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| Author | : Tom M. Apostol |
| Publisher | : Mathematical Association of America (MAA) |
| Total Pages | : 492 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : |
Selected papers reprinted from American mathematical monthly (Volumes 1 - 75) and Mathematics magazine (Volumes 1 - 40).
| Author | : H. H. Goldstine |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 427 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461381061 |
The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathemati cians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861.
| Author | : John Stillwell |
| Publisher | : Springer Nature |
| Total Pages | : 400 |
| Release | : 2020-11-07 |
| Genre | : Mathematics |
| ISBN | : 3030551938 |
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
| Author | : Carl B. Boyer |
| Publisher | : Courier Corporation |
| Total Pages | : 369 |
| Release | : 2012-10-09 |
| Genre | : Mathematics |
| ISBN | : 0486175383 |
Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.
| Author | : Lynn Arthur Steen |
| Publisher | : MAA Press |
| Total Pages | : 280 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shape of calculus for a new century. The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of teaching must be repaired, but do not agree on the most promising avenues for improvement. The document contains: (1) a record of presentations prepared for a colloquium; (2) a collage of reactions to the colloquium by a variety of individuals representing diverse calculus constituencies; (3) summaries of 16 discussion groups that elaborate on particular themes of importance to reform efforts; (4) a series of background papers providing context for the calculus colloquium; (5) a selection of final examinations from Calculus I, II, and III from universities, colleges, and two-year colleges around the country; (6) a collection of reprints of documents related to calculus; and (7) a list of colloquium participants. (PK)
| Author | : David M. Bressoud |
| Publisher | : Princeton University Press |
| Total Pages | : 242 |
| Release | : 2021-05-04 |
| Genre | : Mathematics |
| ISBN | : 0691218781 |
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 | : Florian Cajori |
| Publisher | : |
| Total Pages | : 472 |
| Release | : 1913 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Steven Strogatz |
| Publisher | : Eamon Dolan Books |
| Total Pages | : 389 |
| Release | : 2019 |
| Genre | : History |
| ISBN | : 1328879984 |
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.
| Author | : Jeff Suzuki |
| Publisher | : MAA |
| Total Pages | : 432 |
| Release | : 2009-08-27 |
| Genre | : Mathematics |
| ISBN | : 9780883855706 |
An exploration of the interaction between mathematics, mathematicians and society. What would Newton see if he looked out his window?
| Author | : C.H.Jr. Edwards |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461262305 |
The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.
