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Mathematics
Complex Analysis (Video)
Syllabus
Co-ordinated by :
IIT Guwahati
Available from :
2013-05-06
Lec :
1
Modules / Lectures
The Arithmetic, Geometric and Topological Properties of the Complex Numbers
Introduction
Introduction to Complex Numbers
de Moivre’s Formula and Stereographic Projection
Topology of the Complex Plane Part-I
Topology of the Complex Plane Part-II
Topology of the Complex Plane Part-III
Complex Functions: Limits, Continuity and Differentiation
Introduction to Complex Functions
Limits and Continuity
Differentiation
Cauchy-Riemann Equations and Differentiability
Analytic functions; the exponential function
Sine, Cosine and Harmonic functions
Branches of Multifunctions; Hyperbolic Functions
Problem Solving Session I
Complex Integration Theory
Integration and Contours
Contour Integration
Introduction to Cauchy’s Theorem
Cauchy’s Theorem for a Rectangle
Cauchy’s theorem Part - II
Cauchy’s Theorem Part - III
Cauchy’s Integral Formula and its Consequences
The First and Second Derivatives of Analytic Functions
Morera’s Theorem and Higher Order Derivatives of Analytic Functions
Problem Solving Session II
Further Properties of Analytic Functions
Introduction to Complex Power Series
Analyticity of Power Series
Taylor’s Theorem
Zeroes of Analytic Functions
Counting the Zeroes of Analytic Functions
Open mapping theorem – Part I
Open mapping theorem – Part II
Mobius Transformations
Properties of Mobius Transformations Part I
Properties of Mobius Transformations Part II
Problem Solving Session III
Isolated Singularities and Residue Theorem
Removable Singularities
Poles Classification of Isolated Singularities
Essential Singularity & Introduction to Laurent Series
Laurent’s Theorem
Residue Theorem and Applications
Problem Solving Session IV
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1
Introduction
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2
Introduction to Complex Numbers
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3
de Moivre’s Formula and Stereographic Projection
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4
Topology of the Complex Plane Part-I
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5
Topology of the Complex Plane Part-II
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6
Topology of the Complex Plane Part-III
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7
Introduction to Complex Functions
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8
Limits and Continuity
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9
Differentiation
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10
Cauchy-Riemann Equations and Differentiability
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