a Functional

Lecture 37 - Steepest Descent Method: Gradient Search

Lecture 38 - Steepest Descent Method: Algorithm and Convergence

Lecture 39 - Introduction to General Projection Methods

Lecture 40 - Residue Norm and Minimum Residual Algorithm

Lecture 41 - Developing computer programs for basic iterative methods

Lecture 42 - Developing computer programs for projection based methods

Lecture 43 - Introduction to Krylov subspace methods

Lecture 44 - Krylov subspace methods for linear systems

Lecture 45 - Iterative methods for solving linear systems using Krylov subspace methods

Lecture 46 - Conjugate gradient methods

Lecture 47 - Conjugate gradient methods (Continued...)

Lecture 48 - Conjugate gradient methods (Continued...) and Introduction to GMRES

Lecture 49 - GMRES (Continued...)

Lecture 50 - Lanczos Biorthogonalization and BCG Algorithm

Lecture 51 - Numerical issues in BICG and polynomial based formulation

Lecture 52 - Conjugate gradient squared and Biconjugate gradient stabilized

Lecture 53 - Line relaxation method

Lecture 54 - Block relaxation method

Lecture 55 - Domain Decomposition and Parallel Computing

Lecture 56 - Preconditioners

Lecture 57 - Preconditioned conjugate gradient

Lecture 58 - Preconditioned GMRES

Lecture 59 - Multigrid methods - I

Lecture 60 - Multigrid methods - II