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Calculus Visualized - by Dennis F Davis
13, Aug, 2024
Time Stamps...
Can you learn calculus in 3 hours? (
00:00:00
)
Calculus is all about performing two operations on functions (
00:02:23
)
Rate of change as slope of a straight line (
00:03:32
)
The dilemma of the slope of a curvy line (
00:05:37
)
The slope between very close points (
00:07:04
)
The limit (
00:11:30
)
The derivative (and differentials of x and y) (
00:15:36
)
Differential notation (
00:21:48
)
The constant rule of differentiation (
00:27:58
)
The power rule of differentiation (
00:29:15
)
Visual interpretation of the power rule (
00:35:36
)
The addition (and subtraction) rule of differentiation (
00:39:19
)
The product rule of differentiation (
00:41:34
)
Combining rules of differentiation to find the derivative of a polynomial (
00:43:08
)
Differentiation super-shortcuts for polynomials (
00:44:53
)
Solving optimization problems with derivatives (
00:48:03
)
The second derivative (
00:52:46
)
Trig rules of differentiation (for sine and cosine) (
00:59:59
)
Knowledge test: product rule example (
01:05:54
)
The chain rule for differentiation (composite functions) (
01:06:32
)
The quotient rule for differentiation (
01:15:23
)
The derivative of the other trig functions (tan, cot, sec, cos) (
01:19:04
)
Algebra overview: exponentials and logarithms (
01:20:55
)
Differentiation rules for exponents (
01:33:12
)
Differentiation rules for logarithms (
01:41:33
)
The anti-derivative (aka integral) (
01:45:32
)
The power rule for integration (
01:46:21
)
The power rule for integration won't work for 1/x (
01:48:32
)
The constant of integration +C (
01:52:37
)
Anti-derivative notation (
01:57:26
)
The integral as the area under a curve (using the limit) (
01:59:59
)
Evaluating definite integrals (
02:12:05
)
Definite and indefinite integrals (comparison) (
02:13:11
)
The definite integral and signed area (
02:15:30
)
The Fundamental Theorem of Calculus visualized (
02:18:10
)
The integral as a running total of its derivative (
02:21:37
)
The trig rule for integration (sine and cosine) (
02:24:25
)
Definite integral example problem (
02:27:07
)
u-Substitution (
02:32:53
)
Integration by parts (
02:42:05
)
The DI method for using integration by parts (
02:56:03
)
0.005261303 seconds
