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