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Mathematics II

Module 1. Instructor: Dr. Tanuja Srivastava, Department of Mathematics, IIT Roorkee
Complex Integration, Contour Integration, Cauchy's Integral Theorem, Cauchy's Integral Formula, Application of Cauchy Integral Formula, Complex Valued Function on Real Domain, Improper Integral to Definite Integral, Complex function on Complex Domain.

Module 2. Instructor: Dr. Sunita Gakkhar, Department of Mathematics, IIT Roorkee
Matrix Algebra, Determinants, Linear Algebra, Inner Product, Linear Transformation, Eigenvalues, Eigenvectors, Quadratic Forms, Diagonalization, Functions of Complex Variables, Taylor Series, Laurent Series, Rank of a Matrix.

Module 3. Instructor: Prof. H.G. Sharma, Department of Mathematics, IIT Roorkee
Complex Numbers and their Geometrical Representation.
(from nptel.ac.in)

Complex Integration


Lecture 01 - Complex Integration
Lecture 02 - Contour Integration
Lecture 03 - Cauchy's Integral Theorem
Lecture 04 - Cauchy's Integral Formula
Lecture 05 - Applications of Cauchy's Integral Formula
Lecture 06 - Zeros, Singularities and Poles
Lecture 07 - Residue Integration Method
Lecture 08 - Residue Theorem
Lecture 09 - Evaluation of Real Integrals
Lecture 10 - Evaluation of Real Improper Integrals 1
Lecture 11 - Evaluation of Real Improper Integrals 2
Lecture 12 - Evaluation of Real Improper Integrals 3
Lecture 13 - Evaluation of Real Improper Integrals 4
Lecture 14 - Evaluation of Real Improper Integrals: Revision
Lecture 15 - Matrix Algebra - Part 1
Lecture 16 - Matrix Algebra - Part 2
Lecture 17 - Determinants - Part 1
Lecture 18 - Determinants - Part 2
Lecture 19 - Solution of System Equation
Lecture 20 - Linear Algebra Part 1: Vector Spaces
Lecture 21 - Linear Algebra Part 2: Complex Vector Spaces, Subspaces
Lecture 22 - Linear Algebra Part 3: Linear Independence and Dependence
Lecture 23 - Linear Algebra Part 4: Complementary Subspaces, Change of Basis
Lecture 24 - Inner Product
Lecture 25 - Linear Transformation - Part 1
Lecture 26 - Linear Transformation - Part 2
Lecture 27 - Eigenvalues and Eigenvectors - Part 1
Lecture 28 - Eigenvalues and Eigenvectors - Part 2
Lecture 29 - Quadratic Forms
Lecture 30 - Diagonalization - Part 1
Lecture 31 - Diagonalization - Part 2
Lecture 32 - Solution of System of Linear Equation
Lecture 33 - Functions of Complex Variables - Part 1
Lecture 34 - Functions of Complex Variables - Part 2
Lecture 35 - Taylor Series of Complex Variables
Lecture 36 - Laurent Series
Lecture 37 - Rank of a Matrix
Lecture 38 - Complex Numbers and Their Geometrical Representation

References
Mathematics II
Instructors: Dr. Tanuja Srivastava, Dr. Sunita Gakkhar and Prof. H.G. Sharma, Department of Mathematics, IIT Roorkee. Complex Variables and Linear Algebra.