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Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology andTopological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales [MR35 #4725], an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

The present volume comprises Chapters 1-6 in English translation (a second volume will contain the remaining Chapters 7-9). The individual fascicles of the original French edition have been extensively reviewed [Chs. 1--4, MR 14, 960, 2e édn. MR 36 #2763; Ch. 5, MR 18, 881, 2e edn. MR 35 #322; Ch.6, MR 23 #A2033; Chs. 7-8, MR31 #3539; Ch. 9, MR 43 #2183].

Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chs. 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations). ... Read more

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This book is a compilation of the most important andwidely applicable methods for evluating and approximating integrals.It is an indispensable time saver for engineers and scientists needingto evaluate integrals in their work. ... Read more

Customer Reviews (1)

A good reference
This is a nice, thorough handbook that gives just enough detail to allow you easily find something, and in each section lists plenty of references to dig deeper if you want.

The author seems to get the right balance between documenting everything and just pointing out things which may not be obvious or problem spots.

He has a nice format of how things are laid out; it makes sense and is easy to grab for quick lookup.As I am not a mathematician, I appreciate the glossary of math terms related to integration.

... Read more

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This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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With Classified Reference Tables Of Integrals And Methods Of Integration. ... Read more

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When you need just the essentials of calculus, this Easy Outlines book is there to help

If you are looking for a quick nuts-and-bolts overview of calculus, it’s got to be Schaum's Easy Outline. This book is a pared-down, simplified, and tightly focused version of its Schaum’s Outline cousin, with an emphasis on clarity and conciseness.

Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give you quick pointers to the essentials.

• Perfect if you have missed class or need extra review
• Gives you expert help from teachers who are authorities in their fields
• So small and light that it fits in your backpack!

Topics include: Functions, Sequences, Limits, and Continuity, Differentiation, Maxima and Minima, Differentiation of Special Functions, The Law of the Mean, Indeterminate Forms, Differentials, and Curve Sketching, Fundamental Integration Techniques and Applications, The Definite Integral, Plane Areas by Integration, Improper Integrals, Differentiation Formulas for Common Mathematical Functions, Integration Formulas for Common Mathematical Functions

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Adopts a user-friendly approach, with an emphasis on worked examples and exercises, rather than abstract theory

The computer algebra and graphical package MAPLE is used to illustrate many of the ideas and provides an additional aid to teaching and learning

Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web

Customer Reviews (1)

A source of robust examples and challenging exercises.
Hirst's text does an effective job of introducing the techniques and applications of differential and integral calculus.Hirst does this by providing robust examples that enable the reader to develop the skills necessary to solve the quite complicated problems that he poses in the exercises.Since Hirst provides answers to nearly all of these exercises, the text lends itself to self-study.The text feels somewhat incomplete because it does not develop the underlying theory.It also does not cover sequences and series, which Hirst covers in his text Numbers, Sequences and Series (Modular Mathematics Series).While its scope is somewhat limited, working through the text is worthwhile since it helps you develop sophisticated problem solving skills.

This text is an introduction to college calculus for students who have been exposed to calculus while completing the A level course in pure mathematics.It would be appropriate for American students who have completed an Advanced Placement Calculus course and wish to develop their skills further.The prerequisites covered in the introductory chapter include functions and graphs, domain and range, odd and even functions, composite functions, inverse functions, and piecewise-defined functions.These prerequisites are discussed in the context of polynomial, rational, exponential, logarithmic, trigonometric, and hyperbolic functions and both trigonometric and hyperbolic identities.

The next chapter covers limits of functions, including the definition of limits and one-sided limits, algebraic techniques for finding them, properties of limits, infinite limits, limits at infinity, and the Squeeze Theorem.Since some exposure to differential calculus is assumed, Hirst also introduces L'Hopital's Rule here, although it could be deferred until later without interrupting the flow of the text.

Hirst then devotes several chapters to differentiation, covering the definition, properties of the derivative, the Chain Rule, higher derivatives, implicit differentiation, logarithmic differentiation, parametric differentiation, the differentiation of inverse functions, and Leibniz's Theorem.Once these skills have been introduced, Hirst shows you how to apply them to finding gradients and tangents, maxima and minima, optimization problems, linear motion problems, growth and decay problems, and the Newton-Raphson method of finding the roots of an equation.Related rates are not covered.

Hirst concludes his coverage of differentiation with a chapter on Taylor polynomials.The chapter begins with a discussion of linear approximation, the Mean Value Theorem, and quadratic approximation. He then demonstrates how to find the Taylor polynomial and the error associated with the Taylor polynomial approximation of a function.While I generally found this book to be fairly clear, I had to refer to Tom M. Apostol's text Calculus:Volume I in order to clarify the discussion in this chapter and to learn how to solve some of the problems.

The remainder of the text is devoted to integral calculus.After he introduces the anti-derivative (indefinite integral), Hirst discusses the logarithmic integral, integrals with variable limits, infinite integrals, and improper integrals before devoting chapters to integration by parts, integration by substitution, and integration by partial fractions.These chapters are particularly worthwhile since Hirst goes beyond the standard topics in order to cover reduction formulae, the Gamma function, inverse substitutions, trigonometric substitutions (including half-angle substitutions), hyperbolic substitutions, and partial fractions with repeated linear and quadratic factors.The text concludes with a chapter on applications of integration, including calculations of arc length, surface area of revolution, volume of revolution, density and mass, and center of mass.

This text would make a good companion to a more theoretical text such as Serge Lang's A First Course in Calculus (Undergraduate Texts in Mathematics), Tom M. Apostol'sCalculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition), or Michael Spivak's Calculus. ... Read more

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The main theme of this book is the "path integral technique" and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the Feynman-Kac formula. Also included is a simple exposition of stochastic Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman-Kac-Itô formula).

Among other topics discussed are the probabilistic approach to the bound of the number of ground states of correlation inequalities (the Birman-Schwinger principle, Lieb's formula, etc.), the calculation of asymptotics for functional integrals of Laplace type (the theory of Donsker-Varadhan) and applications, scattering theory, the theory of crushed ice, and the Wiener sausage.

Written with great care and containing many highly illuminating examples, this classic book is highly recommended to anyone interested in applications of functional integration to quantum physics. It can also serve as a textbook for a course in functional integration. ... Read more

Customer Reviews (1)

introduction to brownian motion and its applications
This is the best introduction to brownian motion. The writing by Barry Simon is extremely clear, comparable to Donald Knuth. It covers:

-clear construction of Brownian motion

-demonstration of the Feynmann Katzformula -usual Simon work: Schrodinger operators, remarquable inequalitieslike the CLK, eigenvalues problems

-geometric theory of brownianmotion

-very extensive bibliography for further reading

Nevertheless itlacks:

-conformal theory of brownian motion

-statistical mechanics(there is an explanation of feynmann series in a particular case) ... Read more

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An introduction to an area of numerical analysis used in situations where the problem is easy to define, but the solution proves less straight-forward, especially when the restrictions of numerical stability are taken into account. ... Read more

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Presents a general approach to integration theory, as well as some advanced topics. A self-contained introduction suitable for a graduate student doing self-study or for an advanced course on integration theory. ... Read more

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This text discusses computational integration methods and the fundamental mathematical principles they are based on. It includes sections on one-dimensional and multi-dimensional integration formulas, and it deals with issues concerning the construction of numerical integration algorithms. ... Read more