#1
April 22nd, 2015, 01:00 PM
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Video Lectures IIT Madras
I missed some Lectures of my course curriculum at IIT Madaras. Will you please tell how I can use the E-learning resource NPTEL offered by IIT Madaras for getting video lectures given by the faculty members of the IIT Madras.
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#2
March 1st, 2017, 03:17 PM
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Re: Video Lectures IIT Madras
Hii sir, I Wants to get the modules of the lecturer of Advanced Complex Analysis - Part 1:Zeros of Analytic Functions, of the IIT Madras Video Lecturer ?
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#3
March 1st, 2017, 03:17 PM
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Re: Video Lectures IIT Madras
Indian Institute of Technology Madras is a public engineering and research institute located in Chennai, Tamil Nadu and is one of India's most prestigious universities. As you Asking for the modules of the lecturer of Advanced Complex Analysis - Part 1:Zeros of Analytic Functions, of the IIT Madras Video Lecturer the Modules Are Shown below UNIT 1: Theorems of Rouche and Hurwitz Fundamental Theorems Connected with Zeros of Analytic Functions The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of Algebra Morera's Theorem and Normal Limits of Analytic Functions Hurwitz's Theorem and Normal Limits of Univalent Functions UNIT 2: Open Mapping Theorem Local Constancy of Multiplicities of Assumed Values The Open Mapping Theorem UNIT 3: Inverse Function Theorem Introduction to the Inverse Function Theorem Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse Function Univalent Analytic Functions have never-zero Derivatives and are Analytic Isomorphisms UNIT 4: Implicit Function Theorem Introduction to the Implicit Function Theorem Proof of the Implicit Function Theorem: Topological Preliminaries Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit Function UNIT 5: Riemann Surfaces for Multi-Valued Functions Doing Complex Analysis on a Real Surface: The Idea of a Riemann Surface F(z,w)=0 is naturally a Riemann Surface Constructing the Riemann Surface for the Complex Logarithm Constructing the Riemann Surface for the m-th root function The Riemann Surface for the functional inverse of an analytic mapping at a critical point The Algebraic nature of the functional inverses of an analytic mapping at a critical point UNIT 6: Analytic Continuation The Idea of a Direct Analytic Continuation or an Analytic Extension General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence Analytic Continuation Along Paths via Power Series Part A Analytic Continuation Along Paths via Power Series Part B Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along Paths UNIT 7: Monodromy Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy Theorem Maximal Domains of Direct and Indirect Analytic Continuation: SecondVersion of the Monodromy Theorem Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) Version Existence and Uniqueness of Analytic Continuations on Nearby Paths Proof of the First (Homotopy) Version of the Monodromy Theorem Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical Point Unit 8: Harmonic Functions, Maximum Principles, Schwarz Lemma and Uniqueness of Riemann Mappings The Mean-Value Property, Harmonic Functions and the Maximum Principle Proofs of Maximum Principles and Introduction to Schwarz Lemma Proof of Schwarz Lemma and Uniqueness of Riemann Mappings Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit Disc Unit 9: Pick Lemma and Hyperbolic Geometry on the Unit Disc Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc. Hyperbolic Geodesics for the Hyperbolic Metric on the Unit Disc Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit Disc Unit 10: Theorems of Arzela-Ascoli and Montel Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform Sequential Compactness are Equivalent Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels Theorem The Proof of Montels Theorem Unit 11: Existence of a Riemann Mapping The Candidate for a Riemann Mapping Completion of Proof of The Riemann Mapping Theorem Completion of Proof of The Riemann Mapping Theorem For more details you may Contact to the IIT Madras the contact details Are given below Contact details : IIT Madras Address: Beside Adyar Cancer Institute, Opposite to C.L.R.I, Sardar Patel Road, Adyar, Chennai, Tamil Nadu 600036 Phone: 044 2257 8280 |