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Nahin P.J. Ч When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible
Nahin P.J. Ч When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible

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Ќазвание: When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible

јвтор: Nahin P.J.

јннотаци€:

This book does so many things well, that I would get bored trying to explain them all. What really impressed me was the explanation of the Euler-Lagrange equation. What is incredible about the treatment is that it is so easy to understand but doesn't leave out any of the math. For anyone trying to teach themselves the calculus of variations I recommend this book as an intro before jumping into a textbook.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2007

 оличество страниц: 400

ƒобавлена в каталог: 24.08.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
action      see "Least action"
Algorithm, computational efficiency of      295 309Ч310 see
Almgren, Frederick      262 274
Anti-solar line      179Ч180 187 189 see
Apollonius of Perga      37
Appel, Kenneth      90
Archimedes      15 37 47
Area, of a figure      15 39 218Ч219 252 352Ч358
Aristotle      46 105
Bacon, Roger      192
Basketball      158Ч165
Bellman, Richard      312Ч314 316Ч317
Beltrami's identity      240 248Ч249 261 see
Beltrami, Eugenio      240
Berkeley, George      140 166
Bernoulli, Daniel      211
Bernoulli, Jacob      172 219 244Ч245
Bernoulli, Johann      139 172 174 197Ч198 210Ч212 214Ч215 217 219Ч221 228 233 240Ч245 249
Bertrand, Joseph      61
Besicovitch, Abram      60
Bird, Larry      160
Bolzano, Bernard      115
Boscovich, Ruggero      344
Bouvelles, Charles      217
Boys, C.V.      270 273Ч274
Boys, Marion      273Ч274
Brachistochrone      210Ч217 219Ч226 229Ч231 233Ч234 238Ч241 246
Calculus, differential      117Ч119 123 140Ч147 Calculus integral
Carroll, Lewis (Sylvie and Bruno Concluded)      230
Catenary      241Ч251
Catenoid      262 266Ч269
Cavalieri, B.F.      279
Chain rule      22 117 126 169 185 218 227 236 350
Chebyshev, Pafnuty      61Ч62
Clifford, William Kingdon      301
Computers, use of      24Ч36 79 84Ч85 88Ч94
Concave figure      54 60 Concave
Convex, figure      53Ч54 345Ч346 353Ч354
Convex, function      63 336Ч337 339Ч341 Convex hull
Cooper, Paul      229Ч230
Cuts, method of      see "Integer programming"
Cycloid      217Ч224 228Ч229 234 see
da Vinci, Leonardo      134
Dantzig, George      294Ч295 298 308Ч310
De L'Hospital, G-F-A      171Ч172 174 211 215
Delta Airline problem      284Ч285
Derivative of composite function      124Ч126 198Ч199 Derivative definition
Derivative of product      144Ч145 173 Derivative
Derivative, partial      236 358Ч359
Descartes, Rene      99Ч101 103Ч108 117 119Ч120 131 139 187Ч188 190 192
Dido, Queen of Carthage      45Ч46
Diet problems      297Ч304 308
Differential, arc length      221 238 243 247 252 260 Differential equation
Directed graph      290Ч293
Dirichlet, Peter      59
Dispersion of refracted light      138Ч139
Dorfman, Robert      308
Double bubble conjecture      269Ч271
Douglas, Jesse      263
Duality      6 13 55Ч56 68
Dynamic programming      291 295 305 312Ч329
Ehlers, G.      13
Ellipsoid algorithm      310
Elliptic integral      202 351
Energy, conservation of      167 204 214 221 347 Energy kinetic
Energy, potential      204 214 247 347
Equilibrium, stable      176Ч177 242 243
Erdos, Paul      62
Escape velocity      21 23Ч24
Euclid      7Ч8 60 72 101 134 331
Euler Ч Lagrange equation      145 231Ч242 248Ч250 252Ч257 260Ч262 359Ч360 see
Euler, Leonhard      70 233 259 262 264 351
Exponential time      309 311 see computational
Extrema, definition      3 7 112 142 155 Extrema global
Extrema, maximum/minimum      26Ч33 62Ч69 72Ч79 113 136 142Ч144 147 149Ч152 158 177 185
Factory problem      284
Fagnano, G.C.T.      65
Fagnano, G.F.      65
Feasible solution set      29Ч30 32Ч33 301Ч304 306 311 324
Fejer, Lipot      66
Fermat's point      279
Fermat, Pierre      90 99Ч100 104 106Ч115 117Ч120 123Ч124 127Ч128 130Ч134 140 211 279
fibonacci      71
Fields medal      309
Fizeau, Hippolyte      106
Folded envelope problem      79Ч85
Folium of Descartes      119Ч120
Fontana, Niccolo      see "Tartaglia"
Forysth, Andrew      274
Foucault, Jean      106
Four-color conjecture      90
Fourier, Joseph      296
Functional      210 222 233
Functional equation      313Ч314 316 318Ч319 324Ч328 see
Fundamental lemma, of calculus of variations      238
Galileo, Galilei      200Ч202 204 208Ч211 214 217 221 223 240Ч241 351
Gamma function      70
Gauss, C.F.      272 292
Geodesic      38
Ghost hubs      285Ч286
Goldschmidt, G.W.B.      266 271Ч272
Goldstein, Rebecca (Strange Attractors)      191 274
Golf      157Ч158
Gomory, Ralph      307
Gravitational field, motion in      21Ч24 95 152Ч171 200Ч210 347Ч351
Gregory, David      232
Gunnery problem      165Ч171
Haken, Wolfgang      90
Hales, Thomas      51 90
Halley, Edmond      166Ч168 171 198 220
Hanging chain problem      240Ч247 262
Hanging picture problem      73Ч77 91Ч94 147Ч148
Hariot, Thomas      103 106
Hawking, Stephen      197
Helprin, Mark (Winte's Tale)      246Ч247
Heron's formula      15 39 43
Heron, of Alexandria      15 102 127 132Ч134
Hoelder, Otto      341
Hoffmann, J.E.      280
Honeycomb conjecture      51 90
Hooke, Robert      250
Hudde, Johann      115
Huygens, Christiaan      7 104 220Ч221 241
Index of refraction      137Ч139 182 188
Induction, proof by      13 315Ч316 333 339Ч341
Inequality, AM-GM      13Ч20 49 75 77 331Ч333 338 Inequality AM-QM
Inequality, constraint      29 276 278 296Ч306 310Ч311 313 Inequality Jensen's
Inflection point      145
Integer programming      304Ч307 324 326
Integration, by parts      145 236Ч237 254
Interior algorithm      311
Isoperimetric problem      6 37Ч38 45Ч47 53Ч59 219 231 251Ч257 354;
Isoperimetric quotient      47Ч51 62
Jefferson, Thomas      250
Jensen, J.L.W.V.      53
Jungius, Joachim      241
Kakeya, S.      60
Kantorovich, Leonid      308Ч309
Karmarkar, Narendra      311Ч312
Kepler sphere packing conjecture      90
Kepler, Johannes      102 108Ч109
Khachiyan, Leonid      310
Kierkegaard, Soren      320
Klee, Victor      310Ч311
Koenig, J.S.      134 344
Koopmans, Tjalling      308
l'Hospital's rule      172Ч174
Lagrange multiplier      63 248 253 257 274
Lagrange, Joseph      117 134 233 262Ч263
Laplace, P.S.      117
Least action, principle of      134
Least time, principle of      107Ч108 127Ч128 174 210Ч211 221 231
Legendre, A.M.      351
Leibniz's rule      see "Derivative of
Leibniz, Gottfried      90 99 109 115 117 126 132 134 140 145 172 200 210 215 219 241 348
Length, of a curve      230 238 252 259
Leonardo of Pisa      see "Fibonacci"
Lhuilier, Simon      54
Light as particles      104 Light as waves
Linear programming      29 295Ч304 308Ч312
Maclaurin, Colin      331
Mailable package paradox      149Ч152
Mascheroni, Lorenzo      250
MATLAB      79 365
Maupertuis, P.L.M.      133Ч134
Mean, arithmetic      13 331 334;
Mean, geometric      13 331 Mean quadratic
Melville, Herman (Moby-Dick)      228
Minty, George      310Ч311
Muddy wheel problem      94Ч97
Mueller, Johann      see "Regiomontanus"
Nash, John      309
Newton Ч Raphson method      120Ч123 223 264
Newton's equation, for the Nth order rainbow      194
Newton's function      120Ч123
Newton, Isaac      21 90 99 109 115 117Ч120 122Ч123 140 143 166 171Ч172 193 197Ч198 200 210 215 219Ч220 231Ч232 250 351
Nobel Prize in economics      308Ч309
Nonlinear programming      326
Objective function      296 300Ч303 305Ч306 313
Optimal location problem      283Ч286
Optimal policy      314 319 321Ч329
Optimality, principle of      313Ч314 316Ч318
Pappus Of Alexandria      47 113 343
parabola      110Ч111 118Ч119 154 241 245Ч247 336Ч337
Parametric equations      217Ч219 222 224 252 259 352Ч353
Pipe-and-corner problem      85Ч89
Plateau problem      262 269
Plateau's rules      269Ч270 272 274 279
Plateau, Joseph      262 269 272
Polybius      38Ч39 45
Polynomial time      see "Algorithm computational
Polytope      see "Simplex"
Prime numbers      60Ч62 90
probability      8Ч9 183Ч184 251 328
Proclus      39 45
Ptolemy      102
Pulley problem      174Ч178 247
Rado, Tibor      263
Rainbow, infrared      198 Rainbow Nth
Rainbow, secondary      180 187Ч192 Rainbow tertiary
Raphson, Joseph      120 123
Recurrence, additive      318 Recurrence multiplicative
Reflection, law of      101Ч102 127 132Ч133 181 see
Refraction, law of      100Ч105 107Ч108 127 see
Regiomontanus      71 73Ч74
Riccati, J.R.      243 249
Roemer, Olaus      106
Saturn problem      77Ч79
Schmidt, Erhard      70
Schwarz, H.A.      70 263
Second law of motion      21 176 277
Shepard, Alan      2
simplex      301
Simplex algorithm      294 298Ч304 308Ч313 326
Simplicius      47
SIMPSON, THOMAS      123
Snel, Willebrord      102Ч104 127
Snell's law      102Ч108 127Ч132 138Ч139 179 182 184Ч185 187 190 193Ч195 201 210Ч213 231 see "Refraction"
Snowflake curve      40Ч45
Soap films      262Ч274 279
Solar line      196Ч197 see
Spanning circle      67Ч68
Steiner span      285
Steiner's number      199
Steiner's point      see "Fermat's point"
Steiner, Jacob      54Ч59 146Ч147 279
Stigler, George      297Ч298
Strange attractors      see "Goldstein Rebecca"
Surface, area of      15Ч19 259Ч271 352Ч358
Surface, energy of      262 269
Sylvester, J.J.      68
Tanenbaum, Robert K. (No Lesser Plea)      297
Tangent line      54 97 102 110Ч111 118 120Ч123 242 266
Tartaglia      71Ч72
Tautochrone      220 223Ч226 see
Taylor, Jean      262 269 274
Theodoric of Freiberg      192
Theon of Alexandria      47
Torricelli's point      see "Fermat's point"
Torricelli, Evangelisto      279
Toth, L.F.      344
Traveling salesman problem      293Ч294
Vector      11Ч12 31 357
Verne, Jules      24
Viviani, Vincenzo      279
Voltaire      134
Von Freiberg, Dietrich      see "Theodoric of Freiberg"
von Koch, Helge      40
Vos Savant, Marilyn      196
Water crossing problems      24Ч33 135Ч137
Weierstrass, Karl      251Ч252
Wells, H.G.      273
Wine barrel problem      108Ч109 148Ч149
Woods, Tiger      230
Zenodorus      47 49 51 54
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