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Maxima and Minima without Calculus

Part of Dolciani Mathematical Expositions

Author: Ivan Niven, University of Oregon

Date Published: April 2006
availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
format: Hardback
isbn: 9780883853061

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About the Authors

The purpose of this book is to put together in one place the basic elementary techniques for solving problems in maxima and minima other than the methods of calculus and linear programming. The emphasis is not on the individual problems, but on methods that solve large classes of problems. The many chapters of the book can be read independently, without references to what precedes or follows. Besides the many problems solved in the book, others are left to the reader to solve, with sketches of solutions given in the later pages.
- A new printing of this MAA classic first published in 1981
- Each chapter can be read independently of the rest
- Many exercises included with sketch solutions provided at the end of the book
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Reviews & endorsements
'A book superb in its exposition and teeming with a variety of elegant mathematical results... All instructors in calculus courses should keep this book within easy reach and administer generous doses of its contents to students who are seized by a fit of differentiation frenzy when confronted with any kind of extremum problem.' Mathematical Reviews
'As befits a volume in the Dolciani series, the expository style is above reproach: it is particularly impressive that the author manages, without frightening his readers, to be honest about the difference between a proof which assumes the existence of an extremal solution and one which does not. This is a book which deserves to be read very widely.' The Times Higher Education Supplement
'… An endless source of fascinating problems which appear at first thought to be elementary, but usually turn out to be unresponsive to normal methods, with elegant and easily understandable solutions by the methods given in the text.' The Mathematical Gazette
'The purpose of this book is to put together in one place the basic elementary techniques for solving problems in maxima and minima other than the methods of calculus and linear programming. [The emphasis is] on methods that solve large classes of problems.' L'enseignement mathematique
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Product details
- Date Published: April 2006
- format: Hardback
- isbn: 9780883853061
- length: 320 pages
- dimensions: 223 x 144 x 21 mm
- weight: 0.477kg
- contains: 85 b/w illus. 194 exercises
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table of Contents
Preface
1. Background material
2. Simple algebraic results
3. Elementary geometric questions
4. Isoperimetric results
5. Basic trigonometric inequalities
6. Polygons inscribed and circumscribed
7. Ellipses
8. The bees and their hexagons
9. Further geometric results
10. Applied and miscellaneous problems
11. Euclidean three-space
12. Isoperimetric results not assuming existence
Postscript on calculus
Solutions of problems
References
Index.
Author
Ivan Niven, University of Oregon
Ivan Niven was an Emeritus Professor of University of Oregon