93:
36:
1584:
1853:
1570:
1863:
1350:
prepares students for algebra. While pre-algebra often has extensive coverage of basic algebraic concepts, precalculus courses might see only small amounts of calculus concepts, if at all, and often involves covering algebraic topics that might not have been given attention in earlier algebra
1103:: Introduction to the Analysis of the Infinite), which "was meant as a survey of concepts and methods in analysis and analytic geometry preliminary to the study of differential and integral calculus." He began with the fundamental concepts of
1307:
1337:
in his precalculus. Today's course may cover arithmetic and geometric sequences and series, but not the application by Saint-Vincent to gain his hyperbolic logarithm, which Euler used to finesse his precalculus.
199:
1359:, and other topics needed for calculus, used in fields such as medicine or engineering. A college preparatory/regular class might focus on topics used in business-related careers, such as
1722:
1183:
1212:
1235:
1152:
1757:
1745:
1617:
1240:
92:
1351:
courses. Some precalculus courses might differ with others in terms of content. For example, an honors-level course might spend more time on
1808:
536:
57:
1715:
1095:
1158:’s calculus suffices to establish the natural logarithm. This part of precalculus prepares the student for integration of the monomial
595:
1762:
1032:
1750:
1676:
1525:
1508:
1480:
1463:
551:
274:
79:
1065:, thus the name precalculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.
541:
1866:
872:
546:
526:
208:
1887:
1856:
1828:
1708:
1838:
1813:
654:
601:
487:
1155:
313:
285:
396:
905:
518:
356:
328:
118:
50:
44:
776:
740:
522:
401:
295:
290:
280:
381:
61:
1403:
675:
240:
1778:
1399:
1116:
989:
781:
670:
1783:
1456:
1439:
1431:
1371:
1108:
1104:
1025:
954:
915:
799:
735:
659:
1731:
1660:
1313:
in financial mathematics may motivate this limit. Another difference in the modern text is avoidance of
1046:
999:
665:
556:
441:
386:
347:
253:
1583:
1130:
is obtained by taking as base "the number for which the hyperbolic logarithm is one", sometimes called
1823:
1518:
1427:
1375:
1360:
1120:
1086:
1004:
984:
910:
579:
503:
477:
391:
1695:
1419:
1415:
979:
949:
939:
826:
680:
482:
338:
221:
216:
1803:
1668:
1589:
1318:
944:
847:
831:
771:
725:
606:
530:
436:
431:
235:
1326:
766:
761:
230:
1788:
1672:
1521:
1504:
1476:
1459:
1395:
1383:
1310:
1131:
1127:
1018:
852:
630:
513:
466:
323:
318:
1833:
1575:
1490:
1411:
1407:
1379:
1356:
1119:. The general logarithm, to an arbitrary positive base, Euler presents as the inverse of an
862:
756:
730:
591:
508:
472:
1161:
1334:
1188:
1078:
994:
867:
821:
816:
703:
616:
561:
1554:
1793:
1597:
1473:
1435:
1364:
1314:
1220:
1137:
1112:
1090:
877:
685:
457:
1881:
1642:
1607:
1352:
857:
621:
376:
333:
1656:
1330:
1322:
1058:
611:
361:
1346:
Precalculus prepares students for calculus somewhat differently from the way that
1659:(1980). "Chapter 2: Newton, Leibniz and the Leibnizian tradition chapter 2". In
1612:
1602:
1501:
1387:
1347:
1302:{\displaystyle e=\lim _{n\rightarrow \infty }\left(1+{\frac {1}{n}}\right)^{n}}
1798:
1565:
1391:
1074:
720:
644:
371:
366:
270:
1639:
Teaching mathematics in secondary and middle school, an interactive approach
1548:
649:
639:
17:
1538:
1569:
1818:
1542:
1423:
1082:
1062:
715:
462:
419:
108:
96:
Diagram for the deriving the power-reducing formula for the sine function
1700:
1089:, particularly in modification and transformation of such expressions.
1054:
1665:
From the
Calculus to Set Theory, 1630 – 1910: An Introductory History
1100:
1061:
at a level which is designed to prepare students for the study of
1704:
29:
1438:
may be demonstrated, but generally coursework involves
1430:
are other common topics of precalculus. Sometimes the
1243:
1223:
1191:
1164:
1140:
121:
1154:. This appropriation of the significant number from
1771:
1738:
1398:are developed. Algebraic skills are exercised with
1451:Roland E. Larson & Robert P. Hostetler (1989)
1434:method of proof for propositions dependent upon a
1301:
1229:
1206:
1177:
1146:
193:
1468:Margaret L. Lial & Charles D. Miller (1988)
1251:
1093:wrote the first precalculus book in 1748 called
1053:is a course, or a set of courses, that includes
194:{\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}
27:Course designed to prepare students for calculus
1333:. Euler used not only complex numbers but also
1498:Precalculus Mathematics: a functional approach
1716:
1547:David Lippman & Melonie Rasmussen (2017)
1026:
8:
1723:
1709:
1701:
1618:Mathematics education in the United States
1549:Precalculus: an investigation of functions
1033:
1019:
899:
805:
709:
585:
425:
259:
99:
1317:, except as they may arise as roots of a
1293:
1278:
1254:
1242:
1222:
1190:
1169:
1163:
1139:
1111:. His innovation is noted for its use of
154:
131:
126:
120:
80:Learn how and when to remove this message
91:
43:This article includes a list of general
1629:
1073:For students to succeed at finding the
839:
808:
748:
629:
557:Differentiating under the integral sign
495:
449:
346:
305:
262:
107:
7:
1862:
1696:Precalculus information at Mathworld
1553:Carl Stitz & Jeff Zeager (2013)
1517:, third edition, Dellen imprint of
1096:Introductio in analysin infinitorum
1261:
1217:Today's precalculus text computes
103:Part of a series of articles about
49:it lacks sufficient corresponding
25:
1861:
1852:
1851:
1582:
1568:
34:
1537:Jay Abramson and others (2014)
1489:, PWS-Kent Publishing Company (
1085:, they will need facility with
1258:
188:
182:
173:
167:
151:
145:
1:
488:Integral of inverse functions
1370:A standard course considers
1382:, often in connection with
906:Calculus on Euclidean space
329:Logarithmic differentiation
1904:
1485:Jerome E. Kaufmann (1988)
1847:
1637:Cangelosi, J. S. (2012).
1156:Grégoire de Saint-Vincent
640:Summand limit (term test)
1513:Michael Sullivan (1993)
1404:trigonometric identities
1117:transcendental functions
324:Implicit differentiation
314:Differentiation notation
241:Inverse function theorem
1400:trigonometric functions
782:Helmholtz decomposition
64:more precise citations.
1661:Grattan-Guinness, Ivor
1457:D.C. Heath and Company
1432:mathematical induction
1303:
1231:
1208:
1179:
1148:
916:Limit of distributions
736:Directional derivative
397:FaĂ di Bruno's formula
195:
97:
1888:Mathematics education
1732:Mathematics education
1496:Karl J. Smith (1990)
1304:
1232:
1209:
1180:
1178:{\displaystyle x^{p}}
1149:
1087:algebraic expressions
1047:mathematics education
1000:Mathematical analysis
911:Generalized functions
596:arithmetico-geometric
442:Leibniz integral rule
196:
95:
1519:Macmillan Publishers
1442:rather than theory.
1416:parametric equations
1376:function composition
1241:
1221:
1207:{\displaystyle p=-1}
1189:
1162:
1138:
1121:exponential function
1005:Nonstandard analysis
478:Lebesgue integration
348:Rules and identities
119:
1309:. An exposition on
1185:in the instance of
676:Cauchy condensation
483:Contour integration
209:Fundamental theorem
136:
1829:Cognitively guided
1669:Duckworth Overlook
1590:Mathematics portal
1500:, fourth edition,
1455:, second edition,
1396:rational functions
1329:as application of
1319:quadratic equation
1299:
1265:
1227:
1204:
1175:
1144:
848:Partial derivative
777:generalized Stokes
671:Alternating series
552:Reduction formulae
527:tangent half-angle
514:Cylindrical shells
437:Integral transform
432:Lists of integrals
236:Mean value theorem
191:
122:
98:
1875:
1874:
1814:Modern elementary
1789:Three-part lesson
1412:polar coordinates
1390:. In particular,
1380:inverse functions
1357:Euclidean vectors
1311:compound interest
1286:
1250:
1230:{\displaystyle e}
1147:{\displaystyle e}
1128:natural logarithm
1115:to introduce the
1043:
1042:
923:
922:
885:
884:
853:Multiple integral
789:
788:
693:
692:
660:Direct comparison
631:Convergence tests
569:
568:
542:Partial fractions
409:
408:
319:Second derivative
90:
89:
82:
16:(Redirected from
1895:
1865:
1864:
1855:
1854:
1725:
1718:
1711:
1702:
1683:
1682:
1653:
1647:
1646:
1634:
1592:
1587:
1586:
1578:
1576:Education portal
1573:
1572:
1408:binomial theorem
1342:Variable content
1321:with a negative
1308:
1306:
1305:
1300:
1298:
1297:
1292:
1288:
1287:
1279:
1264:
1236:
1234:
1233:
1228:
1213:
1211:
1210:
1205:
1184:
1182:
1181:
1176:
1174:
1173:
1153:
1151:
1150:
1145:
1035:
1028:
1021:
969:
934:
900:
896:
863:Surface integral
806:
802:
710:
706:
666:Limit comparison
586:
582:
473:Riemann integral
426:
422:
382:L'HĂ´pital's rule
339:Taylor's theorem
260:
256:
200:
198:
197:
192:
144:
135:
130:
100:
85:
78:
74:
71:
65:
60:this article by
51:inline citations
38:
37:
30:
21:
1903:
1902:
1898:
1897:
1896:
1894:
1893:
1892:
1878:
1877:
1876:
1871:
1843:
1767:
1734:
1729:
1692:
1687:
1686:
1679:
1655:
1654:
1650:
1636:
1635:
1631:
1626:
1588:
1581:
1574:
1567:
1564:
1534:
1448:
1365:power functions
1344:
1335:infinite series
1327:Euler's formula
1315:complex numbers
1271:
1267:
1266:
1239:
1238:
1219:
1218:
1187:
1186:
1165:
1160:
1159:
1136:
1135:
1079:antiderivatives
1071:
1039:
1010:
1009:
995:Integration Bee
970:
967:
960:
959:
935:
932:
925:
924:
897:
894:
887:
886:
868:Volume integral
803:
798:
791:
790:
707:
702:
695:
694:
664:
583:
578:
571:
570:
562:Risch algorithm
537:Euler's formula
423:
418:
411:
410:
392:General Leibniz
275:generalizations
257:
252:
245:
231:Rolle's theorem
226:
201:
137:
117:
116:
86:
75:
69:
66:
56:Please help to
55:
39:
35:
28:
23:
22:
15:
12:
11:
5:
1901:
1899:
1891:
1890:
1880:
1879:
1873:
1872:
1870:
1869:
1859:
1848:
1845:
1844:
1842:
1841:
1836:
1831:
1826:
1821:
1816:
1811:
1809:Computer-based
1806:
1801:
1796:
1791:
1786:
1781:
1775:
1773:
1769:
1768:
1766:
1765:
1760:
1758:United Kingdom
1755:
1754:
1753:
1742:
1740:
1736:
1735:
1730:
1728:
1727:
1720:
1713:
1705:
1699:
1698:
1691:
1690:External links
1688:
1685:
1684:
1677:
1671:. p. 76.
1648:
1628:
1627:
1625:
1622:
1621:
1620:
1615:
1610:
1605:
1600:
1598:AP Precalculus
1594:
1593:
1579:
1563:
1560:
1559:
1558:
1551:
1545:
1533:
1530:
1529:
1528:
1511:
1494:
1483:
1474:Scott Foresman
1466:
1447:
1444:
1436:natural number
1353:conic sections
1343:
1340:
1296:
1291:
1285:
1282:
1277:
1274:
1270:
1263:
1260:
1257:
1253:
1249:
1246:
1226:
1203:
1200:
1197:
1194:
1172:
1168:
1143:
1134:, and written
1132:Euler's number
1113:exponentiation
1091:Leonhard Euler
1070:
1067:
1041:
1040:
1038:
1037:
1030:
1023:
1015:
1012:
1011:
1008:
1007:
1002:
997:
992:
990:List of topics
987:
982:
977:
971:
966:
965:
962:
961:
958:
957:
952:
947:
942:
936:
931:
930:
927:
926:
921:
920:
919:
918:
913:
908:
898:
893:
892:
889:
888:
883:
882:
881:
880:
875:
870:
865:
860:
855:
850:
842:
841:
837:
836:
835:
834:
829:
824:
819:
811:
810:
804:
797:
796:
793:
792:
787:
786:
785:
784:
779:
774:
769:
764:
759:
751:
750:
746:
745:
744:
743:
738:
733:
728:
723:
718:
708:
701:
700:
697:
696:
691:
690:
689:
688:
683:
678:
673:
668:
662:
657:
652:
647:
642:
634:
633:
627:
626:
625:
624:
619:
614:
609:
604:
599:
584:
577:
576:
573:
572:
567:
566:
565:
564:
559:
554:
549:
547:Changing order
544:
539:
534:
516:
511:
506:
498:
497:
496:Integration by
493:
492:
491:
490:
485:
480:
475:
470:
460:
458:Antiderivative
452:
451:
447:
446:
445:
444:
439:
434:
424:
417:
416:
413:
412:
407:
406:
405:
404:
399:
394:
389:
384:
379:
374:
369:
364:
359:
351:
350:
344:
343:
342:
341:
336:
331:
326:
321:
316:
308:
307:
303:
302:
301:
300:
299:
298:
293:
288:
278:
265:
264:
258:
251:
250:
247:
246:
244:
243:
238:
233:
227:
225:
224:
219:
213:
212:
211:
203:
202:
190:
187:
184:
181:
178:
175:
172:
169:
166:
163:
160:
157:
153:
150:
147:
143:
140:
134:
129:
125:
115:
112:
111:
105:
104:
88:
87:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1900:
1889:
1886:
1885:
1883:
1868:
1860:
1858:
1850:
1849:
1846:
1840:
1837:
1835:
1832:
1830:
1827:
1825:
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1802:
1800:
1797:
1795:
1792:
1790:
1787:
1785:
1782:
1780:
1777:
1776:
1774:
1770:
1764:
1761:
1759:
1756:
1752:
1749:
1748:
1747:
1746:United States
1744:
1743:
1741:
1737:
1733:
1726:
1721:
1719:
1714:
1712:
1707:
1706:
1703:
1697:
1694:
1693:
1689:
1680:
1678:0-7156-1295-6
1674:
1670:
1666:
1662:
1658:
1657:Bos, H. J. M.
1652:
1649:
1644:
1643:Prentice Hall
1640:
1633:
1630:
1623:
1619:
1616:
1614:
1611:
1609:
1608:AP Statistics
1606:
1604:
1601:
1599:
1596:
1595:
1591:
1585:
1580:
1577:
1571:
1566:
1561:
1556:
1552:
1550:
1546:
1544:
1540:
1536:
1535:
1532:Online access
1531:
1527:
1526:0-02-418421-7
1523:
1520:
1516:
1512:
1510:
1509:0-534-11922-0
1506:
1503:
1499:
1495:
1492:
1488:
1484:
1482:
1481:0-673-15872-1
1478:
1475:
1471:
1467:
1465:
1464:0-669-16277-9
1461:
1458:
1454:
1450:
1449:
1445:
1443:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1405:
1401:
1397:
1393:
1389:
1385:
1381:
1377:
1373:
1368:
1366:
1362:
1358:
1354:
1349:
1341:
1339:
1336:
1332:
1328:
1324:
1320:
1316:
1312:
1294:
1289:
1283:
1280:
1275:
1272:
1268:
1255:
1247:
1244:
1237:as the limit
1224:
1215:
1201:
1198:
1195:
1192:
1170:
1166:
1157:
1141:
1133:
1129:
1124:
1122:
1118:
1114:
1110:
1106:
1102:
1098:
1097:
1092:
1088:
1084:
1080:
1076:
1068:
1066:
1064:
1060:
1056:
1052:
1048:
1036:
1031:
1029:
1024:
1022:
1017:
1016:
1014:
1013:
1006:
1003:
1001:
998:
996:
993:
991:
988:
986:
983:
981:
978:
976:
973:
972:
964:
963:
956:
953:
951:
948:
946:
943:
941:
938:
937:
929:
928:
917:
914:
912:
909:
907:
904:
903:
902:
901:
891:
890:
879:
876:
874:
871:
869:
866:
864:
861:
859:
858:Line integral
856:
854:
851:
849:
846:
845:
844:
843:
838:
833:
830:
828:
825:
823:
820:
818:
815:
814:
813:
812:
807:
801:
800:Multivariable
795:
794:
783:
780:
778:
775:
773:
770:
768:
765:
763:
760:
758:
755:
754:
753:
752:
747:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
713:
712:
711:
705:
699:
698:
687:
684:
682:
679:
677:
674:
672:
669:
667:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
637:
636:
635:
632:
628:
623:
620:
618:
615:
613:
610:
608:
605:
603:
600:
597:
593:
590:
589:
588:
587:
581:
575:
574:
563:
560:
558:
555:
553:
550:
548:
545:
543:
540:
538:
535:
532:
528:
524:
523:trigonometric
520:
517:
515:
512:
510:
507:
505:
502:
501:
500:
499:
494:
489:
486:
484:
481:
479:
476:
474:
471:
468:
464:
461:
459:
456:
455:
454:
453:
448:
443:
440:
438:
435:
433:
430:
429:
428:
427:
421:
415:
414:
403:
400:
398:
395:
393:
390:
388:
385:
383:
380:
378:
375:
373:
370:
368:
365:
363:
360:
358:
355:
354:
353:
352:
349:
345:
340:
337:
335:
334:Related rates
332:
330:
327:
325:
322:
320:
317:
315:
312:
311:
310:
309:
304:
297:
294:
292:
291:of a function
289:
287:
286:infinitesimal
284:
283:
282:
279:
276:
272:
269:
268:
267:
266:
261:
255:
249:
248:
242:
239:
237:
234:
232:
229:
228:
223:
220:
218:
215:
214:
210:
207:
206:
205:
204:
185:
179:
176:
170:
164:
161:
158:
155:
148:
141:
138:
132:
127:
123:
114:
113:
110:
106:
102:
101:
94:
84:
81:
73:
63:
59:
53:
52:
46:
41:
32:
31:
19:
1664:
1651:
1638:
1632:
1514:
1497:
1486:
1469:
1452:
1446:Sample texts
1388:real numbers
1369:
1345:
1331:trigonometry
1323:discriminant
1216:
1125:
1094:
1072:
1059:trigonometry
1050:
1044:
974:
519:Substitution
281:Differential
254:Differential
76:
67:
48:
18:Pre-Calculus
1779:Traditional
1613:Pre-algebra
1603:AP Calculus
1555:Precalculus
1539:Precalculus
1515:Precalculus
1502:Brooks/Cole
1487:Precalculus
1470:Precalculus
1453:Precalculus
1392:polynomials
1348:pre-algebra
1075:derivatives
1051:precalculus
975:Precalculus
968:Miscellanea
933:Specialized
840:Definitions
607:Alternating
450:Definitions
263:Definitions
62:introducing
1624:References
1418:, and the
955:Variations
950:Stochastic
940:Fractional
809:Formalisms
772:Divergence
741:Identities
721:Divergence
271:Derivative
222:Continuity
70:March 2022
45:references
1794:Singapore
1763:Australia
1739:Geography
1491:Wadsworth
1440:exercises
1424:sequences
1372:functions
1262:∞
1259:→
1199:−
1126:Then the
1109:functions
1105:variables
945:Malliavin
832:Geometric
731:Laplacian
681:Dirichlet
592:Geometric
177:−
124:∫
1882:Category
1857:Category
1839:Critical
1824:Informal
1784:Exercise
1772:Approach
1751:New York
1562:See also
1543:OpenStax
1361:matrices
1325:, or in
1083:calculus
1063:calculus
985:Glossary
895:Advanced
873:Jacobian
827:Exterior
757:Gradient
749:Theorems
716:Gradient
655:Integral
617:Binomial
602:Harmonic
467:improper
463:Integral
420:Integral
402:Reynolds
377:Quotient
306:Concepts
142:′
109:Calculus
1867:Commons
1663:(ed.).
1069:Concept
1055:algebra
980:History
878:Hessian
767:Stokes'
762:Green's
594: (
521: (
465: (
387:Inverse
362:Product
273: (
58:improve
1804:Reform
1675:
1524:
1507:
1479:
1462:
1428:series
1420:limits
1406:. The
1378:, and
822:Tensor
817:Matrix
704:Vector
622:Taylor
580:Series
217:Limits
47:, but
1834:Ethno
1799:Saxon
1557:(pdf)
1541:from
1363:, or
1101:Latin
1081:with
645:Ratio
612:Power
531:Euler
509:Discs
504:Parts
372:Power
367:Chain
296:total
1673:ISBN
1522:ISBN
1505:ISBN
1477:ISBN
1460:ISBN
1426:and
1402:and
1394:and
1386:and
1384:sets
1107:and
1077:and
1057:and
726:Curl
686:Abel
650:Root
1819:New
1422:of
1252:lim
1045:In
357:Sum
1884::
1667:.
1641:.
1472:,
1414:,
1410:,
1374:,
1367:.
1355:,
1214:.
1123:.
1049:,
529:,
525:,
1724:e
1717:t
1710:v
1681:.
1645:.
1493:)
1295:n
1290:)
1284:n
1281:1
1276:+
1273:1
1269:(
1256:n
1248:=
1245:e
1225:e
1202:1
1196:=
1193:p
1171:p
1167:x
1142:e
1099:(
1034:e
1027:t
1020:v
598:)
533:)
469:)
277:)
189:)
186:a
183:(
180:f
174:)
171:b
168:(
165:f
162:=
159:t
156:d
152:)
149:t
146:(
139:f
133:b
128:a
83:)
77:(
72:)
68:(
54:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
