Fundamentals of Real Analysis


Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
ISBN: 9780387984803
Category: Mathematics
Page: 479
View: 303

Continue Reading →

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS

A First Course in Real Analysis


Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
ISBN: 1441985484
Category: Mathematics
Page: 240
View: 3414

Continue Reading →

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

Fundamentals of Mathematical Analysis


Author: Paul J. Sally, Jr.
Publisher: American Mathematical Soc.
ISBN: 0821891413
Category: Mathematics
Page: 362
View: 7461

Continue Reading →

This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.

Fundamentals of Functional Analysis


Author: Douglas Farenick
Publisher: Springer
ISBN: 3319456334
Category: Mathematics
Page: 451
View: 6047

Continue Reading →

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.

Fundamentals of Real Analysis


Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
ISBN: 9780387984803
Category: Mathematics
Page: 479
View: 6596

Continue Reading →

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS

The Real Numbers and Real Analysis


Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 0387721762
Category: Mathematics
Page: 553
View: 9781

Continue Reading →

This rigorous, detailed introduction to real analysis presents the fundamentals clearly and includes definitions, theorems and proofs. Mirroring the structure of standard calculus courses makes it especially accessible to university students of mathematics.

Mathematical Analysis Fundamentals


Author: Agamirza Bashirov
Publisher: Academic Press
ISBN: 0128010509
Category: Mathematics
Page: 362
View: 9292

Continue Reading →

The author’s goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options. Friendly and well-rounded presentation of pre-analysis topics such as sets, proof techniques and systems of numbers. Deeper discussion of the basic concept of convergence for the system of real numbers, pointing out its specific features, and for metric spaces Presentation of Riemann integration and its place in the whole integration theory for single variable, including the Kurzweil-Henstock integration Elements of multiplicative calculus aiming to demonstrate the non-absoluteness of Newtonian calculus.

Real Analysis and Foundations


Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 9780849371561
Category: Mathematics
Page: 312
View: 2752

Continue Reading →

Real Analysis and Foundations is an advanced undergraduate and first-year graduate textbook that introduces students to introductory topics in real analysis (or real variables), point set topology, and the calculus of variations. This classroom-tested book features over 350 end-of-chapter exercises that clearly develop and reinforce conceptual topics. It also provides an excellent review chapter on math foundations topics, as well as accessible coverage of classical topics, such as Weirstrass Approximation Theorem, Ascoli-Arzela Theorem and Schroeder-Bernstein Theorem. Explanations and discussions of key concepts are so well done that Real Analysis and Foundations will also provide valuable information for professional aerospace and structural engineers.

Basic Real Analysis


Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817644415
Category: Mathematics
Page: 656
View: 3490

Continue Reading →

Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

Fundamentals of Mathematical Logic


Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Category: Mathematics
Page: 896
View: 9227

Continue Reading →

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Foundations of Statistical Analyses and Applications with SAS


Author: Michael Falk,Frank Marohn,Bernward Tewes
Publisher: Birkhäuser
ISBN: 3034881959
Category: Mathematics
Page: 402
View: 8384

Continue Reading →

This book links up the theory of a selection of statistical procedures used in general practice with their application to real world data sets using the statistical software package SAS (Statistical Analysis System). These applications are intended to illustrate the theory and to provide, simultaneously, the ability to use the knowledge effectively and readily in execution.

Measure and Integration


Author: Sterling K. Berberian
Publisher: American Mathematical Soc.
ISBN: 9780821853283
Category: Mathematics
Page: 312
View: 6349

Continue Reading →

This highly flexible text is organized into two parts: Part I is suitable for a one-semester course at the first-year graduate level, and the book as a whole is suitable for a full-year course. Part I treats the theory of measure and integration over abstract measure spaces. Prerequisites are a familiarity with epsilon-delta arguments and with the language of naive set theory (union, intersection, function). The fundamental theorems of the subject are derived from first principles, with details in full. Highlights include convergence theorems (monotone, dominated), completeness of classical function spaces (Riesz-Fischer theorem), product measures (Fubini's theorem), and signed measures (Radon-Nikodym theorem). Part II is more specialized; it includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic representation of positive linear forms, and Haar measure on a locally compact group. The group algebra of a locally compact group is constructed in the last chapter, by an especially transparent method that minimizes measure-theoretic difficulties. Prerequisites for Part II include Part I plus a course in general topology. To quote from the Preface: ``Finally, I am under no illusions as to originality, for the subject of measure theory is an old one which has been worked over by many experts. My contribution can only be in selection, arrangement, and emphasis. I am deeply indebted to Paul R. Halmos, from whose textbook I first studied measure theory; I hope that these pages may reflect their debt to his book without seeming to be almost everywhere equal to it.''

Linear Functional Analysis


Author: Bryan Rynne,M.A. Youngson
Publisher: Springer Science & Business Media
ISBN: 9781848000056
Category: Mathematics
Page: 324
View: 2389

Continue Reading →

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality.

Fundamentals of Complex Analysis

With Applications to Engineering and Science (Classic Version)
Author: Edward Saff,Arthur D. Snider
Publisher: Math Classics
ISBN: 9780134689487
Category: Mathematics
Page: 576
View: 4198

Continue Reading →

Originally published in 2003, reissued as part of Pearson's modern classic series.

Linear Functional Analysis

An Application-Oriented Introduction
Author: Hans Wilhelm Alt
Publisher: Springer
ISBN: 1447172809
Category: Mathematics
Page: 435
View: 9521

Continue Reading →

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.

Fundamentals of Mathematical Analysis


Author: Rod Haggarty
Publisher: Addison-Wesley Longman
ISBN: 9780201631975
Category: Calculus
Page: 332
View: 6925

Continue Reading →

Providing students with an introduction to the fundamentals of analysis, this book continues to present the fundamental concepts of analysis in as painless a manner as possible. To achieve this aim, the second edition has made many improvements in exposition.

Foundations of Potential Theory


Author: Oliver Dimon Kellogg
Publisher: Courier Corporation
ISBN: 9780486601441
Category: Science
Page: 384
View: 1441

Continue Reading →

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 Analysis


Author: Eberhard Freitag,Rolf Busam
Publisher: Springer Science & Business Media
ISBN: 3540939830
Category: Mathematics
Page: 532
View: 1194

Continue Reading →

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included

Introductory Complex Analysis


Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486318524
Category: Mathematics
Page: 400
View: 2056

Continue Reading →

Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Fundamentals of Functional Analysis


Author: Douglas Farenick
Publisher: Springer
ISBN: 3319456334
Category: Mathematics
Page: 451
View: 1604

Continue Reading →

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.