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Course11110307040 lectures

Complex Analysis

Prof. P. A. S. Sree Krishna · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

The Arithmetic, Geometric and Topological Properties of the Complex Numbers

  1. Introduction Video
  2. Introduction to Complex Numbers Video
  3. de Moivre’s Formula and Stereographic Projection Video
  4. Topology of the Complex Plane Part-I Video
  5. Topology of the Complex Plane Part-II Video
  6. Topology of the Complex Plane Part-III Video

Complex Functions: Limits, Continuity and Differentiation

  1. Introduction to Complex Functions Video
  2. Limits and Continuity Video
  3. Differentiation Video
  4. Cauchy-Riemann Equations and Differentiability Video
  5. Analytic functions; the exponential function Video
  6. Sine, Cosine and Harmonic functions Video
  7. Branches of Multifunctions; Hyperbolic Functions Video
  8. Problem Solving Session I Video

Complex Integration Theory

  1. Integration and Contours Video
  2. Contour Integration Video
  3. Introduction to Cauchy’s Theorem Video
  4. Cauchy’s Theorem for a Rectangle Video
  5. Cauchy’s theorem Part - II Video
  6. Cauchy’s Theorem Part - III Video
  7. Cauchy’s Integral Formula and its Consequences Video
  8. The First and Second Derivatives of Analytic Functions Video
  9. Morera’s Theorem and Higher Order Derivatives of Analytic Functions Video
  10. Problem Solving Session II Video

Further Properties of Analytic Functions

  1. Introduction to Complex Power Series Video
  2. Analyticity of Power Series Video
  3. Taylor’s Theorem Video
  4. Zeroes of Analytic Functions Video
  5. Counting the Zeroes of Analytic Functions Video
  6. Open mapping theorem – Part I Video
  7. Open mapping theorem – Part II Video

Mobius Transformations

  1. Properties of Mobius Transformations Part I Video
  2. Properties of Mobius Transformations Part II Video
  3. Problem Solving Session III Video

Isolated Singularities and Residue Theorem

  1. Removable Singularities Video
  2. Poles Classification of Isolated Singularities Video
  3. Essential Singularity & Introduction to Laurent Series Video
  4. Laurent’s Theorem Video
  5. Residue Theorem and Applications Video
  6. Problem Solving Session IV Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mathematics
Teacher
Prof. P. A. S. Sree Krishna
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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