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.
Author(s): Hemant Kumar Pathak
Edition: 1
Publisher: Springer
Year: 2019
Language: English
Pages: 940
Front Matter ....Pages i-xxv
Complex Numbers and Metric Topology of \(\mathbb {C}\) (Hemant Kumar Pathak)....Pages 1-65
Analytic Functions, Power Series, and Uniform Convergence (Hemant Kumar Pathak)....Pages 67-190
Complex Integrations (Hemant Kumar Pathak)....Pages 191-305
Singularities of Complex Functions and Principle of Argument (Hemant Kumar Pathak)....Pages 307-375
Calculus of Residues and Applications to Contour Integration (Hemant Kumar Pathak)....Pages 377-486
Bilinear Transformations and Applications (Hemant Kumar Pathak)....Pages 487-557
Conformal Mappings and Applications (Hemant Kumar Pathak)....Pages 559-623
Spaces of Analytic Functions (Hemant Kumar Pathak)....Pages 625-648
Entire and Meromorphic Functions (Hemant Kumar Pathak)....Pages 649-713
Analytic Continuation (Hemant Kumar Pathak)....Pages 715-752
Harmonic Functions and Integral Functions (Hemant Kumar Pathak)....Pages 753-805
Canonical Products and Convergence of Entire Functions (Hemant Kumar Pathak)....Pages 807-840
The Range of an Analytic Function (Hemant Kumar Pathak)....Pages 841-858
Univalent Functions and Applications (Hemant Kumar Pathak)....Pages 859-888
Function Theory of Several Complex Variables (Hemant Kumar Pathak)....Pages 889-907
Back Matter ....Pages 909-928
