Elementary Analysis Through Examples And Exercises

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Elementary Analysis through Examples and Exercises

Author : John Schmeelk
Publisher : Springer Science & Business Media
ISBN 13 : 940158589X
Total Pages : 329 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Elementary Analysis through Examples and Exercises by : John Schmeelk

Download or read book Elementary Analysis through Examples and Exercises written by John Schmeelk and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is hard to imagine that another elementary analysis book would contain ma terial that in some vision could qualify as being new and needed for a discipline already abundantly endowed with literature. However, to understand analysis, be ginning with the undergraduate calculus student through the sophisticated math ematically maturing graduate student, the need for examples and exercises seems to be a constant ingredient to foster deeper mathematical understanding. To a talented mathematical student, many elementary concepts seem clear on their first encounter. However, it is the belief of the authors, this understanding can be deepened with a guided set of exercises leading from the so called "elementary" to the somewhat more "advanced" form. Insight is instilled into the material which can be drawn upon and implemented in later development. The first year graduate student attempting to enter into a research environment begins to search for some original unsolved area within the mathematical literature. It is hard for the student to imagine that in many circumstances the advanced mathematical formulations of sophisticated problems require attacks that draw upon, what might be termed elementary techniques. However, if a student has been guided through a serious repertoire of examples and exercises, he/she should certainly see connections whenever they are encountered.

Elementary Analysis

Author : Kenneth A. Ross
Publisher : CUP Archive
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4./5 ( download)

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Book Synopsis Elementary Analysis by : Kenneth A. Ross

Download or read book Elementary Analysis written by Kenneth A. Ross and published by CUP Archive. This book was released on 2014-01-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis through Examples and Exercises

Author : E. Pap
Publisher : Springer Science & Business Media
ISBN 13 : 9401711062
Total Pages : 344 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Complex Analysis through Examples and Exercises by : E. Pap

Download or read book Complex Analysis through Examples and Exercises written by E. Pap and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book Complex Analysis through Examples and Exercises has come out from the lectures and exercises that the author held mostly for mathematician and physists . The book is an attempt to present the rat her involved subject of complex analysis through an active approach by the reader. Thus this book is a complex combination of theory and examples. Complex analysis is involved in all branches of mathematics. It often happens that the complex analysis is the shortest path for solving a problem in real circum stances. We are using the (Cauchy) integral approach and the (Weierstrass) power se ries approach . In the theory of complex analysis, on the hand one has an interplay of several mathematical disciplines, while on the other various methods, tools, and approaches. In view of that, the exposition of new notions and methods in our book is taken step by step. A minimal amount of expository theory is included at the beinning of each section, the Preliminaries, with maximum effort placed on weil selected examples and exercises capturing the essence of the material. Actually, I have divided the problems into two classes called Examples and Exercises (some of them often also contain proofs of the statements from the Preliminaries). The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercisesj the answers, and, occasionally, some hints, are still given.

Elementary Classical Analysis

Author : Jerrold E. Marsden
Publisher : Macmillan
ISBN 13 : 9780716721055
Total Pages : 760 pages
Book Rating : 4.7/5 (21 download)

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Book Synopsis Elementary Classical Analysis by : Jerrold E. Marsden

Download or read book Elementary Classical Analysis written by Jerrold E. Marsden and published by Macmillan. This book was released on 1993-03-15 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for courses in advanced calculus and introductory real analysis, Elementary Classical Analysis strikes a careful balance between pure and applied mathematics with an emphasis on specific techniques important to classical analysis without vector calculus or complex analysis. Intended for students of engineering and physical science as well as of pure mathematics.

Exercises in Basic Ring Theory

Author : Grigore Calugareanu
Publisher : Springer Science & Business Media
ISBN 13 : 9780792349181
Total Pages : 226 pages
Book Rating : 4.3/5 (491 download)

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Book Synopsis Exercises in Basic Ring Theory by : Grigore Calugareanu

Download or read book Exercises in Basic Ring Theory written by Grigore Calugareanu and published by Springer Science & Business Media. This book was released on 1998-02-28 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.

Real Mathematical Analysis

Author : Charles Chapman Pugh
Publisher : Springer Science & Business Media
ISBN 13 : 0387216847
Total Pages : 445 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Real Mathematical Analysis by : Charles Chapman Pugh

Download or read book Real Mathematical Analysis written by Charles Chapman Pugh and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Exploratory Examples for Real Analysis

Author : Joanne E. Snow
Publisher : American Mathematical Soc.
ISBN 13 : 1470458357
Total Pages : 160 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Exploratory Examples for Real Analysis by : Joanne E. Snow

Download or read book Exploratory Examples for Real Analysis written by Joanne E. Snow and published by American Mathematical Soc.. This book was released on 2003-12-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text supplement contains 12 exploratory exercises designed to facilitate students' understanding of the most elemental concepts encountered in a first real analysis course: notions of boundedness, supremum/infimum, sequences, continuity and limits, limit suprema/infima, and pointwise and uniform convergence. In designing the exercises, the [Author];s ask students to formulate definitions, make connections between different concepts, derive conjectures, or complete a sequence of guided tasks designed to facilitate concept acquisition. Each exercise has three basic components: making observations and generating ideas from hands-on work with examples, thinking critically about the examples, and answering additional questions for reflection. The exercises can be used in a variety of ways: to motivate a lecture, to serve as a basis for in-class activities, or to be used for lab sessions, where students work in small groups and submit reports of their investigations. While the exercises have been useful for real analysis students of all ability levels, the [Author];s believe this resource might prove most beneficial in the following scenarios: A two-semester sequence in which the following topics are covered: properties of the real numbers, sequences, continuity, sequences and series of functions, differentiation, and integration. A class of students for whom analysis is their first upper division course. A group of students with a wide range of abilities for whom a cooperative approach focusing upon fundamental concepts could help to close the gap in skill development and concept acquisition. An independent study or private tutorial in which the student receives a minimal level of instruction. A resource for an instructor developing a cooperative, interactive course that does not involve the use of a standard text. Ancillary materials, including Visual Guide Sheets for those exercises that involve the use of technology and Report Guides for a lab session approach are provided online at: http:www.saintmarys.edu/~jsnow. In designing the exercise, the [Author];s were inspired by Ellen Parker's book, Laboratory Experiences in Group Theory, also published by the MAA.

Elementary Analysis

Author : Kenneth A. Ross
Publisher : Springer Science & Business Media
ISBN 13 : 1461462711
Total Pages : 417 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Elementary Analysis by : Kenneth A. Ross

Download or read book Elementary Analysis written by Kenneth A. Ross and published by Springer Science & Business Media. This book was released on 2013-04-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Elementary Real Analysis

Author : Brian S. Thomson
Publisher :
ISBN 13 : 9781434896209
Total Pages : 0 pages
Book Rating : 4.8/5 (962 download)

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Book Synopsis Elementary Real Analysis by : Brian S. Thomson

Download or read book Elementary Real Analysis written by Brian S. Thomson and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: VolumeTwo contains Chapters 9-13 of Elementary Real Analysis, by Thomson, Bruckner and Bruckner. Originally published by Prentice Hall (Pearson) in 2001. This is the second corrected edition. Volume One and the full text are also available as trade paperbacks. All of our textbooks are available for FREE DOWNLOAD in versions for on-screen viewing. Information is at ClassicalRealAnalysis.com.Chapter 9. Sequences and Series of FunctionsChapter 10. Power SeriesChapter 11. Euclidean Space R^nChapter 12. Differentiation on R^nChapter 13. Metric Spaces.

Understanding Analysis

Author : Stephen Abbott
Publisher : Springer Science & Business Media
ISBN 13 : 0387215069
Total Pages : 269 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Understanding Analysis by : Stephen Abbott

Download or read book Understanding Analysis written by Stephen Abbott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Complex Analysis

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Complex Analysis by : Elias M. Stein

Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Real Analysis via Sequences and Series

Author : Charles H.C. Little
Publisher : Springer
ISBN 13 : 1493926519
Total Pages : 483 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Real Analysis via Sequences and Series by : Charles H.C. Little

Download or read book Real Analysis via Sequences and Series written by Charles H.C. Little and published by Springer. This book was released on 2015-05-28 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

A Problem Book in Real Analysis

Author : Asuman G. Aksoy
Publisher : Springer Science & Business Media
ISBN 13 : 1441912967
Total Pages : 257 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Problem Book in Real Analysis by : Asuman G. Aksoy

Download or read book A Problem Book in Real Analysis written by Asuman G. Aksoy and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

Analysis I

Author : Terence Tao
Publisher : Springer
ISBN 13 : 9811017891
Total Pages : 366 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Analysis I by : Terence Tao

Download or read book Analysis I written by Terence Tao and published by Springer. This book was released on 2016-08-29 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Foundations of Mathematical Analysis

Author : Saminathan Ponnusamy
Publisher : Springer Science & Business Media
ISBN 13 : 0817682910
Total Pages : 575 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Foundations of Mathematical Analysis by : Saminathan Ponnusamy

Download or read book Foundations of Mathematical Analysis written by Saminathan Ponnusamy and published by Springer Science & Business Media. This book was released on 2011-12-16 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

Basic Real Analysis

Author : Houshang H. Sohrab
Publisher : Springer
ISBN 13 : 1493918419
Total Pages : 687 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Basic Real Analysis by : Houshang H. Sohrab

Download or read book Basic Real Analysis written by Houshang H. Sohrab and published by Springer. This book was released on 2014-11-15 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews

Measure, Integration & Real Analysis

Author : Sheldon Axler
Publisher : Springer Nature
ISBN 13 : 3030331431
Total Pages : 430 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler

Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/