Introduction to complex variables and applications
著者
書誌事項
Introduction to complex variables and applications
（Cambridge texts in applied mathematics）
Cambridge University Press, 2021
- : hbk.
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注記
Includes bibliographical references (p. [403]-405) and index
内容説明・目次
内容説明
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painleve equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
目次
- 1. Complex numbers and elementary functions
- 2. Analytic functions and integration
- 3. Sequences, series and singularities of complex functions
- 4. Residue calculus and applications of contour integration
- 5. Conformal mappings and applications
- Appendix. Answers to selected odd-numbered exercises
- References
- Index.
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