Mod-03 Lec-09 Morera's Theorem and Higher Order Derivatives of Analytic Functions

Course Lectures

• Mod-01 Introduction

  Prof. P. A. S. Sree Krishna

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• Mod-01 Lec-01 Introduction to Complex Numbers

  Prof. P. A. S. Sree Krishna

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• Mod-01 Lec-02 de Moivre's Formula and Stereographic Projection

  Prof. P. A. S. Sree Krishna

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• Mod-01 Lec-03 Topology of the Complex Plane Part-I

  Prof. P. A. S. Sree Krishna

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• Mod-01 Lec-04 Topology of the Complex Plane Part-II

  Prof. P. A. S. Sree Krishna

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• Mod-01 Lec-05 Topology of the Complex Plane Part-III

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-01 Introduction to Complex Functions

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-02 Limits and Continuity

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-03 Differentiation

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-04 Cauchy-Riemann Equations and Differentiability

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-05 Analytic functions; the exponential function

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-06 Sine, Cosine and Harmonic functions

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-07 Branches of Multifunctions; Hyperbolic Functions

  Prof. P. A. S. Sree Krishna

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• Mod-02 Lec-08 Problem Solving Session I

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-01 Integration and Contours

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-02 Contour Integration

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-03 Introduction to Cauchy's Theorem

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-04 Cauchy's Theorem for a Rectangle

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-05 Cauchy's theorem Part - II

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-06 Cauchy's Theorem Part - III

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-07 Cauchy's Integral Formula and its Consequences

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-08 The First and Second Derivatives of Analytic Functions

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-09 Morera's Theorem and Higher Order Derivatives of Analytic Functions

  Prof. P. A. S. Sree Krishna

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• Mod-03 Lec-10 Problem Solving Session II

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-01 Introduction to Complex Power Series

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-02 Analyticity of Power Series

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-03 Taylor's Theorem

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-04 Zeroes of Analytic Functions

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-05 Counting the Zeroes of Analytic Functions

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-06 Open mapping theorem -- Part I

  Prof. P. A. S. Sree Krishna

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• Mod-04 Lec-07 Open mapping theorem -- Part II

  Prof. P. A. S. Sree Krishna

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• Mod-05 Lec-01 Properties of Mobius Transformations Part I

  Prof. P. A. S. Sree Krishna

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• Mod-05 Lec-02 Properties of Mobius Transformations Part II

  Prof. P. A. S. Sree Krishna

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• Mod-05 Lec-03 Problem Solving Session III

  Prof. P. A. S. Sree Krishna

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• Mod-06 Lec-01 Removable Singularities

  Prof. P. A. S. Sree Krishna

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• Mod-06 Lec-02 Poles Classification of Isolated Singularities

  Prof. P. A. S. Sree Krishna

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• Mod-06 Lec-03 Essential Singularity & Introduction to Laurent Series

  Prof. P. A. S. Sree Krishna

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• Mod-06 Lec-04 Laurent's Theorem

  Prof. P. A. S. Sree Krishna

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• Mod-06 Lec-05 Residue Theorem and Applications

  Prof. P. A. S. Sree Krishna

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• Mod-06 Lec-06 Problem Solving Session IV

  Prof. P. A. S. Sree Krishna

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