Maxima and Minima Without Calculus不用微积分求最大值和最小值
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作者： Ivan Niven，Lester H. Lance著
出 版 社：
出版时间： 1981-12-1字数：版次： 1页数： 303印刷时间： 1918/12/01开本： 大32开印次： 1纸张： 胶版纸I S B N ： 9780883853061包装： 精装内容简介
The purpose of the 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 individual problems，but on methods that solve large classes of problems。These methods are organized in terms of the mathematical ideas used，whether from algebra，geometry，the theory of inequalities，and so on。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。
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。Each of the self-contained chapters cover methods that solve large classes of problems，and helpful exercises are provided。
目录
PREFACE
CHAPTER ONE. BACKGROUND MATERIAL
1.1. Language and Notation
1.2. Geometry and Trigonometry
1.3. Areas and Volumes
1.4. Inequalities
1.5. The Sigma Notation
CHAPTER TWO. SIMPLE ALGEBRAIC RESULTS
2.1. Sums and Products
2.2. Any Square Is Positive or Zero
2.3. The Inequality of the Arithmetic-Geometric Means
2.4. An Alternative Approach
2.5. Cauchy's Proof
2.6. Techniques for Finding Extrema
2.7. The Inequality of the Arithmetic-Harmonic Means
2.8. The Numbere
2.9. Cauchy's Inequality
CHAPTER THREE. ELEMENTARY GEOMETRIC QUESTIONS
3.1. Introduction
3.2. Triangles
3.3. Quadrilaterals
3.4. Miscellaneous Results in Geometry
3.5. The Reflection Principle
3.6. Equivalent Results
3.7. Auxiliary Circles
CHAFFER FOUR. ISOPERIMETRIC RESULTS
4.1. Some Definitions
4.2. Polygons
4.3. The Isoperimetric Theorem
4.4. The Isoperimetric Quotient
4.5. Existence and Uniqueness
……
CHAPTER FIVE.BASIC TRIGONGMETRIC INEQUALITIES
CHAPTER SIX.POLYGONS INSCRIBED AND CIRCUMSCRIBED
CHAPTER SEVEN.ELLIPSES
CHAPTER EIGHT.THE BEES AND THEIR HEXAGONS
GHAPTER NINE.FURTHER GEOMETRIC RESULTS
CHAPTER TEN.APPLIED AND MISCELLANEOUS PROBLEMS
CHAPTER ELEVEN.EUCLIDEAN THREE-SPACE
CHAPTER TWELVE.ISOPERIMETRIC RESULTS NOT ASSUMING EXISTENGE
POSTSCRITP ON CALCULUS
SOLUTIONS OF PROBLEMS
REFERENCES
INDEX