Undergraduate Texts in Mathematics

Variational Calculus with Elementary Convexity

Authors: Troutman, J.L.

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  • ISBN 978-1-4684-0158-5
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About this Textbook

The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How­ ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.

Table of contents (10 chapters)

  • Review of Optimization in ℝd

    Troutman, John L.

    Pages 1-9

  • Standard Optimization Problems

    Troutman, John L.

    Pages 13-34

  • Linear Spaces and Gâteaux Variations

    Troutman, John L.

    Pages 35-51

  • Minimization of Convex Functions

    Troutman, John L.

    Pages 52-92

  • The Lemmas of Lagrange and du Bois-Reymond

    Troutman, John L.

    Pages 93-98

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4684-0158-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4684-0160-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Variational Calculus with Elementary Convexity
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1983
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4684-0158-5
DOI
10.1007/978-1-4684-0158-5
Softcover ISBN
978-1-4684-0160-8
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XIV, 365
Topics