鲁宾逊非标准微积分与国内高等数学“秀肌肉”

     大家知道，数学概念与词组相互对应。对于数学教科书而言，所谓“秀肌肉”就是显示该教科书包含有多少“微概念”，也就是说，展示自己的词组索引的丰富度即可。                   

    根据初步统计，鲁宾逊非标准微积分教科书具有各类数学概念词组大约有1800多个。然而，很可惜的是，我们国内高等数学教材一般没有本书的词组索引，无法直接对比“秀肌肉”。        

袁萌  陈启清 10月26日

附：鲁宾逊非标准微积分的词组索引

Index

trapezoidal, 226 surface, 825 Absolute value, 12 within E, 284 surface of revolution, 328 of a complex number, 876 Arc, 323, 365 under a curve, 188 Absolute value function, 12 length, 324, 366, 420 Argand diagram, 876 Acceleration, 94 arccos, 384 Argument, complex number, vector, 565, 623 Arccosecant, 384 876 Addition formulas for sine derivative, 387 Associative Law, 905 and cosine, 372 Arccosine, 384 inner product, 597 Addition Property, 190, 303 derivative, 387 scalar multiples, 570 variables integral, 392 vector product, failure, 602 two, 712, 720 arccot, 384 vector sum, 568 three, 760 Arccotangent, 384 Asymptote Adiabatic process, 490 derivative, 387 of a hyperbola, 270 Almqst parallel vectors, 632 arccsc, 384 vertical, 251 Alternating series, 517 Archimedes, 902 Average slope, 22, 168 harmonic, 520, 546 arcsec, 384 Average speed, 339 Alternating Series Test, 518 Arcsecant, 384 Average value, 337 Amplitude, 886 derivative, 387 Average velocity, 169, 339 Angle, 77, 365 integral, 473 Axioms between vectors, 573 arcsin, 384 for hyperreal numbers, 906 three dimensions, 588 Arcsine, 384 for real numbers, 905 Angular measure, 367 derivative, 387 Axis Anticommutative Law for integral, 392 coordinates vector products, 604 power series, 560 plane, 3 Antiderivative, 192 arctan, 384 space, 585 Approximation Arctangent, 384 ellipse, 264 by alternating series, 518 derivative, 387 hyperbola, 268 arctan x, 541 integral, 472 parabola, 257 by derivatives, 286 power series, 536 e, 442, 551 Area Barrow, Isaac, 902 In x, 541 below a curve, 188 Basis vectors by Newton's method, 290 between two curves, 220, plane, 570 pi, 542 304 space, 587 by power series, 541 double integral, 722 Bell-shaped curve, 537 by Riemann sums, 178 geometric figures, 115 Berkeley, Bishop, 903 Simpson's, 230 by Green's Theorem, 818 Binomial series, 558 sin x, 552 infinite, 353 Binomial Theorem, 559 by Taylor's Formula, 547 polar, 421 Bound variable, 119, 178

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