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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.
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
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
Answers to Selected Exercises and Miscellaneous Exercises
- No. of pages:
- © Pergamon 1973
- 1st January 1973
- eBook ISBN:
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