'Cauchy-Riemann Equations and Differentiability' Video Lecture

Cauchy-Riemann Equations and Differentiability

  • Course: Complex Analysis
  • Discipline: Mathematics
  • Faculty: Prof. P. A. S. Sree Krishna
  • Institute: IIT Guwahati

    • NEXT LECTURE >> Analytic functions; the exponential function
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    Course Video Lectures Introduction Introduction to Complex Numbers de Moivre’s Formula and Stereographic Projec.. 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 Differentiabilit.. Analytic functions; the exponential function Sine, Cosine and Harmonic functions Branches of Multifunctions; Hyperbolic Functi.. 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 Consequenc.. The First and Second Derivatives of Analytic .. Morera’s Theorem and Higher Order Derivative.. 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 Singularitie.. Essential Singularity & Introduction to Laure.. Laurent’s Theorem Residue Theorem and Applications Problem Solving Session IV
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