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Calculus 2
Getting started
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Antiderivatives and indefinite integrals
introduction to integrals (5:55)
indefinite integrals (6:10)
properties of integrals (5:34)
find f given f'' (4:42)
find f given f''' (7:19)
initial value problems (6:53)
find f given f'' and initial conditions (8:26)
Definite integrals
definite integrals (5:06)
area under or enclosed by the curve (5:55)
definite integrals of even and odd functions (12:38)
Riemann sums
summation notation, finding the sum (3:46)
summation notation, expanding (3:19)
summation notation, collapsing (5:02)
riemann sums, left endpoints (9:00)
riemann sums, right endpoints (15:15)
riemann sums, midpoints (10:21)
Other approximation methods
moving from summation notation to the integral
over and underestimation (10:07)
limit process to find area under the curve (28:54)
trapezoidal rule (10:30)
simpson's rule (10:24)
Error bounds
error bounds (62:44)
Fundamental theorem of calculus
part 1 of the ftc (11:32)
part 2 of the ftc (7:26)
net change theorem (6:34)
U-substitution
introduction to solving integrals (8:18)
u-substitution (8:03)
u-substitution in definite integrals (10:36)
Integration by parts
integration by parts (7:45)
integration by parts two times (13:36)
integration by parts three times (10:30)
integration by parts with u-substitution (8:55)
prove the reduction formula (7:13)
tabular integration (8:49)
Partial fractions
introduction to partial fractions
distinct linear factors (30:15)
distinct quadratic factors (40:23)
repeated linear factors (12:37)
repeated quadratic factors (31:14)
rationalizing substitution (12:29)
how to factor difficult denominators (20:21)
two ways to find the constants (19:28)
Trigonometric integrals
trigonometric integrals (14:16)
sin^m cos^n, odd m (9:58)
sin^m cos^n, odd n (11:04)
sin^m cos^n, m and n even (7:19)
tan^m sec^n, odd m (5:24)
tan^m sec^n, even n (10:45)
sin(mx) cos(nx) (3:37)
sin(mx) sin(nx) (4:12)
cos(mx) cos(nx) (4:22)
hyperbolic integrals (2:36)
inverse hyperbolic integrals (3:53)
Trigonometric substitution
trigonometric substitution setup (13:12)
trigonometric substitution with secant (13:35)
trigonometric substitution with sine (27:09)
trigonometric substitution with tangent (36:24)
quadratic functions (14:03)
Improper integrals
introduction to improper integrals
improper integrals, case 1 (7:42)
improper integrals, case 2 (5:39)
improper integrals, case 3 (12:20)
improper integrals, case 4 (14:05)
improper integrals, case 5 (6:50)
improper integrals, case 6 (8:36)
comparison theorem (11:17)
Reduction formulas
integrals using reduction formulas (7:13)
Area between curves
area between curves (17:32)
sketching the area between curves (10:43)
dividing the area between curves into equal parts (6:24)
Arc length
arc length (29:09)
Average value
average value (6:00)
mean value theorem for integrals (3:58)
Surface area of revolution
surface area of revolution (21:18)
surface of revolution equation (5:08)
Volume of revolution
volume of revolution, major axes of revolution (36:05)
disks (42:15)
washers (29:14)
cylindrical shells (35:19)
Work
work done to lift a mass or weight (7:39)
work done on elastic springs (8:15)
work done to empty a tank (18:29)
work done by a variable force (4:08)
Physics
moments and center of mass of the system (13:00)
hydrostatic pressure and force (15:16)
vertical motion (9:50)
rectilinear motion (5:39)
Geometry
centroids of plane regions (22:05)
area of a triangle with given vertices (11:35)
Economics
present and future value (16:51)
consumer and producer surplus (7:11)
Probability
probability density functions (6:45)
Biology
cardiac output (16:20)
poiseuille's law (2:25)
theorem of pappus (12:23)
Introduction to parametric curves
eliminating the parameter (7:07)
derivative of a parametric curve (2:59)
second derivative of a parametric curve (3:52)
sketching parametric curves by plotting points (5:46)
Calculus with parametric curves
tangent line to the parametric curve (6:56)
area under a parametric curve (14:37)
area under one arc or loop (6:53)
arc length (41:30)
surface area of revolution (20:23)
volume of revolution (8:42)
Introduction to polar curves
introduction to polar coordinates (7:12)
polar coordinates (4:35)
converting rectangular equations (3:38)
converting polar equations (2:57)
distance between polar points (8:57)
sketching polar curves (10:41)
sketching polar curves from cartesian curves (6:10)
Calculus with polar curves
tangent line to the polar curve (9:48)
vertical and horizontal tangent lines to the polar curve (10:21)
intersection of polar curves (12:56)
area inside a polar curve (6:07)
area bounded by one loop of a polar curve (12:26)
area between polar curves (14:21)
area inside both polar curves (12:34)
arc length of a polar curve (14:11)
surface area of revolution of a polar curve (7:13)
Introduction to sequences
sequences vs. series
listing the first terms (2:52)
calculating the first terms (3:36)
formula for the general term (6:27)
convergence of a sequence (7:46)
limit of a convergent sequence (5:03)
increasing, decreasing, and not monotonic (11:33)
bounded sequences (12:12)
Partial sums
calculating the first terms of a series of partial sums (5:01)
sum of the series of partial sums (4:41)
Geometric series
geometric series test (11:39)
sum of the geometric series (10:15)
values for which the series converges (5:52)
geometric series for repeating decimals (8:37)
Telescoping series
convergence of a telescoping series (6:49)
sum of a telescoping series (8:59)
Basic convergence tests
strategy for testing series
limit vs. sum of the series (5:05)
integral test (11:15)
p-series test (3:02)
nth term test (8:53)
Comparison tests
comparison test (10:33)
limit comparison test (5:55)
error or remainder of a series (11:57)
Ratio and root tests
ratio test (8:32)
ratio test with factorials (10:54)
root test (4:30)
absolute and conditional convergence (13:44)
Alternating series test
alternating series test (13:37)
alternating series estimation theorem (13:05)
Power series
power series representation (19:55)
power series multiplication (6:52)
power series division (5:14)
power series differentiation (16:31)
radius and interval of convergence (26:06)
estimating definite integrals (11:16)
estimating indefinite integrals (12:03)
binomial series (27:19)
Taylor series
taylor series (7:59)
radius and interval of convergence of a taylor series (20:44)
taylor's inequality (12:06)
Maclaurin series
maclaurin series (9:00)
sum of the maclaurin series (6:08)
radius and interval of convergence of a maclaurin series (9:34)
indefinite integral as an infinite series (8:00)
maclaurin series to estimate an indefinite integral (9:38)
maclaurin series to estimate a definite integral (7:18)
maclaurin series to evaluate a limit (5:39)
Final exam
calculus 2 final exam
trigonometric substitution with tangent
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