Maxima and Minima Without Calculus, Volume 6

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Cambridge University Press, 1981 - Mathematics - 303 pages
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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.
 

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Contents

PREFACE
1
CHAPTER TWO SIMPLE ALGEBRAIC RESULTS
15
CHAPTER THREE ELEMENTARY GEOMETRIC QUESTIONS
47
CHAPTER FOUR ISOPERIMETRIC RESULTS
77
CHAPTER FIVE BASIC TRIGONOMETRIC INEQUALITIES
92
CHAPTER SIX POLYGONS INSCRIBED AND CIRCUMSCRIBED
111
CHAPTER SEVEN ELLIPSES
126
CHAPTER EIGHT THE BEES AND THEIR HEXAGONS
144
CHAPTER NINE FURTHER GEOMETRIC RESULTS
156
CHAPTER TEN APPLIED AND MISCELLANEOUS PROBLEMS
179
CHAPTER ELEVEN EUCLIDEAN THREESPACE
211
CHAPTER TWELVE ISOPERIMETRIC RESULTS NOT ASSUMING EXISTENCE
226
POSTSCRIPT ON CALCULUS
239
REFERENCES
293
INDEX
299
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About the author (1981)

Ivan Niven was an Emeritus Professor of University of Oregon

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