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Books in Analysis

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21-30 of 42 results in All results

Infinitesimal Methods of Mathematical Analysis

  • 1st Edition
  • May 1, 2004
  • J S Pinto
  • English
  • Paperback
    9 7 8 - 1 - 8 9 8 5 6 3 - 9 9 - 0
  • eBook
    9 7 8 - 0 - 8 5 7 0 9 - 9 5 0 - 1
This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.

Geometric Computations with Interval and New Robust Methods

  • 1st Edition
  • December 1, 2003
  • H Ratschek + 1 more
  • English
  • eBook
    9 7 8 - 0 - 8 5 7 0 9 - 9 5 1 - 8
This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free.

Foundations of Complex Analysis in Non Locally Convex Spaces

  • 1st Edition
  • Volume 193
  • November 11, 2003
  • A. Bayoumi
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 1 9 2 - 2
All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field.Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory.Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem.Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions.The new concept of Quasi-differentiability introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one.The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems.bull; The book contains new generalized versions of:i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others.ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author.bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995.bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

A Primer of Lebesgue Integration

  • 2nd Edition
  • September 17, 2001
  • H. S. Bear
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 2 5 7 3 - 0
The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.

An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93

  • 2nd Edition
  • May 16, 2001
  • Robert M. Young
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 7 7 2 9 5 5 - 8
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 9 5 7 4 - 3
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Introductory Analysis

  • 1st Edition
  • June 14, 2000
  • Richard J. Bagby
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 4 9 4 2 - 2
Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.

Problems in Real Analysis

  • 2nd Edition
  • October 7, 1998
  • Charalambos D. Aliprantis + 1 more
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 0 5 0 2 5 3 - 0
A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods. Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.

Principles of Real Analysis

  • 3rd Edition
  • August 26, 1998
  • Charalambos D. Aliprantis
  • Owen Burkinshaw
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 0 5 0 2 5 7 - 8
With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

Projects for Calculus

  • 2nd Edition
  • August 26, 1998
  • Keith D. Stroyan
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 9 9 4 - 2
Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.

Inequalities for Differential and Integral Equations

  • 1st Edition
  • Volume 197
  • November 12, 1997
  • William F. Ames + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 4 6 4 - 0
Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.