Author | George Pedrick | |

ISBN-10 | 9781441985545 | |

Release | 2012-09-10 | |

Pages | 279 | |

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This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation. |

Author | E. G. Phillips | |

ISBN-10 | 9781316626139 | |

Release | 2016-10-06 | |

Pages | 382 | |

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Originally published in 1962, this book covers all of the cornerstones of complex mathematical analyses. Chapters include, 'Bounds and limits of sequences', 'Integral calculus' and 'Functions of more than one variable'. Multiple examples are included at the end of every chapter to support and illustrate the fundamental concepts. |

Author | Niels Jacob | |

ISBN-10 | 9789814689106 | |

Release | 2015-08-18 | |

Pages | 768 | |

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Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis. Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions. Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions. |

Author | M.H. Protter | |

ISBN-10 | 9781461599906 | |

Release | 2012-12-06 | |

Pages | 507 | |

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The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction. |

Author | John B. Conway | |

ISBN-10 | 9781107173149 | |

Release | 2017-07-31 | |

Pages | 375 | |

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This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject. |

Author | Martin A. Moskowitz | |

ISBN-10 | 981024780X | |

Release | 2002 | |

Pages | 149 | |

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Organized in an especially efficient manner, presenting basic complex analysis. Includes about 50 exercises |

Author | Raymond Bernard Blakney | |

ISBN-10 | UCSC:32106008993401 | |

Release | 1948 | |

Pages | 131 | |

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A course in the analysis of Chinese characters has been writing in one form or another for most of life. You can find so many inspiration from A course in the analysis of Chinese characters also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A course in the analysis of Chinese characters book for free. |

Author | E. T. Whittaker | |

ISBN-10 | 0521588073 | |

Release | 1996-09-13 | |

Pages | 608 | |

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This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever. |

Author | ||

ISBN-10 | ||

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A course of analysis has been writing in one form or another for most of life. You can find so many inspiration from A course of analysis also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A course of analysis book for free. |

Author | Thomas William Körner | |

ISBN-10 | 9780821834473 | |

Release | 2004 | |

Pages | 590 | |

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This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique. |

Author | Andrew Browder | |

ISBN-10 | 9781461207153 | |

Release | 2012-12-06 | |

Pages | 335 | |

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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 | Donald Yau | |

ISBN-10 | 9789814417853 | |

Release | 2013 | |

Pages | 195 | |

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This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real analysis. Since this book is aimed at students who do not have much prior experience with proofs, the pace is slower in earlier chapters than in later chapters. There are hundreds of exercises, and hints for some of them are included. |

Author | D. J. H. Garling | |

ISBN-10 | 9781107032040 | |

Release | 2014-05-22 | |

Pages | 332 | |

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"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. Volume I focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theoryit 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 II goes on to consider metric and topological spaces, and functions of several variables. Volume III covers complex analysis and the theory of measure and integration"-- |

Author | Sudhir R. Ghorpade | |

ISBN-10 | 9780387364254 | |

Release | 2006-10-14 | |

Pages | 432 | |

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This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses. |

Author | Niels Jacob | |

ISBN-10 | 9814689084 | |

Release | 2015-10-06 | |

Pages | 768 | |

Download Link | Click Here |

Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers.Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions. |

Author | D. J. H. Garling | |

ISBN-10 | 9781107355422 | |

Release | 2014-01-23 | |

Pages | ||

Download Link | Click Here |

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 teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration. |

Author | Shanti Narayan | |

ISBN-10 | UVA:X000874230 | |

Release | 1966 | |

Pages | 436 | |

Download Link | Click Here |

A Course of Mathematical Analysis has been writing in one form or another for most of life. You can find so many inspiration from A Course of Mathematical Analysis also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A Course of Mathematical Analysis book for free. |