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Author : Norman B. Haaser
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (59 download)
Download or read book A Course in Mathematical Analysis: Introduction to analysis. v. 2. Intermediate analysis written by Norman B. Haaser and published by . This book was released on 1959 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : V. A. Zorich
Publisher : Springer
ISBN 13 : 3662489937
Total Pages : 729 pages
Book Rating : 4.6/5 (624 download)
Download or read book Mathematical Analysis II written by V. A. Zorich and published by Springer. This book was released on 2016-02-12 with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.
Author : Andrew Browder
Publisher : Springer Science & Business Media
ISBN 13 : 1461207150
Total Pages : 348 pages
Book Rating : 4.4/5 (612 download)
Download or read book Mathematical Analysis written by Andrew Browder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
ISBN 13 : 0821847910
Total Pages : 610 pages
Book Rating : 4.8/5 (218 download)
Download or read book Advanced Calculus written by Patrick Fitzpatrick and published by American Mathematical Soc.. This book was released on 2009 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.
Author : William R. Parzynski
Publisher : McGraw-Hill Companies
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.3/5 (91 download)
Download or read book Introduction to Mathematical Analysis written by William R. Parzynski and published by McGraw-Hill Companies. This book was released on 1982 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gerald B. Folland
Publisher : John Wiley & Sons
ISBN 13 : 1118626397
Total Pages : 368 pages
Book Rating : 4.1/5 (186 download)
Download or read book Real Analysis written by Gerald B. Folland and published by John Wiley & Sons. This book was released on 2013-06-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
Author : Bernd S. W. Schröder
Publisher : John Wiley & Sons
ISBN 13 : 9780470226766
Total Pages : 584 pages
Book Rating : 4.2/5 (267 download)
Download or read book Mathematical Analysis written by Bernd S. W. Schröder and published by John Wiley & Sons. This book was released on 2008-01-28 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
Author : Victor Bryant
Publisher : Cambridge University Press
ISBN 13 : 1107717221
Total Pages : 304 pages
Book Rating : 4.1/5 (77 download)
Download or read book Yet Another Introduction to Analysis written by Victor Bryant and published by Cambridge University Press. This book was released on 1990-06-28 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education the traditional development of analysis, often rather divorced from the calculus which they learnt at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus at school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate the new ideas are related to school topics and are used to extend the reader's understanding of those topics. A first course in analysis at college is always regarded as one of the hardest in the curriculum. However, in this book the reader is led carefully through every step in such a way that he/she will soon be predicting the next step for him/herself. In this way the subject is developed naturally: students will end up not only understanding analysis, but also enjoying it.
Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
ISBN 13 : 1441985484
Total Pages : 249 pages
Book Rating : 4.4/5 (419 download)
Download or read book A First Course in Real Analysis written by Sterling K. Berberian and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Vladimir A. Zorich
Publisher : Springer Science & Business Media
ISBN 13 : 9783540406334
Total Pages : 708 pages
Book Rating : 4.4/5 (63 download)
Download or read book Mathematical Analysis II written by Vladimir A. Zorich and published by Springer Science & Business Media. This book was released on 2004-01-22 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.
Author : Igor Kriz
Publisher : Springer Science & Business Media
ISBN 13 : 3034806361
Total Pages : 517 pages
Book Rating : 4.0/5 (348 download)
Download or read book Introduction to Mathematical Analysis written by Igor Kriz and published by Springer Science & Business Media. This book was released on 2013-07-25 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis, as understood by a mathematician today.
Author : Jiri Lebl
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781718865488
Total Pages : 196 pages
Book Rating : 4.8/5 (654 download)
Download or read book Basic Analysis II written by Jiri Lebl and published by Createspace Independent Publishing Platform. This book was released on 2018-05-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 2.0. The second volume of Basic Analysis, a first course in mathematical analysis. This volume is the second semester material for a year-long sequence for advanced undergraduates or masters level students. This volume started with notes for Math 522 at University of Wisconsin-Madison, and then was heavily revised and modified for teaching Math 4153/5053 at Oklahoma State University. It covers differential calculus in several variables, line integrals, multivariable Riemann integral including a basic case of Green's Theorem, and topics on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier Series. See http://www.jirka.org/ra/ Table of Contents (of this volume II): 8. Several Variables and Partial Derivatives 9. One Dimensional Integrals in Several Variables 10. Multivariable Integral 11. Functions as Limits
Author : Vladimir A. Zorich
Publisher : Krishna Prakashan Media
ISBN 13 :
Total Pages : 792 pages
Book Rating : 4./5 ( download)
Download or read book Mathematical Analysis II written by Vladimir A. Zorich and published by Krishna Prakashan Media. This book was released on 2010-11-16 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions.
Author : J Martin Speight
Publisher : World Scientific Publishing Company
ISBN 13 : 1783267852
Total Pages : 274 pages
Book Rating : 4.7/5 (832 download)
Download or read book A Sequential Introduction To Real Analysis written by J Martin Speight and published by World Scientific Publishing Company. This book was released on 2015-10-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.
Author : D. J. H. Garling
Publisher : Cambridge University Press
ISBN 13 : 1107311381
Total Pages : 317 pages
Book Rating : 4.1/5 (73 download)
Download or read book A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2013-04-25 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.
Author : Robert A. Rankin
Publisher : Elsevier
ISBN 13 : 1483185036
Total Pages : 624 pages
Book Rating : 4.4/5 (831 download)
Download or read book An Introduction to Mathematical Analysis written by Robert A. Rankin and published by Elsevier. This book was released on 2014-07-10 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of 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)
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.
