A Tour Of The Calculus

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A Tour of the Calculus

David Berlinski
A Tour of the Calculus Book PDF

Author : David Berlinski
Publisher : Vintage
Page : 353 pages
File Size : 51,6 Mb
Release : 2011-04-27
Category : Mathematics
ISBN : 9780307789730

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A Tour of the Calculus by David Berlinski Pdf

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review

The Joy of X

Steven Henry Strogatz
The Joy of X Book PDF

Author : Steven Henry Strogatz
Publisher : Houghton Mifflin Harcourt
Page : 333 pages
File Size : 45,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780547517650

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The Joy of X by Steven Henry Strogatz Pdf

A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

One, Two, Three

David Berlinski
One Two Three Book PDF

Author : David Berlinski
Publisher : Vintage
Page : 225 pages
File Size : 48,7 Mb
Release : 2012-05-01
Category : Mathematics
ISBN : 9781400079100

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One, Two, Three by David Berlinski Pdf

The acclaimed author of A Tour of the Calculus and The Infinite Ascent offers an enlightening and enthralling tour of the basics of mathematics, and reveals a world of fascination in fundamental mathematical ideas. One, Two, Three is David Berlinski’s captivating exploration of the foundation of mathematics, its fundamental ideas, and why they matter. By unraveling the complex answers to these most elementary questions—What is a number? How do addition, subtraction, and other functions actually work? What are geometry and logic?—Berlinski reveals the intricacy behind their seemingly simple exteriors. Peppered with enlightening historical anecdotes and asides on some of history’s most fascinating mathematicians, One, Two, Three, revels in the beauty of numbers as Berlinski shows us how and why these often slippery concepts are as essential to the field of mathematics as to who we are.

The Calculus Story

David Acheson
The Calculus Story Book PDF

Author : David Acheson
Publisher : Oxford University Press
Page : 209 pages
File Size : 49,9 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 9780198804543

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The Calculus Story by David Acheson Pdf

"[Acheson] introduces the fundamental ideas of calculus through the story of how the subject developed, from approximating π to imaginary numbers, and from Newton's falling apple to the vibrations of an electric guitar."--Back cover

Calculus

Morris Kline
Calculus Book PDF

Author : Morris Kline
Publisher : Courier Corporation
Page : 962 pages
File Size : 47,6 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9780486134765

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Calculus by Morris Kline Pdf

Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.

Advanced Calculus

Lynn Harold Loomis,Shlomo Sternberg
Advanced Calculus Book PDF

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 55,8 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Infinite Powers

Steven Strogatz
Infinite Powers Book PDF

Author : Steven Strogatz
Publisher : Eamon Dolan Books
Page : 389 pages
File Size : 50,5 Mb
Release : 2019
Category : History
ISBN : 9781328879981

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Infinite Powers by Steven Strogatz Pdf

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus - how it works and why it makes our lives immeasurably better. Without calculus, we wouldn't have cell phones, TV, GPS, or ultrasound. We wouldn't have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz's brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it's about simplicity. It harnesses an unreal number--infinity--to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to make electricity with magnets; how to ensure your rocket doesn't miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

The Calculus Diaries

Jennifer Ouellette
The Calculus Diaries Book PDF

Author : Jennifer Ouellette
Publisher : Penguin
Page : 336 pages
File Size : 50,9 Mb
Release : 2010-08-31
Category : Mathematics
ISBN : 9781101459034

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The Calculus Diaries by Jennifer Ouellette Pdf

Kiss My Math meets A Tour of the Calculus Jennifer Ouellette never took math in college, mostly because she-like most people-assumed that she wouldn't need it in real life. But then the English-major-turned-award-winning-science-writer had a change of heart and decided to revisit the equations and formulas that had haunted her for years. The Calculus Diaries is the fun and fascinating account of her year spent confronting her math phobia head on. With wit and verve, Ouellette shows how she learned to apply calculus to everything from gas mileage to dieting, from the rides at Disneyland to shooting craps in Vegas-proving that even the mathematically challenged can learn the fundamentals of the universal language.

Financial Calculus

Martin Baxter,Andrew Rennie
Financial Calculus Book PDF

Author : Martin Baxter,Andrew Rennie
Publisher : Cambridge University Press
Page : 252 pages
File Size : 43,5 Mb
Release : 1996-09-19
Category : Business & Economics
ISBN : 0521552893

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Financial Calculus by Martin Baxter,Andrew Rennie Pdf

A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

Advanced Calculus

James J. Callahan
Advanced Calculus Book PDF

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 42,5 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9781441973320

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Advanced Calculus by James J. Callahan Pdf

With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.

A Guided Tour of Mathematical Methods for the Physical Sciences

Roel Snieder,Kasper van Wijk
A Guided Tour of Mathematical Methods for the Physical Sciences Book PDF

Author : Roel Snieder,Kasper van Wijk
Publisher : Cambridge University Press
Page : 583 pages
File Size : 50,6 Mb
Release : 2015-03-16
Category : Mathematics
ISBN : 9781107084964

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A Guided Tour of Mathematical Methods for the Physical Sciences by Roel Snieder,Kasper van Wijk Pdf

This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.

Mathematical Excursions to the World's Great Buildings

Alexander Hahn
Mathematical Excursions to the World s Great Buildings Book PDF

Author : Alexander Hahn
Publisher : Princeton University Press
Page : 344 pages
File Size : 52,5 Mb
Release : 2012-07-22
Category : Architecture
ISBN : 9780691145204

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Mathematical Excursions to the World's Great Buildings by Alexander Hahn Pdf

Describes the mathematics behind the design of famous buildings, including the Parthenon, the Sydney Opera House, and the Bilbao Guggenheim.

Brownian Motion Calculus

Ubbo F. Wiersema
Brownian Motion Calculus Book PDF

Author : Ubbo F. Wiersema
Publisher : John Wiley & Sons
Page : 342 pages
File Size : 55,9 Mb
Release : 2008-12-08
Category : Business & Economics
ISBN : 9780470021705

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Brownian Motion Calculus by Ubbo F. Wiersema Pdf

BROWNIAN MOTION CALCULUS Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the Itō stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is Itō’s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.

Calculus for Everyone

Mitch Stokes
Calculus for Everyone Book PDF

Author : Mitch Stokes
Publisher : Unknown
Page : 490 pages
File Size : 45,6 Mb
Release : 2020-06
Category : Electronic
ISBN : 1944482547

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Calculus for Everyone by Mitch Stokes Pdf

This book is for only two kinds of people: those who are interested in science and math, and those who aren't. And so, motivated by this powerful idea, Calculus for Everyone presents the mathematics of change in an extremely effective way for anyone with a first-year course in algebra. Yet it does so without dumbing calculus down. In fact, Calculus for Everyone is not only for students who would have never dreamt of taking calculus, it is also for those who have already taken a standard calculus course, as well as for those who will go on to take such a course Based on more than a decade of classroom experience, this book provides mastery of calculus's core by focusing on the foundational concepts of limits, derivatives, and integrals, explaining how all three are united in the fundamental theorem of calculus. Moreover, Calculus for Everyone explains how the story of calculus is central to Western culture, from Plato in ancient Greece, to today's modern physics. Indeed, this book explains why calculus is needed at all-and why it is needed so badly. By mastering the core of calculus-as well as seeing its meaning and significance-students will not only better understand math and science in general, but contemporary culture and their place in it.

An Image Processing Tour of College Mathematics

Yevgeniy V. Galperin
An Image Processing Tour of College Mathematics Book PDF

Author : Yevgeniy V. Galperin
Publisher : CRC Press
Page : 349 pages
File Size : 46,6 Mb
Release : 2021-02-10
Category : Computers
ISBN : 9780429683220

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An Image Processing Tour of College Mathematics by Yevgeniy V. Galperin Pdf

An Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies. The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives, most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms – all of that in the context of digital image processing. Features Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain. Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms. Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching. The convolution operation is introduced painlessly and naturally in the context of naïve filtering for denoising and is subsequently used for edge detection and image restoration. An accessible elementary introduction to Fourier analysis is provided in the context of image restoration. Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics. This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.