Lecture 15 of 40Complex Integration Theory
Integration and Contours
Prof. P. A. S. Sree Krishna · IIT Guwahati
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- Complex Analysis, IIT Guwahati (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- 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
- 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
- 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
- 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
- Properties of Mobius Transformations Part I
- Properties of Mobius Transformations Part II
- Problem Solving Session III
- Removable Singularities
- Poles Classification of Isolated Singularities
- Essential Singularity & Introduction to Laurent Series
- Laurent’s Theorem
- Residue Theorem and Applications
- Problem Solving Session IV