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Complex Analysis Free Books


Complex analysis is the branch of mathematical analysis that studies the theory of functions of a complex variable.


It deals investigates functions of complex numbers together with their derivatives, manipulation, and other properties. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics. It is also helpful in many branches of physics, including hydrodynamics, thermodynamics, and particularly quantum mechanics. It is also use in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.

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Free Complex Analysis Books
Abel's Theorem and Theta Functions by H. F. Baker - PDF
This text explains "Abelian functions", "theta functions", "Riemann surfaces", "algebraic curves", and "periods". It shows how integrals on curves relate to algebraic relations and provides a clear foundation for understanding multi-variable complex functions and the geometric structure behind them.
Elliptic Functions: Elementary Treatise by Cayley - PDF
This textbook introduces "elliptic functions" with clear explanations, exploring their properties and applications in "mathematics". The book provides step-by-step examples and exercises, helping students understand "complex analysis" concepts and build a strong foundation in this fundamental area of mathematical study.
Complex Integration and Cauchy's Theorem by G.N. Watson
This is a short text, clear guide to "complex analysis", explaining "Cauchy's theorem", "contour integration", and applications like residue calculus and definite integrals. It also provides historical context, making it useful for students and researchers studying classical analytic functions.
Complex Variables - Robert B. Ash, W. P. Novinger
This text is a clear and rigorous introduction to "complex analysis". It covers analytic functions, integration, and key theorems with examples and exercises, helping students understand theory and applications through "Cauchy’s theorem" and "residue theory".
Complex Variables with Applications - Jeremy Orloff
This book is a beginner-friendly book that explains the basics of "complex analysis" using clear examples and practical uses. It covers complex functions, integrals, and series while showing real "applications" in science and engineering. The book is ideal for students learning "complex variables" for the first time.
Elements of Complex Variable Theory – H. Durege
This text is a classic introduction to early "complex analysis", explaining complex numbers, analytic functions, and Cauchy’s ideas in a clear, traditional style. The book offers a historical look at how "analytic functions" and "conformal mapping" were first taught and understood.
Functions of a Complex Variable- Heinrich Burkhardt PDF
This text gives a clear and structured introduction to "complex analysis", explaining ideas like "analytic functions" and complex mappings. It offers a helpful look at how mathematicians developed and understood complex function theory.
The General Theory of Dirichlet's Series by G.H. Hardy
This textbook explores "Dirichlet series", their "convergence", and methods to sum them effectively. The book examines the behavior of coefficients, multiplication of series, and analytic properties, providing a clear, rigorous foundation for understanding these series in "number theory" and mathematical analysis.
Theory of Analytic Functions by James Harkness - PDF
This text explains "analytic functions", "complex analysis", "power series", "singularities", and "function theory". It provides clear explanations and examples, showing how these functions behave, their convergence, and geometric properties, offering a strong foundation for students and researchers in advanced complex-variable mathematics.
Automorphic Functions Theory – Lester Ford PDF
This text explains "automorphic functions", "Fuchsian groups", and "series expansions". It shows how complex functions stay invariant under group transformations, explores their geometric and analytic structure, and provides a clear foundation for understanding multi-variable complex functions in advanced mathematics.
Riemann's Theory of Algebraic Functions - Felix Klein
This textbook explains "algebraic functions", "Riemann surfaces", and "complex analysis" clearly. It explores "branch points" and "elliptic functions", blending geometric intuition with rigorous theory. The book is a classic guide for understanding the foundations of algebraic and complex function theory.
Theory of Elliptic Functions by Harris Hancock - PDF
This book explores "elliptic functions", including the "Weierstrass P-function" and Jacobi elliptic functions. The book explains their properties, transformations, and applications in "complex functions", providing clear examples and proofs for students, researchers, and anyone studying advanced mathematics and function theory.
Theory of Functions by James Harkness - PDF
This text explains "analytic functions", "complex analysis", "power series", "conformal mappings", and "function theory". It covers continuity, singularities, and geometric behavior of complex functions, providing clear explanations and rigorous proofs for students and researchers in advanced complex-variable mathematics.
Theory of Functions of Complex Variable by A. Forsyth
This textbook explains "complex analysis", "analytic functions", "singularities", "power series", and "function theory". The book covers multiform and periodic functions, branch points, and conformal mappings, providing clear explanations, examples, and rigorous proofs for students and researchers in advanced complex-variable mathematics.
Functions of Two Complex Variables by A. Forsyth - PDF
This textbook explains "complex analysis", "functions of two complex variables", "double power series", "multiform functions", and "function theory". The book introduces analytic functions in two variables, their convergence, branch points, and integrals, providing clear examples and geometric intuition for advanced mathematics.
Theory of Multiply Periodic Functions – H. F. Baker PDF
This text explains how complex functions with several repeating cycles arise from advanced geometry. It introduces "hyperelliptic functions", "theta functions", "Abelian functions", "periods", and "Riemann surfaces", giving a clear foundation for understanding multi-period behavior in higher-level mathematics.
Topics in Complex Analysis - Dan Romik
This text is an advanced mathematics book that explores key ideas of "complex analysis" with clear explanations and strong intuition. It covers analytic functions, conformal mapping, and modern applications, focusing on "rigorous proofs" while showing connections to other fields. The book is ideal for "advanced students" and self-learners.

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