Technical Books

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.

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.

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, Cauchys theorem, The winding number and Cauchys integral formula, Higher derivatives, including Liouvilles theorem, Removable singularities, Taylors 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 Cauchys theorem, Residues, Schwarz reflection principle, Normal families, ArzelaAscoli, Riemann mapping theorem, Analytic continuation, Universal covers and the little Picard theorem.

This note explains the following topics, Complex differentiation, Contour integration and residue calculus.

This PDF covers the following topics related to Complex Analysis, The Real Field, The Complex Field, Properties of holomorphic functions, The Riemann Mapping Theorem, Contour integrals and the Prime Number Theorem, The Poisson representation, Extending Riemann maps.

This note covers the following topics, Compactness and Convergence, Sine Function, Mittag Leffler Theorem, Spherical Representation and Uniform Convergence.

These lecture notes give a framework for generalizations of complex analysis, and a way to classify them. The framework uses wavelets in Banach spaces. A reduced wavelet transform describes the Cauchy integral, Hardy and Bergman spaces, the Cauchy Riemann equation, and the Taylor expansion.

This guide contains below topics, Title Page, The Complex Plane, Holomorphic and Analytic Functions, Line Integrals and Rudimentary Cauchy Theorems, The Logarithm and Cauchy, Counting Zeros and Singularities, Montel and Riemann, Harmonic Functions, Weierstrass Factorization, Rational Approximation, Analytic Continuation, Metric Spaces, Results From Basic Analysis, Basic Notation and Terminology, List of Notation.

This note covers the following topics: Complex Numbers, Euler�s Formula, Roots and multi-valued arithmetic, Functions from C to C, Continuity and Limits, Analytic and entire functions, Harmonic Conjugates, Morera�s Theorem, Taylor�s Theorem, Laurent Series and Residues.

The book is intended as a text, appropriate for use by advanced undergraduates or graduate students who have taken a course in introductory real analysis, or as it is often called, advanced calculus. No background in complex variables is assumed, thus making the text suitable for those encountering the subject for the first time. The Elementary Theory, General Cauchy Theorem , Applications of the Cauchy Theory, Families of Analytic Functions, Factorization of Analytic Functions and The Prime Number Theorem.

This book has plenty of figures, plenty of examples, copious commentary, and even in-text exercises for the students. But, since it is not a formal textbook, it does not have exercise sets. It does not have a Glossary or a Table of Notation. Topics covered includes: The Complex Plane, Complex Line Integrals, Applications of the Cauchy Theory, Isolated Singularities and Laurent Series, The Argument Principle, The Geometric Theory of Holomorphic Functions, Harmonic Functions, Infinite Series and Products, Analytic Continuation .

This book is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics. Topics covered includes, Rings and Ideals, Radicals, Filtered Direct Limits, CayleyHamilton Theorem, Localization of Rings and Modules, KrullCohenSeidenberg Theory, Rings and Ideals, Direct Limits, Filtered direct limit.

Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Basic commutative algebra will be explained in this document.

This PDF book A Term of Commutative Algebra covers the following topics related to Commutative Algebra, Rings and Ideals, Prime Ideals, Radicals, Modules, Exact Sequences, Fitting Ideals, Direct Limits, Filtered direct limits, Tensor Products, Flatness, CayleyHamilton Theorem, Localization of Rings, Localization of Modules, CohenSeidenberg Theory, Noether Normalization, Jacobson Rings, Chain Condition, Noetherian Spaces, Associated Primes, Primary Decomposition, Oldprimary Submodules, Length, Hilbert Functions, etc.

This Lecture note contains the following topics, Prime ideals and localization, Finite and integral homomorphisms, Noetherian rings and modules, Associated Primes and primary decomposition, Noether normalization, Nullstellensatz and the maximal spectrum, Dimension theory, special cases of rings, Tor and Ext, Flatness, Depth and Cohen Macaulay rings and Modules, Regular rings and Graded modules.