Lecture Notes of MTH102
(.pdf file)


 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



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


  Taylor series, Cauchy residue theorem PDF

Lecture 17

  Mobius Transformation PDF