Complex Analysis - A Visual and Interactive Introduction

by Juan Carlos Ponce Campuzano

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The study of complex analysis is important for students in engineering and the physical sciences and is a central subject in mathematics. In addition to being mathematically elegant, complex analysis provides powerful tools for solving problems that are either very difcult or virtually impossible to solve in any other way. In this book you will find examples, problems and applets that allow you to explore complex analysis by using the visual interactive power of the computer (or tablet).

Description from LibreTexts.

Publisher
University of Queensland
Subjects
Mathematics, Analysis
Licence
CC BY-NC-SA, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Introduction
  6. Licensing
  7. License
  8. Acknowledgements
  9. 1: Chapter 1
  10. 1.1: A Brief History
  11. 1.2: Terminology and Notation
  12. 1.3: Geometric Interpretation of the Arithmetic Operations
  13. 1.4: The Principal Argument
  14. 1.5: Roots of Complex Numbers
  15. 1.6: Topology of the Complex Plane
  16. 2: Chapter 2
  17. 2.1: Complex functions
  18. 2.2: Riemann Sphere
  19. 2.3: Complex Differentiation
  20. 2.4: The Logarithmic Function
  21. 2.5: Riemann Surfaces
  22. 3: Chapter 3
  23. 3.1: Mappings
  24. 3.2: The Transformation w=1/z
  25. 3.3: Analytic Landscapes
  26. 3.4: Domain coloring
  27. 3.5: The Complex Power Function
  28. 4: Chapter 4
  29. 4.1: Curves in the Complex Plane
  30. 4.2: Complex Integration
  31. 4.3: Integrals of Functions with Branch Cuts
  32. 5: Chapter 5
  33. 5.1: Series
  34. 5.2: Taylor Series
  35. 5.3: Laurent Series
  36. 5.4: Classification of Singularities
  37. 5.5: The Mandelbrot Set
  38. 5.6: The Julia Set
  39. 6: Chapter 6
  40. 6.1: Applications of Conformal Mappings
  41. 6.2: Complex Potential- Basic examples
  42. 6.3: Uniform Flow Around a Circle
  43. 6.4: Joukowsky Airfoil
  44. Back Matter
  45. Index
  46. Glossary
  47. Bibliography
  48. Detailed Licensing