Complex Analysis RHP5ZNXKPX

URI	`m2://res/RHP5ZNXKPX`
Kind	course
Creators	P. A. S. Sree Krishna (instructor)
Date	2013-11-05
Scope	in
Ids	course 0022nd079:111103070

Expressions

e1: edition

Language	en
Date	2013-11-05

m1: page, IIT Guwahati (record). nptel 111103070
m2: page, 2013-11-05 (record). nptel 111103070

Contents

part 1: The Arithmetic, Geometric and Topological Properties of the Complex Numbers
session 1: Introduction
session 2: Introduction to Complex Numbers
session 3: de Moivre’s Formula and Stereographic Projection
session 4: Topology of the Complex Plane Part-I
session 5: Topology of the Complex Plane Part-II
session 6: Topology of the Complex Plane Part-III
part 2: Complex Functions: Limits, Continuity and Differentiation
session 7: Introduction to Complex Functions
session 8: Limits and Continuity
session 9: Differentiation
session 10: Cauchy-Riemann Equations and Differentiability
session 11: Analytic functions; the exponential function
session 12: Sine, Cosine and Harmonic functions
session 13: Branches of Multifunctions; Hyperbolic Functions
session 14: Problem Solving Session I
part 3: Complex Integration Theory
session 15: Integration and Contours
session 16: Contour Integration
session 17: Introduction to Cauchy’s Theorem
session 18: Cauchy’s Theorem for a Rectangle
session 19: Cauchy’s theorem Part - II
session 20: Cauchy’s Theorem Part - III
session 21: Cauchy’s Integral Formula and its Consequences
session 22: The First and Second Derivatives of Analytic Functions
session 23: Morera’s Theorem and Higher Order Derivatives of Analytic Functions
session 24: Problem Solving Session II
part 4: Further Properties of Analytic Functions
session 25: Introduction to Complex Power Series
session 26: Analyticity of Power Series
session 27: Taylor’s Theorem
session 28: Zeroes of Analytic Functions
session 29: Counting the Zeroes of Analytic Functions
session 30: Open mapping theorem – Part I
session 31: Open mapping theorem – Part II
part 5: Mobius Transformations
session 32: Properties of Mobius Transformations Part I
session 33: Properties of Mobius Transformations Part II
session 34: Problem Solving Session III
part 6: Isolated Singularities and Residue Theorem
session 35: Removable Singularities
session 36: Poles Classification of Isolated Singularities
session 37: Essential Singularity & Introduction to Laurent Series
session 38: Laurent’s Theorem
session 39: Residue Theorem and Applications
session 40: Problem Solving Session IV

Catalogue records

nptel: 111103070 (manifestation)
nptel_video: 111103070 (manifestation)