1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
0:07 introduction to numbers
0:11 equations
0:20 addition
1:24 subtraction
1:34 negative numbers
1:40 e^i*pi = -1, euler's identity
2:16 two negatives cancellation
2:24 multiplication
2:29 the commutative property
2:29 equivalent multiplications
2:35 division
2:37 second division symbol
2:49 division by zero is indeterminate
3:05 Indices/Powers
3:39 One of the laws of indices. Radicals introcuced.
3:43 Irrational Number
3:50 Imaginary numbers
3:59 i^2 = -1
4:01 1^3 = -i = i * -1 = ie^-i*pi
4:02 one of euler's formulas, it equals -1
5:18 Introduction to the complex plane
5:36 Every point with a distance of one from the origin on the complex plane
5:40 radians, a unit of measurement for angles in the complex plane
6:39 circumference / diameter = pi
6:49 sine wave
6:56 cosine wave
7:02 sin^2(θ) + cos^2(θ) = 1
7:19 again, euler's formula
7:35 another one of euler's identities
8:25 it just simplifies to 1 + 1/i
8:32 sin (θ) / cos (θ) = tan (θ)
9:29 infinity.
9:39 span/vector spaces
9:59 limit as x goes to infinity
10:00 reduced to an integral
11:27 the imaginary world
13:04 Gamma(x) = (x-1)!
13:36 zeta, delta and phi
13:46 aleph