Irresistible Integrals

Symbolics, Analysis and Experiments in the Evaluation of Integrals

Author: George Boros,Victor Moll

Publisher: Cambridge University Press

ISBN: 9780521796361

Category: Mathematics

Page: 306

View: 5925

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in nineteenth century analysis and it has now been revived with the appearance of symbolic languages. The authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting-rather than the shortest-path to the results. They illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This is a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Irresistible Integrals

Symbolics, Analysis and Experiments in the Evaluation of Integrals

Author: George Boros,Victor Moll

Publisher: Cambridge University Press

ISBN: 9780521791861

Category: Mathematics

Page: 322

View: 6781

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in nineteenth century analysis and it has now been revived with the appearance of symbolic languages. The authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting-rather than the shortest-path to the results. They illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This is a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Irresistible Integrals

Symbolics, Analysis and Experiments in the Evaluation of Integrals

Author: George Boros,Victor Moll

Publisher: Cambridge University Press

ISBN: 9780521791861

Category: Mathematics

Page: 322

View: 8530

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in nineteenth century analysis and it has now been revived with the appearance of symbolic languages. The authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting-rather than the shortest-path to the results. They illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This is a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Lectures on Complex Integration

Author: Alexander O. Gogolin

Publisher: Springer Science & Business Media

ISBN: 3319002120

Category: Science

Page: 285

View: 3170

The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.

Inside Interesting Integrals

A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)

Author: Paul J. Nahin

Publisher: Springer

ISBN: 1493912771

Category: Science

Page: 412

View: 2469

What’s the point of calculating definite integrals since you can’t possibly do them all?. What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.

The Computer as Crucible

An Introduction to Experimental Mathematics

Author: Jonathan Borwein,Keith Devlin

Publisher: CRC Press

ISBN: 1439876916

Category: Mathematics

Page: 170

View: 9794

Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time.

The Image of the City

Author: Kevin Lynch

Publisher: MIT Press

ISBN: 9780262620017

Category: Architecture

Page: 194

View: 6393

The classic work on the evaluation of city form.

Table of Integrals, Series, and Products

Author: I. S. Gradshteyn,I. M. Ryzhik

Publisher: Academic Press

ISBN: 1483265641

Category: Mathematics

Page: 1206

View: 3549

Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

Confessions of Saint Augustine

Author: Frank J. Sheed

Publisher: A&C Black

ISBN: 0567110052

Category: Religion

Page: 224

View: 5658

Sheed's classic translation of Augustine's Confessions. True to the original, and in a subtle and dignified English translation, let this be a cornerstone of your library.

The Interpretation of Cultures

Author: Clifford Geertz

Publisher: Basic Books

ISBN: 0465093566

Category: Social Science

Page: 576

View: 8949

In The Interpretation of Cultures, the most original anthropologist of his generation moved far beyond the traditional confines of his discipline to develop an important new concept of culture. This groundbreaking book, winner of the 1974 Sorokin Award of the American Sociological Association, helped define for an entire generation of anthropologists what their field is ultimately about.

Mathematics for Physics

A Guided Tour for Graduate Students

Author: Michael Stone,Paul Goldbart

Publisher: Cambridge University Press

ISBN: 1139480618

Category: Science

Page: N.A

View: 9195

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Man and His Symbols

Author: C. G. Jung

Publisher: Dell

ISBN: 0307800555

Category: Social Science

Page: 320

View: 5706

Man and His Symbols owes its existence to one of Jung's own dreams. The great psychologist dreamed that his work was understood by a wide public, rather than just by psychiatrists, and therefore he agreed to write and edit this fascinating book. Here, Jung examines the full world of the unconscious, whose language he believed to be the symbols constantly revealed in dreams. Convinced that dreams offer practical advice, sent from the unconscious to the conscious self, Jung felt that self-understanding would lead to a full and productive life. Thus, the reader will gain new insights into himself from this thoughtful volume, which also illustrates symbols throughout history. Completed just before his death by Jung and his associates, it is clearly addressed to the general reader. Praise for Man and His Symbols “This book, which was the last piece of work undertaken by Jung before his death in 1961, provides a unique opportunity to assess his contribution to the life and thought of our time, for it was also his firsat attempt to present his life-work in psychology to a non-technical public. . . . What emerges with great clarity from the book is that Jung has done immense service both to psychology as a science and to our general understanding of man in society, by insisting that imaginative life must be taken seriously in its own right, as the most distinctive characteristic of human beings.”—Guardian “Straighforward to read and rich in suggestion.”—John Barkham, Saturday Review Syndicate “This book will be a resounding success for those who read it.”—Galveston News-Tribune “A magnificent achievement.”—Main Currents “Factual and revealing.”—Atlanta Times

Elliptic Curves

Function Theory, Geometry, Arithmetic

Author: Henry McKean,Victor Moll

Publisher: Cambridge University Press

ISBN: 9780521658171

Category: Mathematics

Page: 280

View: 3527

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.

The New Spirit of Capitalism

Author: Luc Boltanski,Eve Chiapello

Publisher: Verso Books

ISBN: 1786633272

Category: Political Science

Page: 688

View: 2710

New edition of this major work examining the development of neoliberalism In this established classic, sociologists Luc Boltanski and Eve Chiapello get to the heart of contemporary capitalism. Delving deep into the latest management texts informing the thinking of employers, the authors trace the contours of a new spirit of capitalism. They argue that beginning in the mid-1970s, capitalism abandoned the hierarchical Fordist work structure and developed a new network-based form of organization founded on employee initiative and autonomy in the workplace—a putative freedom bought at the cost of material and psychological security. This was a spirit in tune with the libertarian and romantic currents of the period (as epitomized by dressed-down, cool capitalists such as Bill Gates and Ben and Jerry) and, as the authors argue, a more successful, pernicious, and subtle form of exploitation. In this new edition, the authors reflect on the reception of the book and the debates it has stimulated.

Brave New World

Author: Aldous Huxley

Publisher: RosettaBooks

ISBN: 9780795311253

Category: Fiction

Page: 288

View: 5601

Huxley's bleak future prophesized in Brave New World was a capitalist civilization which had been reconstituted through scientific and psychological engineering, a world in which people are genetically designed to be passive and useful to the ruling class. Satirical and disturbing, Brave New World is set some 600 years ahead, in "this year of stability, A.F. 632"--the A.F. standing for After Ford, meaning the godlike Henry Ford. "Community, Identity, Stability," is the motto. Reproduction is controlled through genetic engineering, and people are bred into a rigid class system. As they mature, they are conditioned to be happy with the roles that society has created for them. The rest of their lives are devoted to the pursuit of pleasure through sex, recreational sports, the getting and having of material possessions, and taking a drug called Soma. Concepts such as family, freedom, love, and culture are considered grotesque. Against this backdrop, a young man known as John the Savage is brought to London from the remote desert of New Mexico. What he sees in the new civilization a "brave new world" (quoting Shakespeare's The Tempest). However, ultimately, John challenges the basic premise of this society in an act that threatens and fascinates its citizens. Huxley uses his entire prowess to throw the idea of utopia into reverse, presenting us what is known as the "dystopian" novel. When Brave New World was written (1931), neither Hitler nor Stalin had risen to power. Huxley saw the enduring threat to society from the dark side of scientific and social progress, and mankind's increasing appetite for simple amusement. Brave New World is a work that indicts the idea of progress for progress sake and is backed up with force and reason.

The Logic of Scientific Discovery

Author: Karl Popper

Publisher: Routledge

ISBN: 1134470029

Category: Philosophy

Page: 480

View: 7234

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

Dynamic Assessment in Practice

Clinical and Educational Applications

Author: H. Carl Haywood,Carol S. Lidz

Publisher: Cambridge University Press

ISBN: 1139462075

Category: Psychology

Page: N.A

View: 7496

Dynamic assessment embeds interaction within the framework of a test-intervene-retest approach to psychoeducational assessment. This book offers an introduction to diagnostic assessors in psychology, education, and speech/language pathology to the basic ideas, principles, and practices of dynamic assessment. Most importantly, the book presents an array of specific procedures developed and used by the authors that can be applied to clients of all ages in both clinical and educational settings. The authors discuss their approach to report-writing, with a number of examples to demonstrate how they incorporate dynamic assessment into a comprehensive approach to assessment. The text concludes with a discussion of issues and questions that need to be considered and addressed. Two appendixes include descriptions of additional tests used by the authors that are adapted for dynamic assessment, as well as information about dynamic assessment procedures developed by others and sources for additional information about this approach.

An Introduction to Mechanics

Author: Daniel Kleppner,Robert Kolenkow

Publisher: Cambridge University Press

ISBN: 0521198119

Category: Science

Page: 566

View: 7719

This second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics.

Probability Theory

The Logic of Science

Author: E. T. Jaynes

Publisher: Cambridge University Press

ISBN: 1139435167

Category: Science

Page: N.A

View: 1731

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

The Theory of Dynamic Efficiency

Author: Jesús Huerta de Soto

Publisher: Taylor & Francis

ISBN: 041542769X

Category: Business & Economics

Page: 359

View: 8790

This book gathers a collection of English language essays by Jesús Huerta de Soto over the past ten years, examining the dynamic processes of social cooperation which characterize the market, with particular emphasis on the role of both entrepreneurship and institutions. The author's multidisciplinary approach to the subject is in keeping with a trend in economic thought established by the Austrian school of economics; a discourse that had witnessed a significant revival over the last thirty years. Areas covered in this book include an introduction to the theory of dynamic efficiency as an alternative to the standard paretian criteria, an explanation of the differences between the Austrian and the neoclassical approach to economics, a generalized definition of socialism that allows the joint application of the analysis of interventionism, a dynamic Austrian approach to the analysis of free market environmentalism, nationalism, the reform of Social Security and the theory of banking and an evaluation of the role of Spanish Scholastics of the Sixteenth Century.