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Calculation Of The Bernoullian Numbers, Rectification Of The Logarithmic Curve, Integration Of Logarithmic Binomials, Etc. ... Read more

Product Description
Calculation Of The Bernoullian Numbers, Rectification Of The Logarithmic Curve, Integration Of Logarithmic Binomials, Etc. ... Read more

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Designed for the full-time analyst, physicists, engineer, or economist, this book attempts to provide its readers with most of the measure theory they will ever need. Given the choice, the author has consistently optedto develop the concrete rather than the abstract aspects of topics treated.

The major new feature of this third edition is the inclusion of a new chapter in which the author introduces the Fourier transform. In that Hermite functions play a central role in his treatment of Parseval's identity andthe inversion formula, Stroock's approach bears greater resemblance to that adopted by Norbert Wiener than that used in most modern introductory texts. A second feature is that solutions to all problems are provided.

As a self-contained text, this book is excellent for both self-study and the classroom. ... Read more

Customer Reviews (2)

Hard to understand!
I bought this book for my class, but honestly I felt hard to understand the concepts presented in this book.

A perfect place to start Real Analysis
This is a perfect textbook for a one-semester course in measure and integration at a graduate level. It's concise but complete and detailed, rigour but motivated and inspiring. It's more technical than Bartle's little book on integration. It also has solution manual in the end to check on. I hope more readers enjoy such a wonderful germ written by a star form MIT. ... Read more

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Introduction to Integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of examples and exercises.Intended as a first course in integration theory for students familiar with real analysis, the book begins with a simplified Lebesgue integral, which is then developed to provide an entry point for important results in the field. The final chapters present selected applications, mostly drawn from Fourier analysis.The emphasis throughout is on integrable functions rather than on measures. Designed as an undergraduate or graduate textbook, it is a companion volume to the author's Introduction to Complex Analysis and is aimed at both pure and applied mathematicians. ... Read more

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Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.  This  includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients.  In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation.  Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes.

This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.

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Chapters: Integral, Antiderivative, Integration by Parts, Sum Rule in Integration, Linearity of Integration, Constant Factor Rule in Integration, Constant of Integration, Riemann Sum, Stochastic Calculus, Shell Integration, Multiple Integral, Differentiation Under the Integral Sign, Arc Length, Order of Integration, Malliavin Calculus, Integration by Substitution, Leibniz Integral Rule, Absolute Convergence, Simpson's Rule, Indicator Function, Fubini's Theorem, Risch Algorithm, Signed Measure, Integral Test for Convergence, Trigonometric Substitution, Surface of Revolution, Solid of Revolution, Rectangle Method, Method of Exhaustion, Locally Integrable Function, Integration Using Euler's Formula, Integration by Parts Operator, Essential Supremum and Essential Infimum, Localization Theorem, Integration by Reduction Formulae, Disk Integration, Quadratic Integral, Product Measure, Dirichlet Integral, Lebesgue's Decomposition Theorem, Singular Measure, Lebesgue's Density Theorem, Nonelementary Integral, Cauchy Formula for Repeated Integration, Conditional Convergence, Integration Using Parametric Derivatives, Absolute Convergence Theorem, Tonelli-hobson Test. Source: Wikipedia. Pages: 221. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Power rule, Product rule, Quotient rule, Chain rule Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function of a real variable x and an interval of the real line, the definite integral is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of , the x-axis, and the vertical lines x = a and x = b. The term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function . In this case...More: http://booksllc.net/?id=15532 ... Read more

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Integration is one of the two cornerstones of analysis. Since the fundamental work of Lebesgue, integration has been interpreted in terms of measure theory. This introductory text starts with the historical development of the notion of the integral and a review of the Riemann integral. From here, the reader is naturally led to the consideration of the Lebesgue integral, where abstract integration is developed via measure theory. The important basic topics are all covered: the Fundamental Theorem of Calculus, Fubini's Theorem, $L_p$ spaces, the Radon-Nikodym Theorem, change of variables formulas, and so on.

The book is written in an informal style to make the subject matter easily accessible. Concepts are developed with the help of motivating examples, probing questions, and many exercises. It would be suitable as a textbook for an introductory course on the topic or for self-study.

For this edition, more exercises and four appendices have been added. ... Read more

Customer Reviews (1)

Full of small errors.Excellent, and brilliant book.Very thorough.
This is an amazing book; its clarity is outstanding throughout.However, I want to voice serious reservations about it due to an abundance of errors; I am reviewing the second edition published by the AMS.

This book has more errors than any other math book I have read.These errors include minor typographical errors like sloppy spacing, to equations with the terms included in the wrong order or on wrong lines, misnumbered references to earlier results, and occasional abuse of notation that hinders mathematical rigour.There are substantive errors as well, including the citing of a source for a proof of a theorem that is not actually proved in the cited source.

Errors aside, this is one of the clearest and best motivated expositions of measure theory I have been able to find.The book moves slowly, but never too slowly; it explores essential questions that a student should consider, like counterexamples, converses, and the subtle distinctions between different strengths of conditions.I find this thoroughness very welcome; most texts in measure theory present the most logically direct path to a bare-bones collection of useful results, an approach that doesn't necessarily help students.

The first chapter, on Riemann integration, is unique.The topic is explored in much more depth than in most analysis texts.Most students feel they understand Riemann integration; this book will likely convince them that they do not--and then it will fill the gaps in their understanding.The counterexamples in this book are outstanding--simple, worked through with clarity, and deep.

I think this book would make an outstanding textbook on measure theory, and it is one of the few texts that is good for self-study.I just wish the errors could be corrected; I would then rate it 5 stars without a doubt. ... Read more

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This easy-to-understand calculus study aid is ideal for those who are new to the subject. It offers a well-illustrated, step-by-step introduction that moves along at an easy-to-keep-up-with pace. Use it with your textbook or for independent study to improve your comprehension and boost your grades. It features 226 solved and 513 skill-building supplementary problems--more than other study guides. Whether you simply want to feel confident at test time or build a solid foundation in calculus for more advanced math, science, and engineering course, Schaum's Outline of Beginning Calculus is students' first choice.level of Ayres/Mendelson, Calculus, 3/e. This will make up the calculus segments of one-semester liberal arts courses and the various one-semester Calculus courses for business or life sciences. This book will also address weaker students in general freshman calculus and high school advanced placement courses. Theory is restricted to fundamentals of differentiation and integration (single-variable) and the solved problems, with no steps ommitted, include reviews of algebra. This updated edition will continue the excellent sales record of the first edition and will include: problems suitable for graphing calculators and existing problems adapted to involve calculator use; emphasis on aogorithmic aspects of Calculus; Newton's method will be given a separate section, a section various approximation techniques for integration, Simpson's Rule the Midpoint rule; a section that presents the traditional treatment of exponential and logarithmic functions, which method some textbooks have gone back to. ... Read more

Customer Reviews (8)

very helpful
This book is very helpful to me as a teacher. I use it to supplement the text examples.

Great supplement to your average math course
This is a great as a supplement for everyone that is following a math course or wants to fresh his knowledge about calculus.

okay
the pages were a little bent when i received it, but it was otherwise in good condition

Just the best book for self study and review
This book can help an alien to math understand a calculus concept.

Good as supplemental text book, NOT good as primary textbook
There are not enough examples to explain everything you would need to know.I've found I had to go to the web or other more basic Calculus books many times to try to solve some of the problems in there.There are better books out there for those of us looking for complete breakdown of the problems and better explanations. ... Read more

Product Description
This work provides clear information about integration. The text is supported by worked examples and includes past examination questions and solutions. This title is from the "Maths Made Simple" series. ... Read more