LINEAR ALGEBRA
| Lecture 1 | Matrices, system of linear equations, elimination method | |
| Lecture 2 | Elementary matrices, invertible matrix , row reduction method | |
| Lecture 3 | Determinant and its properties | |
| Lecture 4 | Determinant and its properties | |
| Lecture 5 | Determinant, system of linear equations, Cramers rule | |
| Lecture 6 | Vector space, subspace, examples | |
| Lecture 7 | Span, linearly independent, basis, examples | |
| Lecture 8 | Dimension, examples | |
| Lecture 9 | Sum and intersection of two subspaces, examples | |
| Lecture 10 | Linear Transformation, Rank-Nullity Theorem, Row and column space | |
| Lecture 11 | Rank of a matrix, solvability of system of linear equations, examples | |
| Lecture 12 | Some applications (Lagrange interpolation, Wronskian), Inner product | |
| Lecture 13 | Orthogonal basis, Gram-Schmidt process, orthogonal projection | |
| Lecture 14 | Orthogonal complement, fundamental subspaces, least square solutions | |
| Lecture 15 | Least square fittings, eigenvalues, eigenvectors | |
| Lecture 16 | Eigenvalues, eigenvectors, characterization of a diagonalizable matrix | |
| Lecture 17 | Diagonalization : Examples, an application | |
| Lecture 18 | Orthogonal matrix, Diagonalization of a real symmetric matrix | |
| Lecture 19 | Representation of linear maps by matrices : Book |
COMPLEX ANALYSIS
|
Lecture 1 |
Complex Numbers and Complex Differentiation | |
|
Lecture 2 |
Complex Differentiation and Cauchy-Riemann Equations | |
|
Lecture 3 |
Analytic Functions and Power Series | |
|
Lecture 4 |
Derivative of Power Series and Complex Exponential | |
|
|
||
|
Lecture 5 |
Complex Logarithm and Trigonometric Functions | |
|
Lecture 6 |
Complex Integration | |
|
Lecture 7 |
Cauchy's Theorem | |
|
Lecture 8 |
Cauchy's Integral Formula I | |
|
Lecture 9 |
Cauchy's Integral Formula II | |
|
Lecture10-12 |
Taylor series, Cauchy residue theorem | |
|
Lecture 17 |
Mobius Transformation | |