The Calculus: A Genetic Approach by Otto Toeplitz (PDF)

Description

When first published posthumously in 1963, this bookpresented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus.Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Current calculus books are massive tomes that are geared to ‘plug and chug’ problems. Once done, the student can then quickly look up the answer in the back of the book.This book provides a realtively brief introduction the integral and differential using a visual (geometric) approach before getting into the algebra. It takes more time to learn the material this way than simply saying ‘the derivative of x^n is nx^n-l : now differentiate x^2’. (I am big on visuals – particularly in real analysis). Rather, Toeplitz goes over the visual idea of differentiation, integration, the fundamental theorem, integration by parts, etc.You will not learn the whole of calculus from this book. Rather, it is a great tool to have in your back-pocket for Calc I-IV and Rudin’s ‘Real Analysis’. If you want to have a better appreciation of calculus, you will get a lot of use out of this book.

⭐I would find a good “genetic” approach to the calculus extremely valuable, and Toeplitz seems perfect for the job: a big German professor of the classical tradition who says all the right things in the preface, and who throws around quotations in Latin that he expects everyone to understand. So far so good. One is all the more dissapointed then when it turns out that the book simply isn’t that good. It covers the calculus from the Greeks and stops after Newton (it seems that there was meant to be a second volume). The topics are the usual ones. Certainly one could learn a lot of calculus from this book, and certainly there are many interesting historical remarks, but the unity of the two does not reach the great heights we had hoped. One can achieve pretty much the same effect by simply pasting together a calculus history book with any old calculus textbook.

⭐This translation from the German by Luise Lange is superbly done. The book can be appreciated by high school level students who have an interest in math. I plan to use some of the examples on my web site which will employ math 101 and Visual Basic programming techniques….Leo JL…programmer at large

⭐Even when translated into English, this book is nearly incomprehensible to the modern reader. It was published in the 1960s, but the author uses turn of the century academic language that is intentionally abstruse. I’ve read terse mathematical works and been able to penetrate many of them, but I certainly feel for anyone who has to use this unreadable book in their course like I do.

⭐

Keywords

Free Download The Calculus: A Genetic Approach in PDF format
The Calculus: A Genetic Approach PDF Free Download
Download The Calculus: A Genetic Approach 2018 PDF Free
The Calculus: A Genetic Approach 2018 PDF Free Download
Download The Calculus: A Genetic Approach PDF
Free Download Ebook The Calculus: A Genetic Approach