Complex Variables - 1st Edition - ISBN: 9780080169392, 9781483139951

Complex Variables

1st Edition

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

Authors: H. R. Chillingworth
Editors: Robert Maxwell
eBook ISBN: 9781483139951
Imprint: Pergamon
Published Date: 1st January 1973
Page Count: 280
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Description

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


Introduction

1. Complex Numbers

2. Point Sets in the Complex Plane. Sequences. Limits

3. Infinite Series. Tests for Convergence

4. Functions of a Complex Variable

5. Elementary Functions

6. Straight Line and Circle

7. Simple Transformations

8. Conformal Transformations

9. Integration

10. Cauchy's Theorem. Derivatives of Regular Functions

11. Taylor's Theorem and Laurent's Theorem

12. Zeros and Singularities. Meromorphic Functions

13. Contour Integration

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


Details

No. of pages:
280
Language:
English
Copyright:
© Pergamon 1973
Published:
Imprint:
Pergamon
eBook ISBN:
9781483139951

About the Author

H. R. Chillingworth

About the Editor

Robert Maxwell