Название: Complex Analysis and Applications
Автор: Pathak H.K.
Издательство: Springer
Год: 2019
Формат: pdf
Страниц: 939
Для сайта: LitMy
Размер: 13 mb
Язык: английский

This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog’s theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz’s rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties.

Preface.
Complex Numbers and Metric Topology of C.
Analytic Functions, Power Series, and Uniform Convergence.
Complex Integrations.
Singularities of Complex Functions and Principle of Argument.
Calculus of Residues and Applications to Contour Integration.
Bilinear Transformations and Applications.
Conformal Mappings and Applications.
Spaces of Analytic Functions.
Entire and Meromorphic Functions.
Analytic Continuation.
Harmonic Functions and Integral Functions.
Canonical Products and Convergence of Entire Functions.
The Range of an Analytic Function.
Univalent Functions and Applications.
Function Theory of Several Complex Variables.
Appendix A: Solution of Selected Problems in Exercises.
References.
Index.