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, RankNullity 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, GramSchmidt 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 CauchyRiemann 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  
Lecture1012 
Taylor series, Cauchy residue theorem  
Lecture 17 
Mobius Transformation  