## SEE: Guide to Download NPTEL Video Lecture

## Lecture Details :

Complex Analysis by Prof. P. A. S. Sree Krishna,Department of Mathematics, IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

## Course Description :

Contents:

Introduction : Introduction and overview of the course, lecture-wise description - The Algebra Geometry and Topology of the Complex Plane : Complex numbers, conjugation, modulus, argument and inequalities - Powers and roots of complex numbers, geometry in the complex plane, the extended complex plane - Topology of the complex plane: Open sets, closed sets, limit points, isolated points, interior points, boundary points, exterior points, compact sets, connected sets, sequences and series of complex numbers and convergence.

Complex Functions: Limits, Continuity and Differentiation : Introduction to complex functions - Limits and continuity - Differentiation and the Cauchy-Riemann equations, analytic functions, elementary functions and their mapping properties, harmonic functions - Complex logarithm multi-function, analytic branches of the logarithm multi-function, complex exponent multi-functions and their analytic branches, complex hyperbolic functions - Problem Session

Complex Integration Theory : Introducing curves, paths and contours, contour integrals and their properties, fundamental theorem of calculus - Cauchy’s theorem as a version of Green’s theorem, Cauchy-Goursat theorem for a rectangle, The anti-derivative theorem, Cauchy-Goursat theorem for a disc, the deformation theorem - Cauchy's integral formula, Cauchy's estimate, Liouville's theorem, the fundamental theorem of algebra, higher derivatives of analytic functions, Morera's theorem - Problem Session

Further Properties of Analytic Functions : Power series, their analyticity, Taylor’s theorem - Zeroes of analytic functions, Rouche’s theorem - Open mapping theorem, maximum modulus theorem.

Mobius Transformations : Properties of Mobius transformations - Problem Session

Isolated Singularities and Residue Theorem : Isolated singularities, removable singularities - Poles, classification of isolated singularities - Casoratti-Weierstrass theorem, Laurent’s theorem - Residue theorem, the argument principle - Problem Session

## Other Resources :

### Syllabus | Citation |

## Other Mathematics Courses

- Regression Analysis by IIT Kharagpur
- University Calculus by The University of New South Wales
- Linear Algebra by MIT
- Finite Mathematics I by Other
- Geometry by Khan Academy
- Analytic Geometry and Calculus,Fall 2011 by UC Berkeley
- Math 95 - Intermediate Algebra by Portland Community College
- California Standards Test: Geometry by Khan Academy
- Advanced Matrix Theory by IISc Bangalore
- Single Variable Calculus by MIT

### » check out the complete list of Mathematics Video lectures

### Get Your Degree!

Find schools and get information on the program that’s right for you.

Powered by Campus Explorer