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The Calculus: A Genetic Approach, Toeplitz, Otto, New Book
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eBay-Artikelnr.:157491873636
Artikelmerkmale
- Artikelzustand
- Book Title
- The Calculus: A Genetic Approach
- ISBN
- 9780226806686
Über dieses Produkt
Product Identifiers
Publisher
University of Chicago Press
ISBN-10
0226806685
ISBN-13
9780226806686
eBay Product ID (ePID)
57034832
Product Key Features
Number of Pages
201 Pages
Publication Name
Calculus : a Genetic Approach
Language
English
Publication Year
2007
Subject
Life Sciences / Genetics & Genomics, Calculus
Type
Textbook
Subject Area
Mathematics, Science
Format
Perfect
Dimensions
Item Height
0.1 in
Item Weight
11.1 Oz
Item Length
0.8 in
Item Width
0.6 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2006-034201
TitleLeading
The
Reviews
Appropriate for students who have completed basic or high school calculus but have not yet stepped up to the rigors of advanced calculus. Here those students will find motivation for understanding techniques in response to the original problems that gave rise to them., "Appropriate for students who have completed basic or high school calculus but have not yet stepped up to the rigors of advanced calculus. Here those students will find motivation for understanding techniques in response to the original problems that gave rise to them."- Scitech Book News
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
517.1
Table Of Content
FOREWORD PREFACE TO THE GERMAN EDITION PREFACE TO THE ENGLISH EDITION I . THE NATURE OF THE INFINITE PROCESS 1 . The Beginnings of Greek Speculation on Infinitesimals 2 . The Greek Theory of Proportions 3 . The Exhaustion Method of the Greeks 4 . The Modern Number Concept 5 . Archimedes' Measurements of the Circle and the Sine Tables 6 . The Infinite Geometric Series 7 . Continuous Compound Interest 8 . Periodic Decimal Fractions 9 . Convergence and Limit 10 . Infinite Series II . THE DEFINITE INTEGRAL 11 . The Quadrature of the Parabola by Archimedes 12 . Continuation after 1. 880 Years 13 . Area and Definite Integral 14 . Non-rigorous Infinitesimal Methods 15 . The Concept of the Definite Integral 16 . Some Theorems on Definite Integrals 17 . Questions of Principle III . DIFFERENTIAL AND INTEGRAL CALCULUS 18 . Tangent Problems 19 . Inverse Tangent Problems 20 . Maxima and Minima 21 . Velocity 22 . Napier 23 . The Fundamental Theorem 24 . The Product Rule 25 . Integration by Parts 26 . Functions of Functions 27. Transformation of Integrals 28 . The Inverse Function 29 . Trigonometric Functions 30 . Inverse Trigonometric Functions 31 . Functions of Several Functions 32 . Integration of Rational Functions 33 . Integration of Trigonometric Expressions 34 . Integration of Expressions Involving Radicals 35 . Limitations of Explicit Integration IV . APPLICATIONS TO PROBLEMS OF MOTION 36 . Velocity and Acceleration 37 . The Pendulum 38 . Coordinate Transformations 39 . Elastic Vibrations 40 . Kepler's First Two Laws 41 . Derivation of Kepler's First Two Laws from Newton's Law 42 . Kepler's Third Law EXERCISES BIBLIOGRAPHY Works on the History of Mathematics Special Works on the History of the Infinitesimal Calculus BIBLIOGRAPHICAL NOTES INDEX
Synopsis
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., When first published posthumously in 1963, this book presented 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.
LC Classification Number
QA303.T6415 2007
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