Principles of Mathematical Analysis

Author: Walter Rudin

Publisher: McGraw-Hill Publishing Company

ISBN: 9780070856134

Category: Mathematics

Page: 342

View: 690

The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Functional Analysis

Author: Walter Rudin

Publisher: Tata McGraw-Hill Education

ISBN: 9780070619883

Category: Functional analysis

Page: 424

View: 2895

COMPLEX ANALYSIS

Author: Lars V. Ahlfors

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 3777

Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh,W.E. Pfaffenberger

Publisher: Courier Corporation

ISBN: 0486134776

Category: Mathematics

Page: 448

View: 2938

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Techniques of Functional Analysis for Differential and Integral Equations

Author: Paul Sacks

Publisher: Academic Press

ISBN: 0128114576

Category: Mathematics

Page: 320

View: 1144

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations, and especially partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and as PhD research preparation in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs are limited, and their sources precisely identifie d, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. Provides an introduction to the mathematical techniques widely used in applied mathematics and needed for advanced research Establishes the advanced background needed for sophisticated literature review and research in both differential and integral equations Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

Vectors, Pure and Applied

A General Introduction to Linear Algebra

Author: T. W. Körner

Publisher: Cambridge University Press

ISBN: 110703356X

Category: Mathematics

Page: 444

View: 6330

Explains both the how and the why of linear algebra to get students thinking like mathematicians.

Control and Nonlinearity

Author: Jean-Michel Coron

Publisher: American Mathematical Soc.

ISBN: 0821849182

Category: Commande non linéaire

Page: 426

View: 9315

This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.

The Ricci Flow

Techniques and Applications. Geometric-analytic aspects

Author: Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther,James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni

Publisher: American Mathematical Soc.

ISBN: 0821846612

Category:

Page: N.A

View: 456

The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

Real Analysis

Series, Functions of Several Variables, and Applications

Author: Miklós Laczkovich,Vera T. Sós

Publisher: Springer

ISBN: 149397369X

Category: Mathematics

Page: 392

View: 6341

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context.

Real and Complex Analysis

Author: Walter Rudin

Publisher: Tata McGraw-Hill Education

ISBN: 9780070619876

Category: Analysis

Page: 416

View: 3299

Transition to Higher Mathematics

Structure and Proof

Author: Bob A. Dumas,John Edward McCarthy

Publisher: McGraw-Hill Education

ISBN: 9780071106474

Category: Logic, Symbolic and mathematical

Page: 296

View: 1324

The authors teach how to organize and structure mathematical thoughts, how to read and manipulate abstract definitions, and how to prove or refute proofs by effectively evaluating them. There is a large array of topics and many exercises.

Modern Real and Complex Analysis

Author: Bernard R. Gelbaum

Publisher: University of Texas Press

ISBN: 9780471107156

Category: Mathematics

Page: 489

View: 7427

Modern Real and Complex Analysis Thorough, well–written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum′s approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up–to–date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman′s kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.

Lecture Notes on Complex Analysis

Author: Ivan Francis Wilde

Publisher: Imperial College Press

ISBN: 1860946429

Category: Technology & Engineering

Page: 245

View: 9420

This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis.Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of ã, in this context, is carefully explained.The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples.A number of relevant results from real analysis are collected, complete with proofs, in an appendix.The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.

The Way of Analysis

Author: Robert S. Strichartz

Publisher: Jones & Bartlett Learning

ISBN: 9780763714970

Category: Mathematics

Page: 739

View: 1929

The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.

An Introduction to Information Theory

Symbols, Signals and Noise

Author: John R. Pierce

Publisher: Courier Corporation

ISBN: 0486134970

Category: Computers

Page: 336

View: 9853

Covers encoding and binary digits, entropy, language and meaning, efficient encoding and the noisy channel, and explores ways in which information theory relates to physics, cybernetics, psychology, and art. 1980 edition.

Mathematical Analysis

Functions, Limits, Series, Continued Fractions

Author: L. A. Lyusternik,A. R. Yanpol'Skii

Publisher: Elsevier

ISBN: 1483194361

Category: Mathematics

Page: 418

View: 8666

Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors. Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers. This book is a valuable resource for mathematicians, engineers, and research workers.

Metric Spaces

Author: E. T. Copson

Publisher: CUP Archive

ISBN: 9780521357326

Category: Mathematics

Page: 152

View: 3521

Professor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.