Complex variables for scientists and engineers : an introduction
著者
書誌事項
Complex variables for scientists and engineers : an introduction
（Oxford graduate texts）
Oxford University Press, c2010
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Norton's Complex Variables for Scientists and Engineers is a new textbook, originally written for the Complex Analysis term of an undergraduate Mathematical Methods of Physics sequence at UCLA. It does not assume any prior knowledge of complex numbers or functions and is therefore suitable for a first course in the subject for undergraduate students who have had an introductory course in the standard calculus of real variables.
The book provides a thorough grounding in the theory of complex functions. The mathematics is careful, yet accessible to any student who knows basic calculus. It covers the subjects essential in any scientific or engineering discipline that uses mathematics beyond the elementary level. The reader will find a clear presentation of complex differentiation and integration, Cauchy's theorem and integral formula, and infinite series and products. There is a long and thorough section on applying the
residue theorem to the evaluation of real integrals, and a section on special functions and their integral representations. The book includes the conformal property of analytic functions and its applications to boundary value problems in electrostatics; a topological analysis that leads to the
extension of the residue theorem to multiply-connected regions and contours; a section on the method of steepest descent; a section on the Riemann zeta function; and a discussion of the convergence of integral representations, which is rarely presented in detail in introductory texts. Those who want to see the mathematics done carefully, and who are looking for more than a 'cook-book' treatment that presents the basic techniques without exploring all the nooks and crannies of the subject, will
find these sections especially satisfying. The preface suggests how to extract a bare-bones course for those in a hurry, without losing sight of the beauty and depth of the subjects.
目次
- 1. Complex Numbers
- 2. Complex Functions
- 3. Differentiation and Analyticity
- 4. Complex Functions as Mappings
- 5. Closed Contours and Homology
- 6. Integration
- 7. Cauchy's Integral Formula
- 8. Multiply Connected Domains
- 9. Power Series
- 10. Sequences, Series, and Infinite Products
- 11. Isolated Singularities
- 12. The Residue Theorem
- 13. Real Integrals
- 14. Infinite Sums
- 15. Factoring Entire and Meromorphic Functions
- 16. Method of Steepest Descent
- 17. Integral Representations of the Gamma and Zeta Functions
- 18. Special Functions and Integral Representations
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