The contents of this
book include: Complex numbers, Polynomials and rational functions, Riemann
surfaces and holomorphic maps, Fractional linear transformations, Power series,
More Series, Exponential and trigonometric functions, Arcs, curves, etc, Inverse
functions and their derivatives, Line integrals, Cauchy’s theorem, The winding
number and Cauchy’s integral formula, Higher derivatives, including Liouville’s
theorem, Removable singularities, Taylor’s theorem, zeros and poles, Analysis of
isolated singularities, Local mapping properties, Maximum principle, Schwarz
lemma, and conformal mappings, Weierstrass’ theorem and Taylor series, Plane
topology, The general form of Cauchy’s theorem, Residues, Schwarz reflection
principle, Normal families, Arzela-Ascoli, Riemann mapping theorem, Analytic
continuation, Universal covers and the little Picard theorem.
This note
covers the following topics: Compactness and Convergence, Sine Function, Mittag Leffler Theorem,
Spherical Representation and Uniform Convergence.
The contents of this
book include: Complex numbers, Polynomials and rational functions, Riemann
surfaces and holomorphic maps, Fractional linear transformations, Power series,
More Series, Exponential and trigonometric functions, Arcs, curves, etc, Inverse
functions and their derivatives, Line integrals, Cauchy’s theorem, The winding
number and Cauchy’s integral formula, Higher derivatives, including Liouville’s
theorem, Removable singularities, Taylor’s theorem, zeros and poles, Analysis of
isolated singularities, Local mapping properties, Maximum principle, Schwarz
lemma, and conformal mappings, Weierstrass’ theorem and Taylor series, Plane
topology, The general form of Cauchy’s theorem, Residues, Schwarz reflection
principle, Normal families, Arzela-Ascoli, Riemann mapping theorem, Analytic
continuation, Universal covers and the little Picard theorem.
The contents of this book include: Complex numbers, Elements of
analysis, Complex integration: path integrals,Laurent series, Winding numbers,
Transforms for representation of processes in frequency domain.
In this note
the student will learn that all the basic functions that arise in calculus,
first derived as functions of a real variable, such as powers and fractional
powers, exponentials and logs, trigonometric functions and their inverses, and
also many new functions that the student will meet, are naturally defined for
complex arguments.
This note
explains the following topics: Complex functions, Analytic functions,
Integration, Singularities, Harmonic functions, Entire functions, The
Riemann mapping theorem and The Gamma function.
This note covers the following topics:
Holomorphic functions, Contour integrals and primitives, The theorems of Cauchy,
Applications of Cauchy’s integral formula, Argument. Logarithm, Powers, Zeros
and isolated singularities, The calculus of residues, The maximum modulus
principle, Mobius transformations.
This text will illustrate and
teach all facets of the subject in a lively manner that will speak to the needs
of modern students. It will give them a powerful toolkit for future work in the
mathematical sciences, and will also point to new directions for additional
learning. Topics covered includes: The Relationship of Holomorphic and Harmonic
Functions, The Cauchy Theory, Applications of the Cauchy Theory, Isolated
Singularities and Laurent Series, The Argument Principle, The Geometric Theory
of Holomorphic Functions, Applications That Depend on Conformal Mapping,
Transform Theory.
This book is designed for
students who, having acquired a good working knowledge of the calculus, desire
to become acquainted with the theory of functions of a complex variable, and
with the principal applications of that theory.Numerous examples have been given
throughout the book, and there is also a set of Miscellaneous Examples, arranged
to correspond with the order of the text.
These are the sample pages from
the textbook, 'Introduction to Complex Variables'. This book covers the
following topics: Complex numbers and inequalities, Functions of a complex
variable, Mappings, Cauchy-Riemann equations, Trigonometric and hyperbolic
functions, Branch points and branch cuts, Contour integration, Sequences and
series, The residue theorem, Evaluation of integrals, Introduction to potential
theory, Applications, Fourier, Laplace and Z-transforms.
This book covers the following
topics: Field of Complex Numbers, Analytic Functions, The Complex
Exponential, The Cauchy-Riemann Theorem, Cauchy’s Integral Formula, Power
Series, Laurent’s Series and Isolated Singularities, Laplace Transforms, Prime
Number Theorem, Convolution, Operational Calculus and Generalized Functions.