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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.

Complex Analysis and Applications

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.