Modules / Lectures

Sl.No | Chapter Name | MP4 Download |
---|---|---|

1 | Fundamental Theorems Connected with Zeros of Analytic Functions | Download |

2 | The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of Algebra | Download |

3 | Morera's Theorem and Normal Limits of Analytic Functions | Download |

4 | Hurwitz's Theorem and Normal Limits of Univalent Functions | Download |

5 | Local Constancy of Multiplicities of Assumed Values | Download |

6 | The Open Mapping Theorem | Download |

7 | Introduction to the Inverse Function Theorem | Download |

8 | Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse Function | Download |

9 | Univalent Analytic Functions have never-zero Derivatives and are Analytic Isomorphisms | Download |

10 | Introduction to the Implicit Function Theorem | Download |

11 | Proof of the Implicit Function Theorem: Topological Preliminaries | Download |

12 | Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit Function | Download |

13 | Doing Complex Analysis on a Real Surface: The Idea of a Riemann Surface | Download |

14 | F(z,w)=0 is naturally a Riemann Surface | Download |

15 | Constructing the Riemann Surface for the Complex Logarithm | Download |

16 | Constructing the Riemann Surface for the m-th root function | Download |

17 | The Riemann Surface for the functional inverse of an analytic mapping at a critical point | Download |

18 | The Algebraic nature of the functional inverses of an analytic mapping at a critical point | Download |

19 | The Idea of a Direct Analytic Continuation or an Analytic Extension | Download |

20 | General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence | Download |

21 | Analytic Continuation Along Paths via Power Series Part A | Download |

22 | Analytic Continuation Along Paths via Power Series Part B | Download |

23 | Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along Paths | Download |

24 | Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy Theorem | Download |

25 | Maximal Domains of Direct and Indirect Analytic Continuation: SecondVersion of the Monodromy Theorem | Download |

26 | Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) Version | Download |

27 | Existence and Uniqueness of Analytic Continuations on Nearby Paths | Download |

28 | Proof of the First (Homotopy) Version of the Monodromy Theorem | Download |

29 | Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical Point | Download |

30 | The Mean-Value Property, Harmonic Functions and the Maximum Principle | Download |

31 | Proofs of Maximum Principles and Introduction to Schwarz Lemma | Download |

32 | Proof of Schwarz Lemma and Uniqueness of Riemann Mappings | Download |

33 | Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit Disc | Download |

34 | Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc | Download |

35 | Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc. | Download |

36 | Hyperbolic Geodesics for the Hyperbolic Metric on the Unit Disc | Download |

37 | Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit Disc | Download |

38 | Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform Sequential Compactness are Equivalent | Download |

39 | Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels Theorem | Download |

40 | The Proof of Montels Theorem | Download |

41 | The Candidate for a Riemann Mapping | Download |

42 | Completion of Proof of The Riemann Mapping Theorem | Download |

43 | Completion of Proof of The Riemann Mapping Theorem. | Download |

Sl.No | Chapter Name | English |
---|---|---|

1 | Fundamental Theorems Connected with Zeros of Analytic Functions | PDF unavailable |

2 | The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of Algebra | PDF unavailable |

3 | Morera's Theorem and Normal Limits of Analytic Functions | PDF unavailable |

4 | Hurwitz's Theorem and Normal Limits of Univalent Functions | PDF unavailable |

5 | Local Constancy of Multiplicities of Assumed Values | PDF unavailable |

6 | The Open Mapping Theorem | PDF unavailable |

7 | Introduction to the Inverse Function Theorem | PDF unavailable |

8 | Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse Function | PDF unavailable |

9 | Univalent Analytic Functions have never-zero Derivatives and are Analytic Isomorphisms | PDF unavailable |

10 | Introduction to the Implicit Function Theorem | PDF unavailable |

11 | Proof of the Implicit Function Theorem: Topological Preliminaries | PDF unavailable |

12 | Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit Function | PDF unavailable |

13 | Doing Complex Analysis on a Real Surface: The Idea of a Riemann Surface | PDF unavailable |

14 | F(z,w)=0 is naturally a Riemann Surface | PDF unavailable |

15 | Constructing the Riemann Surface for the Complex Logarithm | PDF unavailable |

16 | Constructing the Riemann Surface for the m-th root function | PDF unavailable |

17 | The Riemann Surface for the functional inverse of an analytic mapping at a critical point | PDF unavailable |

18 | The Algebraic nature of the functional inverses of an analytic mapping at a critical point | PDF unavailable |

19 | The Idea of a Direct Analytic Continuation or an Analytic Extension | PDF unavailable |

20 | General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence | PDF unavailable |

21 | Analytic Continuation Along Paths via Power Series Part A | PDF unavailable |

22 | Analytic Continuation Along Paths via Power Series Part B | PDF unavailable |

23 | Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along Paths | PDF unavailable |

24 | Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy Theorem | PDF unavailable |

25 | Maximal Domains of Direct and Indirect Analytic Continuation: SecondVersion of the Monodromy Theorem | PDF unavailable |

26 | Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) Version | PDF unavailable |

27 | Existence and Uniqueness of Analytic Continuations on Nearby Paths | PDF unavailable |

28 | Proof of the First (Homotopy) Version of the Monodromy Theorem | PDF unavailable |

29 | Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical Point | PDF unavailable |

30 | The Mean-Value Property, Harmonic Functions and the Maximum Principle | PDF unavailable |

31 | Proofs of Maximum Principles and Introduction to Schwarz Lemma | PDF unavailable |

32 | Proof of Schwarz Lemma and Uniqueness of Riemann Mappings | PDF unavailable |

33 | Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit Disc | PDF unavailable |

34 | Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc | PDF unavailable |

35 | Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc. | PDF unavailable |

36 | Hyperbolic Geodesics for the Hyperbolic Metric on the Unit Disc | PDF unavailable |

37 | Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit Disc | PDF unavailable |

38 | Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform Sequential Compactness are Equivalent | PDF unavailable |

39 | Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels Theorem | PDF unavailable |

40 | The Proof of Montels Theorem | PDF unavailable |

41 | The Candidate for a Riemann Mapping | PDF unavailable |

42 | Completion of Proof of The Riemann Mapping Theorem | PDF unavailable |

43 | Completion of Proof of The Riemann Mapping Theorem. | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |