Modules / Lectures


Sl.No Chapter Name MP4 Download
1Fundamental Theorems Connected with Zeros of Analytic FunctionsDownload
2The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of AlgebraDownload
3Morera's Theorem and Normal Limits of Analytic FunctionsDownload
4Hurwitz's Theorem and Normal Limits of Univalent FunctionsDownload
5Local Constancy of Multiplicities of Assumed ValuesDownload
6The Open Mapping TheoremDownload
7Introduction to the Inverse Function TheoremDownload
8Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse FunctionDownload
9Univalent Analytic Functions have never-zero Derivatives and are Analytic IsomorphismsDownload
10Introduction to the Implicit Function TheoremDownload
11Proof of the Implicit Function Theorem: Topological PreliminariesDownload
12Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit FunctionDownload
13Doing Complex Analysis on a Real Surface: The Idea of a Riemann SurfaceDownload
14 F(z,w)=0 is naturally a Riemann SurfaceDownload
15Constructing the Riemann Surface for the Complex LogarithmDownload
16Constructing the Riemann Surface for the m-th root functionDownload
17The Riemann Surface for the functional inverse of an analytic mapping at a critical pointDownload
18The Algebraic nature of the functional inverses of an analytic mapping at a critical pointDownload
19The Idea of a Direct Analytic Continuation or an Analytic ExtensionDownload
20General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of ConvergenceDownload
21Analytic Continuation Along Paths via Power Series Part ADownload
22Analytic Continuation Along Paths via Power Series Part BDownload
23Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along PathsDownload
24 Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy TheoremDownload
25Maximal Domains of Direct and Indirect Analytic Continuation: SecondVersion of the Monodromy TheoremDownload
26Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) VersionDownload
27Existence and Uniqueness of Analytic Continuations on Nearby PathsDownload
28Proof of the First (Homotopy) Version of the Monodromy TheoremDownload
29Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical PointDownload
30The Mean-Value Property, Harmonic Functions and the Maximum PrincipleDownload
31Proofs of Maximum Principles and Introduction to Schwarz LemmaDownload
32Proof of Schwarz Lemma and Uniqueness of Riemann MappingsDownload
33Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit DiscDownload
34Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit DiscDownload
35Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc.Download
36Hyperbolic Geodesics for the Hyperbolic Metric on the Unit DiscDownload
37Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit DiscDownload
38Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform Sequential Compactness are Equivalent Download
39Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels TheoremDownload
40The Proof of Montels TheoremDownload
41The Candidate for a Riemann Mapping Download
42Completion of Proof of The Riemann Mapping TheoremDownload
43Completion of Proof of The Riemann Mapping Theorem.Download

Sl.No Chapter Name English
1Fundamental Theorems Connected with Zeros of Analytic FunctionsPDF unavailable
2The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of AlgebraPDF unavailable
3Morera's Theorem and Normal Limits of Analytic FunctionsPDF unavailable
4Hurwitz's Theorem and Normal Limits of Univalent FunctionsPDF unavailable
5Local Constancy of Multiplicities of Assumed ValuesPDF unavailable
6The Open Mapping TheoremPDF unavailable
7Introduction to the Inverse Function TheoremPDF unavailable
8Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse FunctionPDF unavailable
9Univalent Analytic Functions have never-zero Derivatives and are Analytic IsomorphismsPDF unavailable
10Introduction to the Implicit Function TheoremPDF unavailable
11Proof of the Implicit Function Theorem: Topological PreliminariesPDF unavailable
12Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit FunctionPDF unavailable
13Doing Complex Analysis on a Real Surface: The Idea of a Riemann SurfacePDF unavailable
14 F(z,w)=0 is naturally a Riemann SurfacePDF unavailable
15Constructing the Riemann Surface for the Complex LogarithmPDF unavailable
16Constructing the Riemann Surface for the m-th root functionPDF unavailable
17The Riemann Surface for the functional inverse of an analytic mapping at a critical pointPDF unavailable
18The Algebraic nature of the functional inverses of an analytic mapping at a critical pointPDF unavailable
19The Idea of a Direct Analytic Continuation or an Analytic ExtensionPDF unavailable
20General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of ConvergencePDF unavailable
21Analytic Continuation Along Paths via Power Series Part APDF unavailable
22Analytic Continuation Along Paths via Power Series Part BPDF unavailable
23Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along PathsPDF unavailable
24 Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy TheoremPDF unavailable
25Maximal Domains of Direct and Indirect Analytic Continuation: SecondVersion of the Monodromy TheoremPDF unavailable
26Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) VersionPDF unavailable
27Existence and Uniqueness of Analytic Continuations on Nearby PathsPDF unavailable
28Proof of the First (Homotopy) Version of the Monodromy TheoremPDF unavailable
29Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical PointPDF unavailable
30The Mean-Value Property, Harmonic Functions and the Maximum PrinciplePDF unavailable
31Proofs of Maximum Principles and Introduction to Schwarz LemmaPDF unavailable
32Proof of Schwarz Lemma and Uniqueness of Riemann MappingsPDF unavailable
33Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit DiscPDF unavailable
34Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit DiscPDF unavailable
35Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc.PDF unavailable
36Hyperbolic Geodesics for the Hyperbolic Metric on the Unit DiscPDF unavailable
37Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit DiscPDF unavailable
38Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform Sequential Compactness are Equivalent PDF unavailable
39Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels TheoremPDF unavailable
40The Proof of Montels TheoremPDF unavailable
41The Candidate for a Riemann Mapping PDF unavailable
42Completion of Proof of The Riemann Mapping TheoremPDF unavailable
43Completion of Proof of The Riemann Mapping Theorem.PDF unavailable


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