Calculus: Concepts and MethodsCambridge University Press, 7 févr. 2002 The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science. |
Table des matières
CV | 268 |
CVI | 275 |
CVII | 277 |
CVIII | 281 |
CX | 282 |
CXI | 287 |
CXII | 289 |
CXIII | 290 |
XII | 38 |
XIII | 40 |
XIV | 43 |
XV | 45 |
XVI | 46 |
XVIII | 47 |
XIX | 48 |
XX | 49 |
XXI | 51 |
XXIV | 52 |
XXVI | 53 |
XXVIII | 55 |
XXIX | 57 |
XXX | 59 |
XXXI | 60 |
XXXII | 61 |
XXXIII | 63 |
XXXIV | 64 |
XXXV | 65 |
XXXVI | 69 |
XXXVII | 71 |
XXXVIII | 72 |
XXXIX | 76 |
XL | 80 |
XLI | 87 |
XLII | 88 |
XLIII | 89 |
XLIV | 92 |
XLV | 96 |
XLVI | 98 |
XLVII | 100 |
XLIX | 106 |
L | 110 |
LI | 111 |
LII | 114 |
LIII | 115 |
LIV | 120 |
LVI | 122 |
LVIII | 125 |
LX | 128 |
LXI | 130 |
LXII | 132 |
LXIII | 135 |
LXIV | 139 |
LXV | 143 |
LXVII | 145 |
LXVIII | 149 |
LXIX | 153 |
LXX | 155 |
LXXI | 162 |
LXXII | 163 |
LXXIII | 168 |
LXXIV | 170 |
LXXV | 174 |
LXXVI | 179 |
LXXVII | 185 |
LXXVIII | 188 |
LXXIX | 193 |
LXXX | 200 |
LXXXI | 203 |
LXXXII | 208 |
LXXXIII | 210 |
LXXXIV | 217 |
LXXXV | 219 |
LXXXVI | 220 |
LXXXVII | 223 |
LXXXVIII | 224 |
LXXXIX | 227 |
XC | 229 |
XCI | 231 |
XCII | 233 |
XCIII | 235 |
XCIV | 237 |
XCV | 238 |
XCVI | 241 |
XCVII | 247 |
XCVIII | 254 |
XCIX | 256 |
C | 259 |
CI | 263 |
CII | 265 |
CIV | 266 |
CXIV | 292 |
CXV | 295 |
CXVII | 297 |
CXVIII | 298 |
CXIX | 300 |
CXX | 302 |
CXXI | 304 |
CXXII | 308 |
CXXIII | 309 |
CXXIV | 311 |
CXXV | 313 |
CXXVI | 316 |
CXXVII | 320 |
CXXVIII | 323 |
CXXIX | 325 |
CXXX | 326 |
CXXXI | 328 |
CXXXII | 329 |
CXXXIII | 330 |
CXXXIV | 331 |
CXXXV | 333 |
CXXXVI | 334 |
CXXXVII | 335 |
CXXXVIII | 336 |
CXXXIX | 339 |
CXL | 341 |
CXLII | 345 |
CXLIII | 347 |
CXLIV | 353 |
CXLV | 360 |
CXLVI | 361 |
CXLVII | 363 |
CXLVIII | 366 |
CL | 367 |
CLI | 368 |
CLII | 369 |
CLIII | 370 |
CLIV | 373 |
CLVI | 374 |
CLVII | 375 |
CLIX | 382 |
CLX | 384 |
CLXI | 387 |
CLXII | 389 |
CLXIII | 392 |
CLXIV | 393 |
CLXV | 395 |
CLXVI | 397 |
CLXVII | 399 |
CLXVIII | 405 |
CLXX | 406 |
CLXXI | 407 |
CLXXII | 409 |
CLXXIII | 410 |
CLXXIV | 412 |
CLXXV | 414 |
CLXXVI | 416 |
CLXXVII | 417 |
CLXXVIII | 419 |
CLXXIX | 421 |
CLXXXI | 423 |
CLXXXII | 425 |
CLXXXIII | 426 |
CLXXXIV | 429 |
CLXXXV | 431 |
CLXXXVI | 434 |
CLXXXVII | 435 |
CLXXXVIII | 441 |
CLXXXIX | 444 |
CXC | 447 |
CXCI | 453 |
CXCII | 454 |
CXCIII | 458 |
CXCIV | 461 |
CXCV | 462 |
CXCVI | 467 |
CXCVII | 471 |
CXCVIII | 549 |
550 | |
556 | |
Expressions et termes fréquents
affine function arbitrary constants arctan boundary conditions calculate chain rule change of variable chapter cobweb model commodity bundle complex numbers concave consider constrained stationary point constraint convergence convex coordinates cos.v cos0 critical points curve det(A diagram difference equation differentiable solution direction dv dv dx dx dx dy eigenvalues equilibrium evaluate Example Exercise Find formula found by solving function f given global maximum graph Hence homogeneous hyperplane implicit function theorem Indifference curve intersection inverse function invertible matrix local maximum lt follows matrix maximise minimum multiple normal Observe obtain orthogonal partial derivatives particular solution polynomial probability density function problem random variable rate of increase real numbers region result roots saddle point satisfies Show sin.v stationary points Substituting Suppose surface tangent hyperplane tangent plane Taylor approximation theorem unique local differentiable unit vector valued function write zero