Complex Variables

Pergamon International Library of Science, Technology, Engineering and Social Studies

H. R. Chillingworth, Robert Maxwell

• Publisher: Pergamon
• Year: 2013
• Print ISBN:
  9780080169392
• eBook ISBN:
  9781483139951
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

Complex Variables covers topics ranging from complex numbers to point sets in the complex plane, elementary functions, straight lines and circles, simple and conformal transformations, and zeros and singularities. Cauchy's theorem, Taylor's theorem, Laurent's theorem, contour integration, and miscellaneous theorems are also discussed. This volume consists of 14 chapters, the first of which introduces the theory of complex numbers and their development either from an algebraic or from a geometrical viewpoint. Emphasis is on the complex plane, modulus, amplitude, number pairs, complex conjugates, the triangle inequality, De Moivre's theorem, and the four mathematical operations (addition, subtraction, multiplication, division). Attention then turns to point sets in the complex plane, infinite series and tests for convergence, functions of a complex variable, and elementary functions. The chapters that follow focus on straight lines and circles, simple and conformal transformations, and integration. Exercises are included in every section of each chapter except the last. This book is written primarily for students and teachers of mathematics.

Table of contents

• Front Cover
• Complex Variables
• Copyright Page
• Table of Contents
• INTRODUCTION
• CHAPTER 1. COMPLEX NUMBERS
• CHAPTER 2. POINT SETS IN THE COMPLEX PLANE. SEQUENCES. LIMITS
• CHAPTER 3. INFINITE SERIES. TESTS FOR CONVERGENCE
• CHAPTER 4. FUNCTIONS OF A COMPLEX VARIABLE
• CHAPTER 5. ELEMENTARY FUNCTIONS
• CHAPTER 6. STRAIGHT LINE AND CIRCLE
• CHAPTER 7. SIMPLE TRANSFORMATIONS
• CHAPTER 8. CONFORMAL TRANSFORMATIONS
• CHAPTER 9. INTEGRATION
• CHAPTER 10. CAUCHY'S THEOREM. DERIVATIVES OF REGULAR FUNCTIONS
• CHAPTER 11. TAYLOR'S THEOREM AND LAURENT'S THEOREM
• CHAPTER 12. ZEROS AND SINGULARITIES. MEROMORPHIC FUNCTIONS
• CHAPTER 13. CONTOUR INTEGRATION
• CHAPTER 14. MISCELLANEOUS THEOREMS
• APPENDIX A: MULTIPLICATION OF COMPLEX NUMBERS
• APPENDIX B: GROUPS
• APPENDIX C: THE MILNE-THOMPSON METHOD
• MISCELLANEOUS EXERCISES
• REFERENCES
• ANSWERS TO SELECTED EXERCISES AND MISCELLANEOUS EXERCISES
• INDEX