Companion to Concrete Mathematics - Mathematical Techniques and Various Applications

Cover......Page 1
Title page......Page 2
Preface......Page 6
Contents (detailed)......Page 8
1. Conic sections......Page 14
2. Areas on a sphere......Page 15
3. Lines in a triangle......Page 20
4. Angle multisection......Page 22
5. Prismoidal formula......Page 24
6. Inversion......Page 25
7. Area and volume equivalence......Page 28
8. Isoperimetric problems for convex hulls......Page 33
9. Reflections and images......Page 39
10. Roulettes and pedals......Page 47
11. Integral geometry......Page 51
12. Convexity......Page 56
13. Curves in n dimensions......Page 62
1. Preliminaries......Page 64
2. Explicit iteration and conjugacy......Page 66
3. Duplication and triplication......Page 69
4. Extension to noninteger iteration......Page 72
5. Newton-Raphson method and iteration......Page 78
6. Approximate iteration......Page 80
7. Multiple recursions......Page 81
8. An application to probability......Page 86
9. Iteration of a function of several variables......Page 87
10. Iteration and orders of magnitude......Page 89
11. Iteration and reliable circuits......Page 91
1. Telescoping cancellation......Page 94
2. Euler\'s identity and Vieta\'s formula......Page 104
3. Euler\'s product and Cantor\'s theorem......Page 105
4. Telescoping coincidence......Page 107
5. Summation of certain series......Page 108
6. Products and factorization......Page 112
7. Infinite products and r-function......Page 114
8. The McLaurin series for tan x and sec x......Page 117
9. Euler acceleration and the Taylor series......Page 119
10. Generalizations of Taylor\'s series......Page 125
11. Blissard-Lucas calculus and the Bernoulli numbers......Page 131
12. Poisson summation formula......Page 135
13. Darboux and Euler-McLaurin formulas......Page 138
14. Lambert series......Page 140
1. Choosing a suitable additional unknown......Page 144
2. Multiplications, additions, and complexity......Page 145
3. Polygonal paths and minimization......Page 151
4. Some types of symmetry......Page 158
5. Extremal problems and extremal points......Page 161
6. Circles on a torus......Page 167
7. Composite estimates......Page 168
8. Sequential localization and maxima of unimodal surfaces......Page 172
9. Working backward from the end and working from both ends......Page 174
10. Computing Pi......Page 177
11. The generalized firing squad synchronization and the labyrinth problems......Page 182
1. Integrals evaluable by Fubini\'s theorem......Page 188
2. Differentiation with respect to a parameter......Page 192
3. Integrals evaluable from first principles......Page 198
4. Dilogarithms......Page 200
5. Crofton\'s theorem and configuration averages......Page 203
6. Forbidden configurations and discontinuous factors......Page 207
7. Miscellaneous......Page 210
8. Integration and Mensuration......Page 214
9. Reduction of multiple integrals to single ones......Page 215
10. Integration as a source of new functions......Page 218
1. Principle of specialization and generating function......Page 226
2. Irrationality proofs......Page 230
3. Partitions and expanding infinite products in series......Page 233
4. Principle of infinite crowding......Page 237
5. Applications of certain special functions......Page 242
6. Continuation principle......Page 249
7. Asymptotic analysis......Page 254
8. Coincidences, forbidden configurations, and hypergraphs......Page 262
BIBLIOGRAPHY......Page 274
INDEX......Page 278