The Calculus Gallery

Author : William Dunham
Publisher : Princeton University Press
Page : 256 pages
File Size : 52,5 Mb
Release : 2018-11-13
Category : Mathematics
ISBN : 9780691184548

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The Calculus Gallery by William Dunham Pdf

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching—a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.

Author : Caren L. Diefenderfer,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 529 pages
File Size : 44,8 Mb
Release : 2010-12-31
Category : Mathematics
ISBN : 9780883857618

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The Calculus Collection by Caren L. Diefenderfer,Roger B. Nelsen Pdf

The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.

Author : David M. Bressoud
Publisher : Princeton University Press
Page : 242 pages
File Size : 46,7 Mb
Release : 2021-05-04
Category : Mathematics
ISBN : 9780691218786

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Calculus Reordered by David M. Bressoud Pdf

Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

Author : Oscar E. Fernandez
Publisher : Princeton University Press
Page : 176 pages
File Size : 44,5 Mb
Release : 2019-07-09
Category : Mathematics
ISBN : 9780691192314

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The Calculus of Happiness by Oscar E. Fernandez Pdf

How math holds the keys to improving one's health, wealth, and love life? What's the best diet for overall health and weight management? How can we change our finances to retire earlier? How can we maximize our chances of finding our soul mate? In The Calculus of Happiness, Oscar Fernandez shows us that math yields powerful insights into health, wealth, and love. Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple "all-weather" investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. Moreover, the important formulas are linked to a dozen free online interactive calculators on the book's website, allowing one to personalize the equations. Fernandez uses everyday experiences--such as visiting a coffee shop--to provide context for his mathematical insights, making the math discussed more accessible, real-world, and relevant to our daily lives. Every chapter ends with a summary of essential lessons and takeaways, and for advanced math fans, Fernandez includes the mathematical derivations in the appendices. A nutrition, personal finance, and relationship how-to guide all in one, The Calculus of Happiness invites you to discover how empowering mathematics can be.

Author : Steven G. Krantz
Publisher : MAA
Page : 395 pages
File Size : 49,8 Mb
Release : 2010-04
Category : Mathematics
ISBN : 9780883857663

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An Episodic History of Mathematics by Steven G. Krantz Pdf

A series of snapshots of the history of mathematics from ancient times to the twentieth century.

Author : William Dunham
Publisher : American Mathematical Society
Page : 185 pages
File Size : 49,6 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9781470466183

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Euler by William Dunham Pdf

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

Author : Steven Strogatz
Publisher : Princeton University Press
Page : 184 pages
File Size : 55,9 Mb
Release : 2011-03-07
Category : Mathematics
ISBN : 1400830885

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The Calculus of Friendship by Steven Strogatz Pdf

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

Author : William Dunham
Publisher : John Wiley & Sons
Page : 323 pages
File Size : 46,8 Mb
Release : 1994-08-16
Category : Mathematics
ISBN : 9780471536567

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The Mathematical Universe by William Dunham Pdf

"Dunham writes for nonspecialists, and they will enjoy his piquantanecdotes and amusing asides -- Booklist "Artfully, Dunham conducts a tour of the mathematical universe. . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are." -- Nature "If you want to encourage anyone's interest in math, get them TheMathematical Universe." * New Scientist

Author : David Berlinski
Publisher : Vintage
Page : 353 pages
File Size : 52,7 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

Author : Philip Brown
Publisher : Mercury Learning and Information
Page : 382 pages
File Size : 42,9 Mb
Release : 2016-03-14
Category : Mathematics
ISBN : 9781944534417

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Foundations of Mathematics by Philip Brown Pdf

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts

Author : Oscar Fernandez
Publisher : Princeton University Press
Page : 270 pages
File Size : 50,7 Mb
Release : 2019-06-11
Category : Juvenile Nonfiction
ISBN : 9780691175393

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Calculus Simplified by Oscar Fernandez Pdf

"In Calculus simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a "Goldilocks approach" to learning calculus : just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure."--Page 4 de la couverture.

Author : William Johnston
Publisher : American Mathematical Society
Page : 456 pages
File Size : 54,5 Mb
Release : 2022-04-01
Category : Mathematics
ISBN : 9781470465650

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The Calculus of Complex Functions by William Johnston Pdf

The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.

Author : Shahriar Shahriari
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 53,6 Mb
Release : 2006
Category : Approximation theory
ISBN : 9780821837504

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Approximately Calculus by Shahriar Shahriari Pdf

Is there always a prime number between $n$ and $2n$? Where, approximately, is the millionth prime? And just what does calculus have to do with answering either of these questions? It turns out that calculus has a lot to do with both questions, as this book can show you. The theme of the book is approximations. Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear--or higher order--approximation is at the heart of calculus. The real star of the book, though, is the task of approximating the number of primes up to a number $x$. This leads to the famous Prime Number Theorem--and to the answers to the two questions about primes. While emphasizing the role of approximations in calculus, most major topics are addressed, such as derivatives, integrals, the Fundamental Theorem of Calculus, sequences, series, and so on. However, our particular point of view also leads us to many unusual topics: curvature, Pade approximations, public key cryptography, and an analysis of the logistic equation, to name a few. The reader takes an active role in developing the material by solving problems. Most topics are broken down into a series of manageable problems, which guide you to an understanding of the important ideas. There is also ample exposition to fill in background material and to get you thinking appropriately about the concepts. Approximately Calculus is intended for the reader who has already had an introduction to calculus, but wants to engage the concepts and ideas at a deeper level. It is suitable as a text for an honors or alternative second semester calculus course.

Author : Otto Toeplitz
Publisher : Unknown
Page : 0 pages
File Size : 54,7 Mb
Release : 1963
Category : Calculus
ISBN : 0226806650

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The Calculus by Otto Toeplitz Pdf

This volume offers insights in current theoretical discussions, observations, and reflections from internationally and regionally celebrated scholars on the theory and practice of teaching English informed by a new school of thought, English as an International Language (EIL). This volume provides readers (scholars, teachers, teacher-educators, researchers in the relevant fields) with: Knowledge of the changing paradigm and attitudes towards English language teaching from teaching a single variety of English to teaching intercultural communication and English language variation. Current thoughts on the theory of teaching English as an international language by internationally-celebrated established scholars and emergent scholars. Scholarly descriptions and discussions of how English language educators and teacher-educators translate the paradigm of English as an International Language into their existing teaching. Delineation of how this newly emerged paradigm is received or responded to by English language educators and students when it is implemented. Readers have a unique opportunity to observe and read the tensions and dilemmas that educators and students are likely to experience in teaching and learning EIL -- back cover.

Author : Roberto Smith
Publisher : Unknown
Page : 0 pages
File Size : 54,6 Mb
Release : 1996-09
Category : Calculus
ISBN : 0669418390

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MathCAD Lab Manual by Roberto Smith Pdf