Save 40% on select Business & Management books + FREE shipping or 50% on Physics eBooks!

Studies in the History of Mathematics and Physical Sciences

A History of the Calculus of Variations from the 17th through the 19th Century

Authors: Goldstine, H. H.

Free Preview

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4613-8106-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-1-4613-8108-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4613-8106-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-1-4613-8108-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
A History of the Calculus of Variations from the 17th through the 19th Century
Authors
Series Title
Studies in the History of Mathematics and Physical Sciences
Series Volume
5
Copyright
1980
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-8106-8
DOI
10.1007/978-1-4613-8106-8
Softcover ISBN
978-1-4613-8108-2
Series ISSN
0172-570X
Edition Number
1
Number of Pages
410
Topics