TY  - BOOK
AU  - D'Angelo,John P.
TI  - Linear and complex analysis for applications
T2  - Advances in applied mathematics
SN  - 9781498756105 (hbk. : acidfree paper)
AV  - QA331.7 .D3564 2017
U1  - 512/.5 23
PY  - 2017///]
CY  - Boca Raton
PB  - CRC Press, Taylor & Francis Group
KW  - Functions of complex variables
KW  - Linear algebraic groups
KW  - Mathematical analysis
N1  - John P. D'Angelo is Professor of Mathematics at the University of Illinois at Urbana-Champaign. He has published more than sixty research papers in complex analysis in several variables and Cauchy-Riemann geometry. He was awarded the Stefan Bergman prize in 1999 for some of this work. He has been recognized for excellence in his teaching and he is a Fellow of the American Mathematical Society; Includes bibliographical references and index; Table of Contents

Chapter 1. Linear algebra; Chapter 2. Complex numbers; Chapter 3. Vector analysis; Chapter 4. Complex analysis; Chapter 5. Transform methods; Chapter 6. Hilbert spaces; Chapter 7. Examples and applications; Chapter 8. Appendix: The language of mathematics; References; Index
N2  - "Linear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author's teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work, to unify many distinct and seemingly isolated topics, to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems. The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III. As the topics are being reviewed, new material is inserted to help the student develop skill in both computation and theory. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Connections among the topics and applications appear throughout the book. The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, whose unifying theme is linear systems. It includes many unusual examples and contains more than 450 exercises" -- From the publisher
ER  -