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source: James Cook 2016年8月3日

Calculus I in a nutshell: a review for Calculus II

These videos are primarily intended for students who are about to take Math 132 at Liberty University under my supervision. However, these may be of use to anyone who wishes a concise review of university calculus.

polynomials, completing the square 18:53 this is a fast review of some essential ideas about polynomials.

functions, graphs, local inverses. 29:39

hyperbolic functions, further trig functions 12:46

basics of differentiation part 1 25:13

basic differentiation part 2 18:45

implicit differentiation 14:21

graphing with calculus part 1 20:26

graphing with calculus part 2 27:06

basic indefinite integrals, part 1 18:15

basic indefinite integration part 2 6:42

basic indefinite integrals, part 3 9:05

antiderivatives applied to initial value problems 7:40

U-substitution for indefinite integrals 29:42

integrals of powers of trig and hyperbolic trig functions 12:27

integrals of powers of trig and hyperbolic trig. part 2 23:46

Riemann sum, signed-area 11:01

Fundamental Theorem of Calculus I, II and III 29:23

FTC II from telescoping sum and the Mean Value Theorem 4:51

solving definite integrals with FTC II, part 1 20:19

solving definite integrals with FTC II, part 2 9:42

finding areas bounded by curves 26:28

integral as continuous sum, the infinitesimal method 6:00

volumes by the slice 13:52

volumes by cylindrical shell or slice 26:01

a word on Test 1 of 2010 3:53

a word on Test 2 of 2010 11:18

a word on Test 3 of 2010 12:17

a word on Test 4 of 2010 18:30

the imaginary exponential technique 28:10

the epsilon-delta definition of the limit 29:42

examples of epsilon-delta limits 22:50

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