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Cover 1 Title 2 Copyright 3 Translator's Preface 4 Table of Contents 6 CHAPER ONE: Foundations. Linear Functions 8 I. Analytic Functions and Conformal Mapping 8 2. Integral Linear Functions 20 3. The Function w =1/z 22 Appendix to § 3: Stereographic Projection 28 4. Linear Functions 30 5. Linear Fllnctions (continued) 40 6. Groups of Linear Functions 50 CHAPTER TWO: Rational Functions 58 7. w = z^n 58 8. Rational Functions 69 CHAPTER THREE: General Considerations 78 9. The Relation Between the ConformalMapping of the Boundary and that of theInterior of a Region 78 10. Schwarz' Principle of Reflection 80 CHAPTER FOUR: Further Study of Mappings Representedby Given Functions 86 11. Further Study of the Geometry of w =z^2 86 12. w = z + I/z 91 13. The Exponential Function andthe Trigonometric Functions 99 14. The Elliptic Integral of the First Kind 102 CHAPTER FIVE: Mappings of Given Regions 116 15. The Mapping of a Given RegionOnto the Interior of a Circle(Illustrative Examples) 116 16. Vitali's Theorem on Double Series 126 17. A Limit Theorem for Simple Mappings 132 18. Proof of Riemann's Mapping Theorem 135 19. On the Actual Construction of theConformal Mapping of a Given RegionOnto

Who reads Conformal Mapping?

Author

L. Bieberbach

Publisher

Chelsea

Published

1964

Language

EN

Category

nonfiction

Subjects

Mathematics, Mathematical Theory, Stem