Applied Nonstandard Analysis


Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486152340
Category: Mathematics
Page: 208
View: 8828

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This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.

Nonstandard Analysis


Author: Alain Robert
Publisher: Courier Corporation
ISBN: 9780486432793
Category: Mathematics
Page: 156
View: 5023

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This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.

Nonstandard Methods in Stochastic Analysis and Mathematical Physics


Author: Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm
Publisher: Courier Dover Publications
ISBN: 0486468992
Category: Mathematics
Page: 526
View: 3416

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Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.

Lectures on the Hyperreals

An Introduction to Nonstandard Analysis
Author: Robert Goldblatt
Publisher: Springer Science & Business Media
ISBN: 1461206154
Category: Mathematics
Page: 293
View: 6838

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An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.

A First Course in Functional Analysis


Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486499839
Category: Mathematics
Page: 110
View: 7453

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Designed for undergraduate mathematics majors, this introductory treatment is based on the distinguished author's lecture notes. The self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. 1966 edition.

Introduction to Analysis


Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 9780486650388
Category: Mathematics
Page: 254
View: 7383

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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.

Elementary Calculus

An Infinitesimal Approach
Author: H. Jerome Keisler
Publisher: Courier Corporation
ISBN: 0486484521
Category: Mathematics
Page: 913
View: 8883

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This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

Introduction to Applied Numerical Analysis


Author: Richard W. Hamming
Publisher: Courier Corporation
ISBN: 0486485900
Category: Mathematics
Page: 331
View: 604

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"This book is appropriate for an applied numerical analysis course for upper-level undergraduate and graduate students as well as computer science students. Actual programming is not covered, but an extensive range of topics includes round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, Fourier series, and much more. 1989 edition"--Provided by publisher.

Analysis for Applied Mathematics


Author: Ward Cheney
Publisher: Springer Science & Business Media
ISBN: 1475735596
Category: Mathematics
Page: 448
View: 9790

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This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value problems, and integral equations. Pragmatic approaches to difficult equations are presented, including the Galerkin method, the method of iteration, Newton’s method, projection techniques, and homotopy methods.

Vector Analysis


Author: Louis Brand
Publisher: Courier Corporation
ISBN: 048615484X
Category: Mathematics
Page: 304
View: 4401

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This text was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications. 1957 edition. 86 figures.

An Introduction to Mathematical Analysis for Economic Theory and Econometrics


Author: Dean Corbae,Maxwell B. Stinchcombe,Juraj Zeman
Publisher: Princeton University Press
ISBN: 1400833086
Category: Business & Economics
Page: 688
View: 3278

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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory

Numbers and Infinity

A Historical Account of Mathematical Concepts
Author: E. H. Sondheimer,Alan Rogerson
Publisher: Courier Corporation
ISBN: 0486452980
Category: Mathematics
Page: 172
View: 7306

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This fresh overview of numbers and infinity avoids tedium and controversy while maintaining historical accuracy and modern relevance. Perfect for undergraduate mathematics or science history courses. 1981 edition.

Infinitesimal Calculus


Author: James M. Henle,Eugene M. Kleinberg
Publisher: Courier Corporation
ISBN: 0486151018
Category: Mathematics
Page: 144
View: 3699

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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

Primer of Quantum Mechanics


Author: Marvin Chester
Publisher: Courier Corporation
ISBN: 0486138208
Category: Science
Page: 328
View: 5429

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Introductory text examines classical quantum bead on a track: state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; bead in spherical shell. 1992 edition.

Counterexamples in Analysis


Author: Bernard R. Gelbaum,John M. H. Olmsted
Publisher: Courier Corporation
ISBN: 0486134911
Category: Mathematics
Page: 224
View: 3475

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These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.

Functional Analysis


Author: George Bachman,Lawrence Narici
Publisher: Courier Corporation
ISBN: 0486136558
Category: Mathematics
Page: 544
View: 4376

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Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.

Numerical Mathematics


Author: Alfio Maria Quarteroni,Riccardo Sacco,Fausto Saleri
Publisher: Springer
ISBN: 0387227504
Category: Mathematics
Page: 655
View: 1397

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The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable
Author: E. Hewitt,K. Stromberg
Publisher: Springer
ISBN: 3642880479
Category: Mathematics
Page: 476
View: 6403

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This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus tomarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we have given elementary avatars of all important theorems, with appro priate suggestions for skipping. We have given complete definitions, ex planations, and proofs throughout, so that the book should be usable for individual study as well as for a course text. Prerequisites for reading the book are the following. The reader is assumed to know elementary analysis as the subject is set forth, for example, in TOM M. ApOSTOL'S Mathematical Analysis [Addison-Wesley Publ. Co., Reading, Mass., 1957], or WALTER RUDIN'S Principles of Mathe nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].

Introduction to the Theory of Random Processes


Author: Iosif Il?ich Gikhman,Anatoli? Vladimirovich Skorokhod
Publisher: Courier Corporation
ISBN: 0486693872
Category: Mathematics
Page: 516
View: 2389

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Rigorous exposition suitable for elementary instruction. Covers measure theory, axiomatization of probability theory, processes with independent increments, Markov processes and limit theorems for random processes, more. A wealth of results, ideas, and techniques distinguish this text. Introduction. Bibliography. 1969 edition.

An Outline of Set Theory


Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486453375
Category: Mathematics
Page: 145
View: 9190

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An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.