Definite integrals via numerical integration (a.k.a. Riemann sums)
MAT135
Definite integrals via numerical integration (a.k.a. Riemann sums)
6:42
Fundamental Theorem of Calculus, part 2 - definite integrals
MAT135
Fundamental Theorem of Calculus, part 2 - definite integrals
5:48
Fundamental Theorem of Calculus, part 1
MAT135
Fundamental Theorem of Calculus, part 1
5:22
Why antiderivatives?
MAT135
Why antiderivatives?
3:03
Antiderivatives (a.k.a. indefinite integrals): an overview
MAT135
Antiderivatives (a.k.a. indefinite integrals): an overview
6:27
Gompertz law of mortality
MAT135
Gompertz law of mortality
13:17
Maximizing a concave-up function
MAT135
Maximizing a concave-up function
1:32
Critical points, and local minima and maxima
MAT135
Critical points, and local minima and maxima
2:45
Logarithmic differentiation
MAT135
Logarithmic differentiation
3:42
Example: derivative of an inverse function
MAT135
Example: derivative of an inverse function
1:05
Derivative of natural logarithm: (ln x)' =1/x.
MAT135
Derivative of natural logarithm: (ln x)' =1/x.
1:24
Derivatives of inverse functions
MAT135
Derivatives of inverse functions
3:06
Chain rule: derivative of a composition of two functions
MAT135
Chain rule: derivative of a composition of two functions
4:32
Derivatives of sine and cosine
MAT135
Derivatives of sine and cosine
4:01
Derivative of an exponential function a^x
MAT135
Derivative of an exponential function a^x
2:28
Graph of a function f(t) and its derivatives f'(t), f''(t).
MAT135
Graph of a function f(t) and its derivatives f'(t), f''(t).
2:34
Another important limit (will be used to compute derivatives of trigonometric functions).
MAT135
Another important limit (will be used to compute derivatives of trigonometric functions).
2:34
One important limit (used for derivatives of exponential functions)
MAT135
One important limit (used for derivatives of exponential functions)
2:20
Position of a tennis ball
MAT135
Position of a tennis ball
3:03
Velocity vs. Speed
MAT135
Velocity vs. Speed
1:39
Average rate of change of a function f(t) on [a,b].
MAT135
Average rate of change of a function f(t) on [a,b].
1:37
Example of a plot on log-log scale
MAT135
Example of a plot on log-log scale
4:37
Design your own rational function
MAT135
Design your own rational function
0:54
arcsin(sin(x))
MAT135
arcsin(sin(x))
1:49
Daylight in Toronto -- using sin(x) and cos(x)
MAT135
Daylight in Toronto -- using sin(x) and cos(x)
7:56
World Population -- exponential growth with constantly changing rates
MAT135
World Population -- exponential growth with constantly changing rates
10:05
Relationship between Log(x) and Ln(x)
MAT135
Relationship between Log(x) and Ln(x)
1:18
Supply and Demand curves
MAT135
Supply and Demand curves
4:45
Continuous growth rate and Euler number e = 2.718281828...
MAT135
Continuous growth rate and Euler number e = 2.718281828...
5:02
Exponential functions: terminology
MAT135
Exponential functions: terminology
2:37
Sign of exponential functions
MAT135
Sign of exponential functions
0:48
Perpendicular lines
MAT135
Perpendicular lines
8:38