Function Theory of One Complex Variable 3rd edition pdf

Function Theory of One Complex Variable 3rd edition pdf

Function Theory of One Complex Variable 3rd edition pdf : Pages 504

By Robert E. Greene and Steven G. Krantz

Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus.

Elementary Properties of the Complex Numbers ; Further Properties of the Complex Numbers ; Complex Polynomials ; Holomorphic Functions, the Cauchy-Riemann Equations, and Harmonic Functions ; Real and Holomorphic Antiderivatives ; Complex Line Integrals ; Real and Complex Line Integrals ; Complex Differentiability and Conformality ; Antiderivatives Revisited ; The Cauchy Integral Formula and the Cauchy Integral Theorem ; The Cauchy Integral Formula : Some Examples ; An Introduction to the Cauchy Integral Theorem and the Cauchy Integral Formula for More General Curves ; Applications of the Cauchy Integral ; Differentiability Properties of Holomorphic Functions ; Complex Power Series ; The Power Series Expansion for a Holomorphic Function ; The Cauchy Estimates and Liouville’s Theorem ; Uniform Limits of Holomorphic Functions ; The Zeros of a Holomorphic Function

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