Geometry of Complex Numbers

Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 4130

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 1470411008

Category: Mathematical analysis

Page: 641

View: 9036

A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 8169

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Complex Numbers and Geometry

Author: Liang-shin Hahn

Publisher: Cambridge University Press

ISBN: 9780883855102

Category: Mathematics

Page: 192

View: 9745

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained - no background in complex numbers is assumed - and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.

How to Solve Applied Mathematics Problems

Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486285227

Category: Mathematics

Page: 336

View: 9305

This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

Distribution Theory and Transform Analysis

An Introduction to Generalized Functions, with Applications

Author: A.H. Zemanian

Publisher: Courier Corporation

ISBN: 0486151948

Category: Mathematics

Page: 400

View: 2435

Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

Complex Analysis in Banach Spaces

Author: Jorge Mujica

Publisher: Courier Corporation

ISBN: 0486474666

Category: Mathematics

Page: 440

View: 4043

The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. A high-level tutorial in pure and applied mathematics, its prerequisites include a familiarity with the basic properties of holomorphic functions, the principles of Banach and Hilbert spaces, and the theory of Lebesgue integration. The four-part treatment begins with an overview of the basic properties of holomorphic mappings and holomorphic domains in Banach spaces. The second section explores differentiable mappings, differentiable forms, and polynomially convex compact sets, in which the results are applied to the study of Banach and Fréchet algebras. Subsequent sections examine plurisubharmonic functions and pseudoconvex domains in Banach spaces, along with Riemann domains and envelopes of holomorphy. In addition to its value as a text for advanced graduate students of mathematics, this volume also functions as a reference for researchers and professionals.

Introduction to Modern Algebra and Matrix Theory

Second Edition

Author: O. Schreier,E. Sperner

Publisher: Courier Corporation

ISBN: 0486278654

Category: Mathematics

Page: 400

View: 8955

This unique text provides students with a basic course in both calculus and analytic geometry — no competitive editions cover both topics in a single volume. Its prerequisites are minimal, and the order of its presentation promotes an intuitive approach to calculus. Algebraic concepts receive an unusually strong emphasis. Numerous exercises appear throughout the text. 1951 edition.

Mathematics for Quantum Chemistry

Author: Jay Martin Anderson

Publisher: Courier Corporation

ISBN: 0486151484

Category: Science

Page: 160

View: 9382

Introduction to problems of molecular structure and motion covers calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics. Answers to problems. 1966 edition.

A Catalog of Special Plane Curves

Author: J. Dennis Lawrence

Publisher: Courier Corporation

ISBN: 0486167666

Category: Mathematics

Page: 218

View: 7674

DIVOne of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus. /div

An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

View: 2643

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Complex Variables

Harmonic and Analytic Functions

Author: Francis J. Flanigan

Publisher: Courier Corporation

ISBN: 0486613887

Category: Mathematics

Page: 353

View: 5759

Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.

Advanced Calculus of Several Variables

Author: Charles Henry Edwards

Publisher: Courier Corporation

ISBN: 9780486683362

Category: Mathematics

Page: 457

View: 9563

Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

Foundations of Potential Theory

Author: Oliver Dimon Kellogg

Publisher: Courier Corporation

ISBN: 9780486601441

Category: Science

Page: 384

View: 755

Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.

Complex Numbers from A to ... Z

Author: Titu Andreescu,Dorin Andrica

Publisher: Springer Science & Business Media

ISBN: 0817684158

Category: Mathematics

Page: 391

View: 6717

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Conformal Mapping

Author: Zeev Nehari

Publisher: Courier Corporation

ISBN: 0486145034

Category: Mathematics

Page: 396

View: 9689

DIVTheoretical and practical approach covers functions of a complex variable and conformal mapping. Only prerequisite is advanced calculus. /div

College Geometry

An Introduction to the Modern Geometry of the Triangle and the Circle

Author: Nathan Altshiller-Court

Publisher: Courier Corporation

ISBN: 0486141373

Category: Mathematics

Page: 336

View: 5910

The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Visual Complex Analysis

Author: Tristan Needham

Publisher: Oxford University Press

ISBN: 9780198534464

Category: Mathematics

Page: 592

View: 5240

Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

A Treatise on the Theory of Determinants

Author: Thomas Muir,William Henry Metzler

Publisher: Courier Corporation

ISBN: 9780486495538

Category: Mathematics

Page: 766

View: 9622

One of the few comprehensive single-volume treatments of determinants, this compilation features nearly all of the known facts about determinants up to the early 1930s. The text begins with the basic elements of permutations and combinations and sets down the notation and general principles of simple determinants, with a full discussion of such topics as row and column transformation, expansion, multiplication, minors, and symmetry. Additional topics include compound determinants, co-factors, adjugates, rectangular arrays and matrices, linear dependence, and many more subjects. Although its primary focus is upon answering reference and research needs, this book's 485 problems (plus scores of numerical examples) make it extremely useful to students and teachers.