1881:
only worry about at the annual calibration.") In this usage, the ordinality of the approximation is not exact, but is used to emphasize its insignificance; the higher the number used, the less important the effect. The terminology, in this context, represents a high level of precision required to account for an effect which is inferred to be very small when compared to the overall subject matter. The higher the order, the more precision is required to measure the effect, and therefore the smallness of the effect in comparison to the overall measurement.
40:
155:
662:
1679:, residents") is generally given. As in the examples above, the term "2nd order" refers to the number of exact numerals given for the imprecise quantity. In this case, "3" and "9" are given as the two successive levels of precision, instead of simply the "4" from the first order, or "a few" from the zeroth order found in the examples above.
444:
1880:
by scientists and engineers to describe phenomena that can be neglected as not significant (e.g. "Of course the rotation of the Earth affects our experiment, but it's such a high-order effect that we wouldn't be able to measure it." or "At these velocities, relativity is a fourth-order effect that we
1652:
is an approximate fit to the data. In this example there is a zeroth-order approximation that is the same as the first-order, but the method of getting there is different; i.e. a wild stab in the dark at a relationship happened to be as good as an "educated guess".
1852:
is an approximate fit to the data. In this case, with only three data points, a parabola is an exact fit based on the data provided. However, the data points for most of the interval are not available, which advises caution (see "zeroth order").
657:{\displaystyle e^{x}=\underbrace {1} _{0^{\text{th}}}+\underbrace {x} _{1^{\text{st}}}+\underbrace {\frac {x^{2}}{2!}} _{2^{\text{nd}}}+\underbrace {\frac {x^{3}}{3!}} _{3^{\text{rd}}}+\underbrace {\frac {x^{4}}{4!}} _{4^{\text{th}}}+\ldots \;,}
1502:
A first-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a linear approximation, straight line with a slope: a polynomial of degree 1. For example:
1499:, residents"). In the case of a first-order approximation, at least one number given is exact. In the zeroth-order example above, the quantity "a few" was given, but in the first-order example, the number "4" is given.
1487:
is the term scientists use for a slightly better answer. Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has
1452:
One should be careful though, because the multiplicative function will be defined for the whole interval. If only three data points are available, one has no knowledge about the rest of the
1667:
is the term scientists use for a decent-quality answer. Few simplifying assumptions are made, and when a number is needed, an answer with two or more significant figures ("the town has
371:. Higher order of approximation is not always more useful than the lower one. For example, if a quantity is constant within the whole interval, approximating it with a second-order
1847:
1647:
867:
1409:
1226:
1024:
825:
1447:
1247:. Thus quoting an average value containing three significant digits in the output with just one significant digit in the input data could be recognized as an example of
785:
746:
968:
896:
1786:
1738:
1599:
1551:
1362:
1314:
1184:
1136:
939:
919:
708:
685:
1460:
could have another component which equals 0 at the ends and in the middle of the interval. A number of functions having this property are known, for example
1861:
While higher-order approximations exist and are crucial to a better understanding and description of reality, they are not typically referred to by number.
2917:
2905:
3027:
2912:
2895:
2890:
2900:
2885:
1999:
136:
1057:
approximation. The zero of "zeroth-order" represents the fact that even the only number given, "a few", is itself loosely defined.
2187:
2880:
1682:
A second-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a
17:
1905:
2497:
2251:
1251:. With the implied accuracy of the data points of ±0.5, the zeroth order approximation could at best yield the result for
2049:
830:
1864:
Continuing the above, a third-order approximation would be required to perfectly fit four data points, and so on. See
2995:
2854:
1937:
195:
2409:
2325:
1414:
The accuracy of the result justifies an attempt to derive a multiplicative function for that average, for example,
1231:
could be – if data point accuracy were reported – an approximate fit to the data, obtained by simply averaging the
364:
2990:
2922:
2547:
2402:
2370:
2129:
336:. However, this may be confusing, as these formal expressions do not directly refer to the order of derivatives.
1244:
2623:
2600:
2315:
1966:
1949:
2713:
2651:
2446:
2320:
1992:
438:
129:
3053:
2199:
2177:
59:
3022:
1792:
3058:
3007:
2773:
2387:
2209:
177:
2392:
2162:
1605:
1373:
2811:
2758:
1190:
973:
790:
2219:
1240:
2927:
2698:
2246:
1985:
1865:
1420:
233:
173:
122:
237:
2693:
2365:
249:
2821:
2703:
2524:
2472:
2278:
2256:
1473:
1453:
1077:
1061:
751:
410:
391:
356:
352:
713:
2947:
2806:
2718:
2375:
2310:
2283:
2273:
2194:
2182:
2167:
2139:
1053:
residents", when it has 3,914 people in actuality. This is also sometimes referred to as an
2763:
2382:
2229:
1683:
402:
110:
100:
944:
872:
8:
2783:
2708:
2595:
2552:
2303:
2288:
2119:
2107:
2094:
2054:
2034:
1895:
1744:
1696:
1557:
1509:
1320:
1272:
1142:
1094:
434:
430:
165:
79:
924:
901:
690:
667:
397:, which is obtained by truncating the Taylor series to this degree. The formal usage of
2872:
2847:
2678:
2631:
2572:
2537:
2532:
2512:
2507:
2502:
2467:
2414:
2397:
2298:
2172:
2157:
2102:
2069:
1260:
1081:
1054:
1046:
333:
329:
3012:
2836:
2768:
2590:
2567:
2441:
2434:
2337:
2152:
2044:
1933:
1042:
340:
39:
2970:
2753:
2666:
2646:
2577:
2487:
2429:
2421:
2355:
2268:
2029:
2024:
406:
282:
245:
344:
3032:
3017:
2801:
2656:
2636:
2605:
2582:
2562:
2456:
2112:
2059:
1248:
379:
74:
2942:
2841:
2688:
2641:
2542:
2345:
1910:
241:
64:
2360:
3047:
2816:
2671:
2557:
2261:
2236:
1900:
1890:
1877:
1469:
1045:
are made, and when a number is needed, an order-of-magnitude answer (or zero
426:
372:
368:
221:
105:
95:
69:
2826:
2796:
2661:
2224:
274:
2074:
2016:
1065:
213:
2791:
2723:
2477:
2350:
2214:
2204:
2147:
1073:
387:
351:
is expected to indicate progressively more refined approximations of a
2985:
2733:
2728:
2039:
1038:
1476:, but the approximation alone does not provide conclusive evidence.
2980:
2482:
2008:
1687:
360:
2831:
2084:
1069:
209:
425:
etc.) used above meaning do not directly give information about
413:. The error usually varies within the interval. Thus the terms (
3000:
2064:
301:
2079:
1971:
in Online
Dictionary and Translations Webster-dictionary.org.
1954:
in Online
Dictionary and Translations Webster-dictionary.org.
1085:
220:
refers to formal or informal expressions for how accurate an
1049:) is often given. For example, you might say "the town has
1977:
1932:
in
Webster's Third New International Dictionary, Könemann,
787:
each higher order term is smaller than the previous. If
367:
to devise a new application or, on the contrary, try to
359:. The choice of order of approximation depends on the
1795:
1747:
1699:
1608:
1560:
1512:
1423:
1376:
1323:
1275:
1193:
1145:
1097:
976:
947:
927:
904:
875:
833:
793:
754:
716:
693:
670:
447:
1456:, which may be a large part of it. This means that
328:is sometimes informally used to mean the number of
227:
1841:
1780:
1732:
1641:
1593:
1545:
1441:
1403:
1356:
1308:
1220:
1178:
1130:
1018:
962:
933:
913:
890:
861:
819:
779:
740:
702:
679:
656:
401:corresponds to the omission of some terms of the
3045:
1690:: a polynomial of degree 2. For example:
339:The choice of series expansion depends on the
1993:
332:, in increasing order of accuracy, or to the
285:are occasionally used in expressions like an
130:
304:that have less formal meaning. Phrases like
176:. There might be a discussion about this on
1255:of ~3.7 ± 2.0 in the interval of
921:is not smaller than the zeroth-order term,
2000:
1986:
1367:the zeroth-order approximation results in
650:
137:
123:
3028:Regiomontanus' angle maximization problem
1088:: a polynomial of degree 0. For example,
1026:is greater than the zeroth-order term.
1015:
816:
314:a roughly approximate value of a quantity
196:Learn how and when to remove this message
2871:
2376:Differentiating under the integral sign
1239:values. However, data points represent
14:
3046:
216:, and other quantitative disciplines,
27:Expressions for approximation accuracy
2252:Inverse functions and differentiation
1981:
1962:
1960:
1842:{\displaystyle y\sim f(x)=x^{2}-x+3}
1266:If the data points are reported as
827:then the first order approximation,
148:
1871:
1041:use for a first rough answer. Many
363:. One may wish to simplify a known
24:
2050:Free variables and bound variables
1259:from −0.5 to 2.5, considering the
1060:A zeroth-order approximation of a
25:
3070:
2855:The Method of Mechanical Theorems
1957:
1642:{\displaystyle y\sim f(x)=x+2.67}
862:{\displaystyle e^{x}\approx 1+x,}
375:will not increase the accuracy.
2410:Partial fractions in integration
2326:Stochastic differential equation
1404:{\displaystyle y\sim f(x)=3.67.}
228:Usage in science and engineering
153:
38:
2548:Jacobian matrix and determinant
2403:Tangent half-angle substitution
2371:Fundamental theorem of calculus
1856:
1659:
1472:is useful and helps predict an
1221:{\displaystyle y\sim f(x)=3.67}
1029:
1019:{\displaystyle 2^{3}/3!=4/3,\,}
820:{\displaystyle |x|<<1,\,}
2624:Arithmetico-geometric sequence
2316:Ordinary differential equation
1943:
1923:
1811:
1805:
1772:
1754:
1724:
1706:
1624:
1618:
1585:
1567:
1537:
1519:
1479:
1392:
1386:
1348:
1330:
1300:
1282:
1209:
1203:
1170:
1152:
1122:
1104:
803:
795:
764:
756:
13:
1:
2447:Integro-differential equation
2321:Partial differential equation
1916:
1442:{\displaystyle y\sim x+2.67.}
869:is often sufficient. But at
2007:
1245:points in Euclidean geometry
970:even the second-order term,
386:th-order approximation is a
7:
2601:Generalized Stokes' theorem
2388:Integration by substitution
1884:
273:, and so forth are used as
232:In formal expressions, the
10:
3075:
2130:(ε, δ)-definition of limit
1876:These terms are also used
1665:Second-order approximation
1035:Zeroth-order approximation
369:fit a curve to data points
3023:Proof that 22/7 exceeds π
2960:
2938:
2864:
2812:Gottfried Wilhelm Leibniz
2782:
2759:e (mathematical constant)
2744:
2616:
2523:
2455:
2336:
2138:
2093:
2015:
1968:to a zeroth approximation
1485:First-order approximation
780:{\displaystyle |x|<1,}
664:the zeroth-order term is
318:to a zeroth approximation
296:The omission of the word
2774:Stirling's approximation
2247:Implicit differentiation
2195:Rules of differentiation
1951:to a first approximation
1866:polynomial interpolation
1243:and they do differ from
741:{\displaystyle x^{2}/2,}
687:the first-order term is
310:to a first approximation
287:order-zero approximation
279:zero-order approximation
3008:Euler–Maclaurin formula
2913:trigonometric functions
2366:Constant of integration
1241:results of measurements
1043:simplifying assumptions
291:order-one approximation
55:Orders of approximation
18:Orders of approximation
2977:Differential geometry
2822:Infinitesimal calculus
2525:Multivariable calculus
2473:Directional derivative
2279:Second derivative test
2257:Logarithmic derivative
2230:General Leibniz's rule
2125:Order of approximation
1843:
1782:
1734:
1643:
1595:
1547:
1443:
1405:
1358:
1310:
1222:
1180:
1132:
1020:
964:
935:
915:
898:the first-order term,
892:
863:
821:
781:
742:
704:
681:
658:
433:. For example, in the
399:order of approximation
349:order of approximation
343:used to investigate a
326:order of approximation
252:. The expressions: a
240:refers to the highest
218:order of approximation
2896:logarithmic functions
2891:exponential functions
2807:Generality of algebra
2685:Tests of convergence
2311:Differential equation
2295:Further applications
2284:Extreme value theorem
2274:First derivative test
2168:Differential operator
2140:Differential calculus
1906:Chapman–Enskog method
1844:
1783:
1735:
1644:
1596:
1548:
1444:
1406:
1359:
1311:
1223:
1181:
1133:
1021:
965:
936:
916:
893:
864:
822:
782:
743:
705:
682:
659:
236:used before the word
2961:Miscellaneous topics
2901:hyperbolic functions
2886:irrational functions
2764:Exponential function
2617:Sequences and series
2383:Integration by parts
1793:
1745:
1697:
1684:quadratic polynomial
1606:
1558:
1510:
1421:
1374:
1321:
1273:
1191:
1143:
1095:
974:
963:{\displaystyle x=2,}
945:
925:
902:
891:{\displaystyle x=1,}
873:
831:
791:
752:
714:
691:
668:
445:
439:exponential function
166:confusing or unclear
111:Scientific modelling
101:Generalization error
3054:Perturbation theory
2948:List of derivatives
2784:History of calculus
2699:Cauchy condensation
2596:Exterior derivative
2553:Lagrange multiplier
2289:Maximum and minimum
2120:Limit of a sequence
2108:Limit of a function
2055:Graph of a function
2035:Continuous function
1930:first approximation
1896:Perturbation theory
1781:{\displaystyle y=,}
1733:{\displaystyle x=,}
1686:, geometrically, a
1677:thirty-nine hundred
1594:{\displaystyle y=,}
1546:{\displaystyle x=,}
1357:{\displaystyle y=,}
1309:{\displaystyle x=,}
1179:{\displaystyle y=,}
1131:{\displaystyle x=,}
1047:significant figures
431:significant figures
365:analytic expression
330:significant figures
306:first approximation
277:. The expression a
174:clarify the article
80:Significant figures
3059:Numerical analysis
2881:rational functions
2848:Method of Fluxions
2694:Alternating series
2591:Differential forms
2573:Partial derivative
2533:Divergence theorem
2415:Quadratic integral
2183:Leibniz's notation
2173:Mean value theorem
2158:Partial derivative
2103:Indeterminate form
1839:
1778:
1730:
1639:
1591:
1543:
1439:
1401:
1354:
1306:
1261:standard deviation
1218:
1176:
1128:
1055:order-of-magnitude
1016:
960:
934:{\displaystyle 1.}
931:
914:{\displaystyle x,}
911:
888:
859:
817:
777:
738:
703:{\displaystyle x,}
700:
680:{\displaystyle 1;}
677:
654:
643:
629:
599:
585:
555:
541:
511:
497:
484:
470:
334:order of magnitude
324:. The expression
88:Other fundamentals
3041:
3040:
2967:Complex calculus
2956:
2955:
2837:Law of Continuity
2769:Natural logarithm
2754:Bernoulli numbers
2745:Special functions
2704:Direct comparison
2568:Multiple integral
2442:Integral equation
2338:Integral calculus
2269:Stationary points
2243:Other techniques
2188:Newton's notation
2153:Second derivative
2045:Finite difference
1474:analytic solution
748:and so forth. If
639:
625:
605:
603:
595:
581:
561:
559:
551:
537:
517:
515:
507:
490:
488:
480:
463:
461:
437:expansion of the
378:In the case of a
347:. The expression
341:scientific method
283:Cardinal numerals
206:
205:
198:
147:
146:
106:Taylor polynomial
33:Fit approximation
16:(Redirected from
3066:
2971:Contour integral
2869:
2868:
2719:Limit comparison
2628:Types of series
2587:Advanced topics
2578:Surface integral
2422:Trapezoidal rule
2361:Basic properties
2356:Riemann integral
2304:Taylor's theorem
2030:Concave function
2025:Binomial theorem
2002:
1995:
1988:
1979:
1978:
1972:
1964:
1955:
1947:
1941:
1927:
1872:Colloquial usage
1848:
1846:
1845:
1840:
1826:
1825:
1787:
1785:
1784:
1779:
1739:
1737:
1736:
1731:
1674:
1672:
1648:
1646:
1645:
1640:
1600:
1598:
1597:
1592:
1552:
1550:
1549:
1544:
1494:
1492:
1448:
1446:
1445:
1440:
1410:
1408:
1407:
1402:
1363:
1361:
1360:
1355:
1315:
1313:
1312:
1307:
1227:
1225:
1224:
1219:
1185:
1183:
1182:
1177:
1137:
1135:
1134:
1129:
1072:to fit multiple
1025:
1023:
1022:
1017:
1008:
991:
986:
985:
969:
967:
966:
961:
940:
938:
937:
932:
920:
918:
917:
912:
897:
895:
894:
889:
868:
866:
865:
860:
843:
842:
826:
824:
823:
818:
806:
798:
786:
784:
783:
778:
767:
759:
747:
745:
744:
739:
731:
726:
725:
710:second-order is
709:
707:
706:
701:
686:
684:
683:
678:
663:
661:
660:
655:
642:
641:
640:
637:
630:
624:
616:
615:
606:
598:
597:
596:
593:
586:
580:
572:
571:
562:
554:
553:
552:
549:
542:
536:
528:
527:
518:
510:
509:
508:
505:
498:
483:
482:
481:
478:
471:
457:
456:
361:research purpose
281:is also common.
246:series expansion
201:
194:
190:
187:
181:
157:
156:
149:
139:
132:
125:
42:
30:
29:
21:
3074:
3073:
3069:
3068:
3067:
3065:
3064:
3063:
3044:
3043:
3042:
3037:
3033:Steinmetz solid
3018:Integration Bee
2952:
2934:
2860:
2802:Colin Maclaurin
2778:
2746:
2740:
2612:
2606:Tensor calculus
2583:Volume integral
2519:
2494:Basic theorems
2457:Vector calculus
2451:
2332:
2299:Newton's method
2134:
2113:One-sided limit
2089:
2070:Rolle's theorem
2060:Linear function
2011:
2006:
1976:
1975:
1965:
1958:
1948:
1944:
1928:
1924:
1919:
1887:
1874:
1859:
1821:
1817:
1794:
1791:
1790:
1746:
1743:
1742:
1698:
1695:
1694:
1670:
1668:
1662:
1656:
1607:
1604:
1603:
1559:
1556:
1555:
1511:
1508:
1507:
1490:
1488:
1482:
1422:
1419:
1418:
1375:
1372:
1371:
1322:
1319:
1318:
1274:
1271:
1270:
1249:false precision
1235:values and the
1192:
1189:
1188:
1144:
1141:
1140:
1096:
1093:
1092:
1032:
1004:
987:
981:
977:
975:
972:
971:
946:
943:
942:
926:
923:
922:
903:
900:
899:
874:
871:
870:
838:
834:
832:
829:
828:
802:
794:
792:
789:
788:
763:
755:
753:
750:
749:
727:
721:
717:
715:
712:
711:
692:
689:
688:
669:
666:
665:
636:
632:
631:
617:
611:
607:
604:
592:
588:
587:
573:
567:
563:
560:
548:
544:
543:
529:
523:
519:
516:
504:
500:
499:
489:
477:
473:
472:
462:
452:
448:
446:
443:
442:
409:. This affects
380:smooth function
355:in a specified
230:
202:
191:
185:
182:
171:
158:
154:
143:
75:False precision
28:
23:
22:
15:
12:
11:
5:
3072:
3062:
3061:
3056:
3039:
3038:
3036:
3035:
3030:
3025:
3020:
3015:
3013:Gabriel's horn
3010:
3005:
3004:
3003:
2998:
2993:
2988:
2983:
2975:
2974:
2973:
2964:
2962:
2958:
2957:
2954:
2953:
2951:
2950:
2945:
2943:List of limits
2939:
2936:
2935:
2933:
2932:
2931:
2930:
2925:
2920:
2910:
2909:
2908:
2898:
2893:
2888:
2883:
2877:
2875:
2866:
2862:
2861:
2859:
2858:
2851:
2844:
2842:Leonhard Euler
2839:
2834:
2829:
2824:
2819:
2814:
2809:
2804:
2799:
2794:
2788:
2786:
2780:
2779:
2777:
2776:
2771:
2766:
2761:
2756:
2750:
2748:
2742:
2741:
2739:
2738:
2737:
2736:
2731:
2726:
2721:
2716:
2711:
2706:
2701:
2696:
2691:
2683:
2682:
2681:
2676:
2675:
2674:
2669:
2659:
2654:
2649:
2644:
2639:
2634:
2626:
2620:
2618:
2614:
2613:
2611:
2610:
2609:
2608:
2603:
2598:
2593:
2585:
2580:
2575:
2570:
2565:
2560:
2555:
2550:
2545:
2543:Hessian matrix
2540:
2535:
2529:
2527:
2521:
2520:
2518:
2517:
2516:
2515:
2510:
2505:
2500:
2498:Line integrals
2492:
2491:
2490:
2485:
2480:
2475:
2470:
2461:
2459:
2453:
2452:
2450:
2449:
2444:
2439:
2438:
2437:
2432:
2424:
2419:
2418:
2417:
2407:
2406:
2405:
2400:
2395:
2385:
2380:
2379:
2378:
2368:
2363:
2358:
2353:
2348:
2346:Antiderivative
2342:
2340:
2334:
2333:
2331:
2330:
2329:
2328:
2323:
2318:
2308:
2307:
2306:
2301:
2293:
2292:
2291:
2286:
2281:
2276:
2266:
2265:
2264:
2259:
2254:
2249:
2241:
2240:
2239:
2234:
2233:
2232:
2222:
2217:
2212:
2207:
2202:
2192:
2191:
2190:
2185:
2175:
2170:
2165:
2160:
2155:
2150:
2144:
2142:
2136:
2135:
2133:
2132:
2127:
2122:
2117:
2116:
2115:
2105:
2099:
2097:
2091:
2090:
2088:
2087:
2082:
2077:
2072:
2067:
2062:
2057:
2052:
2047:
2042:
2037:
2032:
2027:
2021:
2019:
2013:
2012:
2005:
2004:
1997:
1990:
1982:
1974:
1973:
1956:
1942:
1921:
1920:
1918:
1915:
1914:
1913:
1911:Big O notation
1908:
1903:
1898:
1893:
1886:
1883:
1873:
1870:
1858:
1855:
1850:
1849:
1838:
1835:
1832:
1829:
1824:
1820:
1816:
1813:
1810:
1807:
1804:
1801:
1798:
1788:
1777:
1774:
1771:
1768:
1765:
1762:
1759:
1756:
1753:
1750:
1740:
1729:
1726:
1723:
1720:
1717:
1714:
1711:
1708:
1705:
1702:
1661:
1658:
1650:
1649:
1638:
1635:
1632:
1629:
1626:
1623:
1620:
1617:
1614:
1611:
1601:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1569:
1566:
1563:
1553:
1542:
1539:
1536:
1533:
1530:
1527:
1524:
1521:
1518:
1515:
1481:
1478:
1450:
1449:
1438:
1435:
1432:
1429:
1426:
1412:
1411:
1400:
1397:
1394:
1391:
1388:
1385:
1382:
1379:
1365:
1364:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1332:
1329:
1326:
1316:
1305:
1302:
1299:
1296:
1293:
1290:
1287:
1284:
1281:
1278:
1229:
1228:
1217:
1214:
1211:
1208:
1205:
1202:
1199:
1196:
1186:
1175:
1172:
1169:
1166:
1163:
1160:
1157:
1154:
1151:
1148:
1138:
1127:
1124:
1121:
1118:
1115:
1112:
1109:
1106:
1103:
1100:
1068:determining a
1066:mathematically
1051:a few thousand
1031:
1028:
1014:
1011:
1007:
1003:
1000:
997:
994:
990:
984:
980:
959:
956:
953:
950:
930:
910:
907:
887:
884:
881:
878:
858:
855:
852:
849:
846:
841:
837:
815:
812:
809:
805:
801:
797:
776:
773:
770:
766:
762:
758:
737:
734:
730:
724:
720:
699:
696:
676:
673:
653:
649:
646:
635:
628:
623:
620:
614:
610:
602:
591:
584:
579:
576:
570:
566:
558:
547:
540:
535:
532:
526:
522:
514:
503:
496:
493:
487:
476:
469:
466:
460:
455:
451:
316:. The phrase
234:ordinal number
229:
226:
204:
203:
161:
159:
152:
145:
144:
142:
141:
134:
127:
119:
116:
115:
114:
113:
108:
103:
98:
90:
89:
85:
84:
83:
82:
77:
72:
67:
65:Big O notation
62:
60:Scale analysis
57:
49:
48:
44:
43:
35:
34:
26:
9:
6:
4:
3:
2:
3071:
3060:
3057:
3055:
3052:
3051:
3049:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2978:
2976:
2972:
2969:
2968:
2966:
2965:
2963:
2959:
2949:
2946:
2944:
2941:
2940:
2937:
2929:
2926:
2924:
2921:
2919:
2916:
2915:
2914:
2911:
2907:
2904:
2903:
2902:
2899:
2897:
2894:
2892:
2889:
2887:
2884:
2882:
2879:
2878:
2876:
2874:
2870:
2867:
2863:
2857:
2856:
2852:
2850:
2849:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2817:Infinitesimal
2815:
2813:
2810:
2808:
2805:
2803:
2800:
2798:
2795:
2793:
2790:
2789:
2787:
2785:
2781:
2775:
2772:
2770:
2767:
2765:
2762:
2760:
2757:
2755:
2752:
2751:
2749:
2743:
2735:
2732:
2730:
2727:
2725:
2722:
2720:
2717:
2715:
2712:
2710:
2707:
2705:
2702:
2700:
2697:
2695:
2692:
2690:
2687:
2686:
2684:
2680:
2677:
2673:
2670:
2668:
2665:
2664:
2663:
2660:
2658:
2655:
2653:
2650:
2648:
2645:
2643:
2640:
2638:
2635:
2633:
2630:
2629:
2627:
2625:
2622:
2621:
2619:
2615:
2607:
2604:
2602:
2599:
2597:
2594:
2592:
2589:
2588:
2586:
2584:
2581:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2558:Line integral
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2530:
2528:
2526:
2522:
2514:
2511:
2509:
2506:
2504:
2501:
2499:
2496:
2495:
2493:
2489:
2486:
2484:
2481:
2479:
2476:
2474:
2471:
2469:
2466:
2465:
2463:
2462:
2460:
2458:
2454:
2448:
2445:
2443:
2440:
2436:
2433:
2431:
2430:Washer method
2428:
2427:
2425:
2423:
2420:
2416:
2413:
2412:
2411:
2408:
2404:
2401:
2399:
2396:
2394:
2393:trigonometric
2391:
2390:
2389:
2386:
2384:
2381:
2377:
2374:
2373:
2372:
2369:
2367:
2364:
2362:
2359:
2357:
2354:
2352:
2349:
2347:
2344:
2343:
2341:
2339:
2335:
2327:
2324:
2322:
2319:
2317:
2314:
2313:
2312:
2309:
2305:
2302:
2300:
2297:
2296:
2294:
2290:
2287:
2285:
2282:
2280:
2277:
2275:
2272:
2271:
2270:
2267:
2263:
2262:Related rates
2260:
2258:
2255:
2253:
2250:
2248:
2245:
2244:
2242:
2238:
2235:
2231:
2228:
2227:
2226:
2223:
2221:
2218:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2197:
2196:
2193:
2189:
2186:
2184:
2181:
2180:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2149:
2146:
2145:
2143:
2141:
2137:
2131:
2128:
2126:
2123:
2121:
2118:
2114:
2111:
2110:
2109:
2106:
2104:
2101:
2100:
2098:
2096:
2092:
2086:
2083:
2081:
2078:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2022:
2020:
2018:
2014:
2010:
2003:
1998:
1996:
1991:
1989:
1984:
1983:
1980:
1970:
1969:
1963:
1961:
1953:
1952:
1946:
1939:
1938:3-8290-5292-8
1935:
1931:
1926:
1922:
1912:
1909:
1907:
1904:
1902:
1901:Taylor series
1899:
1897:
1894:
1892:
1891:Linearization
1889:
1888:
1882:
1879:
1869:
1867:
1862:
1854:
1836:
1833:
1830:
1827:
1822:
1818:
1814:
1808:
1802:
1799:
1796:
1789:
1775:
1769:
1766:
1763:
1760:
1757:
1751:
1748:
1741:
1727:
1721:
1718:
1715:
1712:
1709:
1703:
1700:
1693:
1692:
1691:
1689:
1685:
1680:
1678:
1666:
1657:
1654:
1636:
1633:
1630:
1627:
1621:
1615:
1612:
1609:
1602:
1588:
1582:
1579:
1576:
1573:
1570:
1564:
1561:
1554:
1540:
1534:
1531:
1528:
1525:
1522:
1516:
1513:
1506:
1505:
1504:
1500:
1498:
1497:four thousand
1486:
1477:
1475:
1471:
1470:Taylor series
1467:
1463:
1459:
1455:
1436:
1433:
1430:
1427:
1424:
1417:
1416:
1415:
1398:
1395:
1389:
1383:
1380:
1377:
1370:
1369:
1368:
1351:
1345:
1342:
1339:
1336:
1333:
1327:
1324:
1317:
1303:
1297:
1294:
1291:
1288:
1285:
1279:
1276:
1269:
1268:
1267:
1264:
1262:
1258:
1254:
1250:
1246:
1242:
1238:
1234:
1215:
1212:
1206:
1200:
1197:
1194:
1187:
1173:
1167:
1164:
1161:
1158:
1155:
1149:
1146:
1139:
1125:
1119:
1116:
1113:
1110:
1107:
1101:
1098:
1091:
1090:
1089:
1087:
1083:
1079:
1075:
1071:
1067:
1063:
1058:
1056:
1052:
1048:
1044:
1040:
1036:
1027:
1012:
1009:
1005:
1001:
998:
995:
992:
988:
982:
978:
957:
954:
951:
948:
928:
908:
905:
885:
882:
879:
876:
856:
853:
850:
847:
844:
839:
835:
813:
810:
807:
799:
774:
771:
768:
760:
735:
732:
728:
722:
718:
697:
694:
674:
671:
651:
647:
644:
633:
626:
621:
618:
612:
608:
600:
589:
582:
577:
574:
568:
564:
556:
545:
538:
533:
530:
524:
520:
512:
501:
494:
491:
485:
474:
467:
464:
458:
453:
449:
440:
436:
435:Taylor series
432:
428:
427:percent error
424:
420:
416:
412:
408:
404:
400:
396:
393:
389:
385:
381:
376:
374:
373:Taylor series
370:
366:
362:
358:
354:
350:
346:
342:
337:
335:
331:
327:
323:
319:
315:
312:may refer to
311:
307:
303:
299:
294:
292:
288:
284:
280:
276:
275:fixed phrases
272:
271:approximation
270:
265:
264:approximation
263:
258:
257:approximation
256:
251:
250:approximation
247:
243:
239:
235:
225:
223:
222:approximation
219:
215:
211:
200:
197:
189:
179:
178:the talk page
175:
169:
167:
162:This article
160:
151:
150:
140:
135:
133:
128:
126:
121:
120:
118:
117:
112:
109:
107:
104:
102:
99:
97:
96:Approximation
94:
93:
92:
91:
87:
86:
81:
78:
76:
73:
71:
70:Curve fitting
68:
66:
63:
61:
58:
56:
53:
52:
51:
50:
46:
45:
41:
37:
36:
32:
31:
19:
2928:Secant cubed
2853:
2846:
2827:Isaac Newton
2797:Brook Taylor
2464:Derivatives
2435:Shell method
2163:Differential
2124:
1967:
1950:
1945:
1929:
1925:
1878:colloquially
1875:
1863:
1860:
1857:Higher-order
1851:
1681:
1676:
1664:
1663:
1660:Second-order
1655:
1651:
1501:
1496:
1484:
1483:
1465:
1461:
1457:
1451:
1413:
1366:
1265:
1256:
1252:
1236:
1232:
1230:
1080:, or a flat
1059:
1050:
1037:is the term
1034:
1033:
1030:Zeroth-order
422:
418:
414:
405:used in the
398:
394:
383:
377:
348:
338:
325:
322:a wild guess
321:
317:
313:
309:
305:
297:
295:
290:
286:
278:
269:second-order
268:
267:
261:
260:
255:zeroth-order
254:
253:
248:used in the
231:
217:
207:
192:
183:
172:Please help
163:
54:
2996:of surfaces
2747:and numbers
2709:Dirichlet's
2679:Telescoping
2632:Alternating
2220:L'Hôpital's
2017:Precalculus
1480:First-order
1074:data points
262:first-order
214:engineering
3048:Categories
2792:Adequality
2478:Divergence
2351:Arc length
2148:Derivative
1917:References
1076:) will be
1064:(that is,
1039:scientists
388:polynomial
345:phenomenon
320:indicates
186:March 2016
168:to readers
2991:of curves
2986:Curvature
2873:Integrals
2667:Maclaurin
2647:Geometric
2538:Geometric
2488:Laplacian
2200:linearity
2040:Factorial
1828:−
1800:∼
1613:∼
1428:∼
1381:∼
1198:∼
845:≈
648:…
627:⏟
583:⏟
539:⏟
495:⏟
468:⏟
407:expansion
300:leads to
2981:Manifold
2714:Integral
2657:Infinite
2652:Harmonic
2637:Binomial
2483:Gradient
2426:Volumes
2237:Quotient
2178:Notation
2009:Calculus
1885:See also
1688:parabola
1454:interval
1084:with no
1078:constant
1062:function
808:<<
411:accuracy
357:interval
353:function
47:Concepts
2918:inverse
2906:inverse
2832:Fluxion
2642:Fourier
2508:Stokes'
2503:Green's
2225:Product
2085:Tangent
1464:= sin π
1070:formula
941:And at
423:second,
302:phrases
293:, etc.
244:in the
210:science
164:may be
3001:Tensor
2923:Secant
2689:Abel's
2672:Taylor
2563:Matrix
2513:Gauss'
2095:Limits
2075:Secant
2065:Radian
1936:
415:zeroth
403:series
392:degree
382:, the
2865:Lists
2724:Ratio
2662:Power
2398:Euler
2215:Chain
2205:Power
2080:Slope
1675:, or
1495:, or
1437:2.67.
1399:3.67.
1086:slope
419:first
298:order
289:, an
242:power
238:order
2734:Term
2729:Root
2468:Curl
1934:ISBN
1770:5.00
1764:3.00
1758:3.00
1722:2.00
1716:1.00
1710:0.00
1637:2.67
1583:5.00
1577:3.00
1571:3.00
1535:2.00
1529:1.00
1523:0.00
1346:5.00
1340:3.00
1334:3.00
1298:2.00
1292:1.00
1286:0.00
1216:3.67
1082:line
769:<
266:, a
259:, a
224:is.
2210:Sum
1669:3.9
1263:.
429:or
390:of
308:or
208:In
3050::
1959:^
1868:.
1673:10
1493:10
1468:.
929:1.
638:th
594:rd
550:nd
506:st
479:th
441:,
421:,
417:,
212:,
2001:e
1994:t
1987:v
1940:.
1837:3
1834:+
1831:x
1823:2
1819:x
1815:=
1812:)
1809:x
1806:(
1803:f
1797:y
1776:,
1773:]
1767:,
1761:,
1755:[
1752:=
1749:y
1728:,
1725:]
1719:,
1713:,
1707:[
1704:=
1701:x
1671:×
1634:+
1631:x
1628:=
1625:)
1622:x
1619:(
1616:f
1610:y
1589:,
1586:]
1580:,
1574:,
1568:[
1565:=
1562:y
1541:,
1538:]
1532:,
1526:,
1520:[
1517:=
1514:x
1491:×
1489:4
1466:x
1462:y
1458:y
1434:+
1431:x
1425:y
1396:=
1393:)
1390:x
1387:(
1384:f
1378:y
1352:,
1349:]
1343:,
1337:,
1331:[
1328:=
1325:y
1304:,
1301:]
1295:,
1289:,
1283:[
1280:=
1277:x
1257:x
1253:y
1237:y
1233:x
1213:=
1210:)
1207:x
1204:(
1201:f
1195:y
1174:,
1171:]
1168:5
1165:,
1162:3
1159:,
1156:3
1153:[
1150:=
1147:y
1126:,
1123:]
1120:2
1117:,
1114:1
1111:,
1108:0
1105:[
1102:=
1099:x
1013:,
1010:3
1006:/
1002:4
999:=
996:!
993:3
989:/
983:3
979:2
958:,
955:2
952:=
949:x
909:,
906:x
886:,
883:1
880:=
877:x
857:,
854:x
851:+
848:1
840:x
836:e
814:,
811:1
804:|
800:x
796:|
775:,
772:1
765:|
761:x
757:|
736:,
733:2
729:/
723:2
719:x
698:,
695:x
675:;
672:1
652:,
645:+
634:4
622:!
619:4
613:4
609:x
601:+
590:3
578:!
575:3
569:3
565:x
557:+
546:2
534:!
531:2
525:2
521:x
513:+
502:1
492:x
486:+
475:0
465:1
459:=
454:x
450:e
395:n
384:n
199:)
193:(
188:)
184:(
180:.
170:.
138:e
131:t
124:v
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
