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Complex Analysis and Applications
~
Pathak, Hemant Kumar.
Complex Analysis and Applications
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Complex Analysis and Applications/ by Hemant Kumar Pathak.
Author:
Pathak, Hemant Kumar.
Description:
XXV, 928 p. 261 illus.online resource. :
Contained By:
Springer Nature eBook
Subject:
Mathematical analysis. -
Online resource:
https://doi.org/10.1007/978-981-13-9734-9
ISBN:
9789811397349
Complex Analysis and Applications
Pathak, Hemant Kumar.
Complex Analysis and Applications
[electronic resource] /by Hemant Kumar Pathak. - 1st ed. 2019. - XXV, 928 p. 261 illus.online resource.
1. Complex Numbers and Metric Topology of C -- 2. Analytic Functions,Power Series and Elementary Complex Functions -- 3. Complex Integrations -- 4. Singularities,Meromorphic Functions and Principle of Argument -- 5. Calculus of Residues -- 6. Bilinear Transformations -- 7. Conformal Mappings -- 8. Spaces of Analytic Functions -- 9. Entire Functions -- 10. Analytic Continuation -- 11. Harmonic Functions, Uniform Convergence and Integral Functions -- 12. Canonical Products and Convergence of Entire Functions -- 13. The Range of an Analytic Function -- 14. Univalent Functions.
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.
ISBN: 9789811397349
Standard No.: 10.1007/978-981-13-9734-9doiSubjects--Topical Terms:
527926
Mathematical analysis.
LC Class. No.: QA299.6-433
Dewey Class. No.: 515
Complex Analysis and Applications
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1. Complex Numbers and Metric Topology of C -- 2. Analytic Functions,Power Series and Elementary Complex Functions -- 3. Complex Integrations -- 4. Singularities,Meromorphic Functions and Principle of Argument -- 5. Calculus of Residues -- 6. Bilinear Transformations -- 7. Conformal Mappings -- 8. Spaces of Analytic Functions -- 9. Entire Functions -- 10. Analytic Continuation -- 11. Harmonic Functions, Uniform Convergence and Integral Functions -- 12. Canonical Products and Convergence of Entire Functions -- 13. The Range of an Analytic Function -- 14. Univalent Functions.
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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.
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