Lecture Notes of MTH102
(.pdf file)

LINEAR ALGEBRA

 Lecture 1 Matrices, system of linear equations, elimination method PDF Lecture 2 Elementary matrices, invertible matrix , row reduction method PDF Lecture 3 Determinant and its properties PDF Lecture 4 Determinant and its properties PDF Lecture 5 Determinant, system of linear equations, Cramers rule PDF Lecture 6 Vector space, subspace, examples PDF Lecture 7 Span, linearly independent, basis, examples PDF Lecture 8 Dimension, examples PDF Lecture 9 Sum and intersection of two subspaces, examples PDF Lecture 10 Linear Transformation, Rank-Nullity Theorem, Row and column space PDF Lecture 11 Rank of a matrix, solvability of system of linear equations, examples PDF Lecture 12 Some applications (Lagrange interpolation, Wronskian), Inner product PDF Lecture 13 Orthogonal basis, Gram-Schmidt process, orthogonal projection PDF Lecture 14 Orthogonal complement, fundamental subspaces, least square solutions PDF Lecture 15 Least square fittings, eigenvalues, eigenvectors PDF Lecture 16 Eigenvalues, eigenvectors, characterization of a diagonalizable matrix PDF Lecture 17 Diagonalization : Examples, an application PDF Lecture 18 Orthogonal matrix, Diagonalization of a real symmetric matrix PDF Lecture 19 Representation of linear maps by matrices : Book PDF

COMPLEX ANALYSIS

 Lecture 1 Complex Numbers and Complex Differentiation PDF Lecture 2 Complex Differentiation and Cauchy-Riemann Equations PDF Lecture 3 Analytic Functions and Power Series PDF Lecture 4 Derivative of Power Series and Complex Exponential PDF Lecture 5 Complex Logarithm and Trigonometric Functions PDF Lecture 6 Complex Integration PDF Lecture 7 Cauchy's Theorem PDF Lecture 8 Cauchy's Integral Formula I PDF Lecture 9 Cauchy's Integral Formula II PDF Lecture10-12 Taylor series, Cauchy residue theorem PDF Lecture 17 Mobius Transformation PDF