I. Polar Coordinates and Complex Numbers 

Polar Coordinates 
29:32 
 
Intro 
0:00  
 
Rectangular vs. Polar Coordinates 
0:04  
 
 Describing a Location of a Point on a Plane: Rectangular 
0:07  
 
 Describing a Location of a Point on a Plane: Polar Coordinate 
3:04  
 
Coordinate Conversion 
4:23  
 
 Using SOHCAHTOA 
4:24  
 
Rectangular to Polar 
6:03  
 
 Rectangular Coordinate to Polar Coordinates 
6:04  
 
Polar to Rectangular 
9:16  
 
 Polar Coordinates to Rectangular Coordinates 
9:19  
 
Equation Conversion 
11:25  
 
 Example: Circle with r = 2 
11:40  
 
Linear Equation with Slope 
14:57  
 
 Example: Describing Line 
14:58  
 
Vertical or Horizontal Line 
18:16  
 
 
19:22  
 
Extra Example 1: Plot the Polar Coordinates 
21:16  
 
Extra Example 2: plot the polar Coordinates 
23:44  
 
Extra Example 3: Convert to Linear Equation 
24:56  
 
Extra Example 4: Convert to Linear Equation 
26:09  

Graphing Polar Coordinates 
64:42 
 
Intro 
0:00  
 
Six Types of Polar Graphs 
0:07  
 
 Line 
0:31  
 
 Circle 
1:08  
 
 Limacon 
1:46  
 
 Rose 
2:16  
 
 Lemniscate 
2:50  
 
 Spirals 
3:15  
 
Step in Graphing 
3:50  
 
 Determine Type of Graph 
4:27  
 
 Use Information Given by a, b, and n 
4:39  
 
 Plot Critical Points 
4:52  
 
Circle 
6:43  
 
 Circle: r = ncosθ 
6:44  
 
Circle Example 
8:10  
 
 Example: r = 6sinθ 
8:13  
 
Limacon 
12:58  
 
 Inner Loop 
13:06  
 
 Cardioid 
20:18  
 
Limacon, cont. 
26:00  
 
 Dimpled 
26:05  
 
 Convex 
31:40  
 
Rose 
33:30  
 
 r = a sin nθ 
33:31  
 
 Length of Petals = a 
33:39  
 
Rose: Even and Odd 
34:06  
 
 Even n (2n Petals) 
34:07  
 
 Odd n (n Petals) 
39:28  
 
Lemniscate 
41:08  
 
 'Bowtie' 
41:09  
 
 Length of Petals 
41:25  
 
 Number of Petals 
41:29  
 
Lemniscate Example 
41:46  
 
 Example: rÂ² = 9sin2θ 
41:47  
 
Spiral 
44:13  
 
 Spiral: r = a + bθ 
44:14  
 
 Example: r = 2θ 
44:34  
 
Other Curves 
46:31  
 
 Conchoid 
47:20  
 
 Hyperbolic Spiral 
47:35  
 
 Strophoid 
47:39  
 
 Logarithmic Spiral 
48:00  
 
Extra Example 1: Identify Graph 
49:20  
 
Extra Example 2: Identify Graph 
51:51  
 
Extra Example 3: Identify Graph 
54:22  
 
Extra Example 4: Identify Graph 
58:42  

Introduction to Complex Numbers 
34:10 
 
Intro 
0:00  
 
Imaginary Numbers 
0:06  
 
 nth Degree Polynomials 
0:40  
 
 Multiplicities and Complex Roots 
1:04  
 
 What is an Imaginary Number? 
2:00  
 
Complex Numbers 
7:27  
 
 Complex Numbers: a + bi 
7:55  
 
 Electrical Engineering 
9:00  
 
Operations with Complex Numbers 
9:53  
 
 Cartesian, Rectangular, or Algebraic Form 
10:13  
 
 1) Addition/ Subtraction 
10:38  
 
 2) Multiplication 
12:30  
 
 3) Rationalizing the Denominator (Using the Complex Conjugate) 
15:05  
 
Powers of i 
20:53  
 
 i = √1 
20:58  
 
Extra Example 1: Add/ Subtract the Complex Numbers 
25:03  
 
Extra Example 2: Multiply the Complex Numbers 
26:09  
 
Extra Example 3: Powers of i 
28:39  
 
Extra Example 4: Rationalize the Denominator Using Complex Conjugate 
30:32  

Simplifying Complex Numbers 
38:44 
 
Intro 
0:00  
 
Negative Sign Under Radical 
1:01  
 
 Example: Simplifying Negative sign Under Radical 
1:02  
 
Like Terms 
3:54  
 
 Example: Simplifying Like Terms 
3:55  
 
Rationalizing the Denominator 
5:36  
 
 Example: Simplify 3/i 
5:52  
 
 Example: Simplify (3+i)/5i 
7:47  
 
Distribution and FOIL 
10:25  
 
 Example: 6i(3  2i) 
10:49  
 
 Example: (2 + 4i)(2  6i) 
12:02  
 
Complex Conjugates 
13:54  
 
 Example: Complex Conjugates 
13:55  
 
Powers of i 
19:17  
 
 Example: Find Powers of i 
19:18  
 
Extra Example 1: Simplify the Expression 
24:28  
 
Extra Example 2: Simplify the Expression 
28:03  
 
Extra Example 3: Simplify the Expression 
32:42  
 
Extra Example 4: Powers of i 
35:10  

Polar Forms of Complex Numbers 
33:50 
 
Intro 
0:00  
 
Complex Plane 
0:25  
 
 Definition and Example of Complex Plane 
0:26  
 
Representing Complex Numbers 
2:51  
 
 Example: Representing Complex Numbers 
2:55  
 
Absolute Value of a Complex Number 
4:25  
 
 Definition of the Absolute Value of a + bi 
4:26  
 
Trigonometric or Polar Form of a Complex Number 
6:38  
 
 Trigonometric Form of the Complex Number z = a + bi 
7:00  
 
 Modulus of z 
8:14  
 
 Argument of z 
8:27  
 
Euler's Formula 
9:36  
 
 Example: Euler's Formula 
9:38  
 
Complex to Trigonometric 
11:11  
 
 Example: Write Complex Number in Trigonometric Form 
11:12  
 
Complex to Standard Form 
16:35  
 
 Example: Write Complex Number in Standard Form 
16:36  
 
Extra Example 1: Give the Polar Coordinates 
21:26  
 
Extra Example 2: Give the Polar Coordinates 
24:11  
 
Extra Example 3: Find the Rectangular Coordinates 
26:03  
 
Extra Example 4: Find the Rectangular Coordinates 
30:01  

Products and Quotients of Complex Numbers in Polar Form 
26:12 
 
Intro 
0:00  
 
Sum and Difference 
0:14  
 
 Example of Sum and Difference Formulas 
0:16  
 
Multiplication 
1:00  
 
 Multiplication Formulas 
1:24  
 
Multiplications Example 
5:53  
 
 Example: Find the Product of 2 Complex Numbers 
5:54  
 
Division 
8:25  
 
 Methods for Division 
8:26  
 
 Euler's Equation 
8:58  
 
Division Example 
10:43  
 
 Example: Find the Quotient of the Complex Numbers 
10:45  
 
Extra Example 1: Find the Product 
14:46  
 
Extra Example 2: Simplify 
17:08  
 
Extra Example 3: Find the Quotient 
20:18  
 
Extra Example 4: Find the Quotient 
22:59  

Powers and Roots of Complex Numbers and de Moivre's Formula 
63:15 
 
Intro 
0:00  
 
Powers of Complex Numbers 
0:19  
 
 Methods of Finding Powers of Complex Numbers 
0:47  
 
De Moivre's Formula 
3:07  
 
 De Moivre's Formula 
3:40  
 
 De Moivre's Theorem 
3:51  
 
 De Moivre's Formula Example 
4:56  
 
 Example: Using De Moivre's Theorem 
4:57  
 
De Moivre's Formula Example 
9:08  
 
 Example: Using De Moivre's Theorem 
9:09  
 
Roots of Complex Numbers 
11:43  
 
 Equation for Finding the nth Roots of a Complex Number 
11:44  
 
Origin of Formula 
13:47  
 
 Fundamental Theorem of Algebra 
13:48  
 
Origin of Formula, cont. 
17:37  
 
 Origin of Formula 
17:38  
 
nth Root Example 
22:53  
 
 Example: Calculate the 6th Roots 
22:54  
 
Extra Example 1: De Moivre's Theorem 
29:59  
 
Extra Example 2: Cube Roots of 8i 
36:50  
 
Extra Example 3: Find the Four Fourth Roots of 16 
44:43  
 
Extra Example 4: Find the 3 Cube Root of 2 + 2i 
52:08  
II. Mathematical Analysis 

Mathematical Induction 
30:39 
 
Intro 
0:00  
 
What is Induction? 
0:07  
 
 Example of Mathematical Induction 
0:09  
 
Historical Background 
1:36  
 
 French Mathematician Pierre de Fermat 
1:42  
 
Euler 
2:55  
 
 Leonhard Euler 
2:57  
 
Principle of Mathematical Induction 
4:05  
 
 Example: Statement Involving Positive Integer 
4:08  
 
Extra Example 1: Mathematical Induction 
6:35  
 
Extra Example 2: Mathematical Induction 
12:18  
 
Extra Example 3: Mathematical Induction 
16:08  
 
Extra Example 4: Mathematical Induction 
21:33  

Fundamental Theorem of Algebra 
28:55 
 
Intro 
0:00  
 
Fundamental Theorem of Algebra 
0:08  
 
 Fundamental Theorem of Algebra 
0:09  
 
 Example of the Fundamental Theorem of Algebra 
1:34  
 
Rational Zero Test 
2:40  
 
 Rational Zero Test 
2:41  
 
 Example of the Rational Zero Test 
3:30  
 
Binomial Factors 
5:47  
 
 Binomial Factors 
5:48  
 
 Example of the Binomial Factors 
6:18  
 
Descarte Rule of Signs 
9:41  
 
 Descarte Rule of Signs 
9:42  
 
Descarte Rule of Signs Example 
11:23  
 
 Example: Describing Polynomial 
11:24  
 
Extra Example 1: Find Zeroes of a Polynomial Function 
13:09  
 
Extra Example 2: Find all the Zeroes 
17:37  
 
Extra Example 3: Find the Polynomial 
21:28  
 
Extra Example 4: Descarte Rule of Signs 
25:37  

Rational Functions 
45:48 
 
Intro 
0:00  
 
Graph of Rational Functions 
0:06  
 
 Rational Functions 
0:07  
 
Vertical Asymptote 
0:53  
 
 Example: y=1/x 
0:55  
 
Horizontal Asymptote 
2:52  
 
 Example: Horizontal Asymptote 
2:53  
 
Horizontal Asymptote Cases 
4:27  
 
 1st Case 
4:40  
 
 2nd Case 
7:15  
 
 3rd Case 
9:00  
 
 Special Case 
10:31  
 
Intercepts 
13:06  
 
 xintercepts 
13:15  
 
 yintercepts 
14:04  
 
Discontinuities 
15:29  
 
 Example: Discontinuities 
15:30  
 
Examples 
17:08  
 
 H(x)= 5/(x + 3) 
17:12  
 
Extra Example 1: Graph and Identify the Function 
22:02  
 
Extra Example 2: Graph and Identify the Function 
29:04  
 
Extra Example 3: Graph and Identify the Function 
34:27  
 
Extra Example 4: Graph and Identify the Function 
41:29  
III. Trigonometry (Functions) 

Angles 
39:05 
 
Intro 
0:00  
 
Degrees 
0:22  
 
 Circle is 360 Degrees 
0:48  
 
 Splitting a Circle 
1:13  
 
Radians 
2:08  
 
 Circle is 2 Pi Radians 
2:31  
 
 One Radian 
2:52  
 
 HalfCircle and Right Angle 
4:00  
 
Converting Between Degrees and Radians 
6:24  
 
 Formulas for Degrees and Radians 
6:52  
 
Coterminal, Complementary, Supplementary Angles 
7:23  
 
 Coterminal Angles 
7:30  
 
 Complementary Angles 
9:40  
 
 Supplementary Angles 
10:08  
 
Example 1: Dividing a Circle 
10:38  
 
Example 2: Converting Between Degrees and Radians 
11:56  
 
Example 3: Quadrants and Coterminal Angles 
14:18  
 
Extra Example 1: Common Angle Conversions 
8:02  
 
Extra Example 2: Quadrants and Coterminal Angles 
7:14  

Sine and Cosine Functions 
43:16 
 
Intro 
0:00  
 
Sine and Cosine 
0:15  
 
 Unit Circle 
0:22  
 
 Coordinates on Unit Circle 
1:03  
 
 Right Triangles 
1:52  
 
 Adjacent, Opposite, Hypotenuse 
2:25  
 
 Master Right Triangle Formula: SOHCAHTOA 
2:48  
 
Odd Functions, Even Functions 
4:40  
 
 Example: Odd Function 
4:56  
 
 Example: Even Function 
7:30  
 
Example 1: Sine and Cosine 
10:27  
 
Example 2: Graphing Sine and Cosine Functions 
14:39  
 
Example 3: Right Triangle 
21:40  
 
Example 4: Odd, Even, or Neither 
26:01  
 
Extra Example 1: Right Triangle 
4:05  
 
Extra Example 2: Graphing Sine and Cosine Functions 
5:23  

Sine and Cosine Values of Special Angles 
33:05 
 
Intro 
0:00  
 
454590 Triangle and 306090 Triangle 
0:08  
 
 454590 Triangle 
0:21  
 
 306090 Triangle 
2:06  
 
Mnemonic: All Students Take Calculus (ASTC) 
5:21  
 
 Using the Unit Circle 
5:59  
 
 New Angles 
6:21  
 
 Other Quadrants 
9:43  
 
 Mnemonic: All Students Take Calculus 
10:13  
 
Example 1: Convert, Quadrant, Sine/Cosine 
13:11  
 
Example 2: Convert, Quadrant, Sine/Cosine 
16:48  
 
Example 3: All Angles and Quadrants 
20:21  
 
Extra Example 1: Convert, Quadrant, Sine/Cosine 
4:15  
 
Extra Example 2: All Angles and Quadrants 
4:03  

Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D 
52:03 
 
Intro 
0:00  
 
Amplitude and Period of a Sine Wave 
0:38  
 
 Sine Wave Graph 
0:58  
 
 Amplitude: Distance from Middle to Peak 
1:18  
 
 Peak: Distance from Peak to Peak 
2:41  
 
Phase Shift and Vertical Shift 
4:13  
 
 Phase Shift: Distance Shifted Horizontally 
4:16  
 
 Vertical Shift: Distance Shifted Vertically 
6:48  
 
Example 1: Amplitude/Period/Phase and Vertical Shift 
8:04  
 
Example 2: Amplitude/Period/Phase and Vertical Shift 
17:39  
 
Example 3: Find Sine Wave Given Attributes 
25:23  
 
Extra Example 1: Amplitude/Period/Phase and Vertical Shift 
7:27  
 
Extra Example 2: Find Cosine Wave Given Attributes 
10:27  

Tangent and Cotangent Functions 
36:04 
 
Intro 
0:00  
 
Tangent and Cotangent Definitions 
0:21  
 
 Tangent Definition 
0:25  
 
 Cotangent Definition 
0:47  
 
Master Formula: SOHCAHTOA 
1:01  
 
 Mnemonic 
1:16  
 
Tangent and Cotangent Values 
2:29  
 
 Remember Common Values of Sine and Cosine 
2:46  
 
 90 Degrees Undefined 
4:36  
 
Slope and Menmonic: ASTC 
5:47  
 
 Uses of Tangent 
5:54  
 
 Example: Tangent of Angle is Slope 
6:09  
 
 Sign of Tangent in Quadrants 
7:49  
 
Example 1: Graph Tangent and Cotangent Functions 
10:42  
 
Example 2: Tangent and Cotangent of Angles 
16:09  
 
Example 3: Odd, Even, or Neither 
18:56  
 
Extra Example 1: Tangent and Cotangent of Angles 
2:27  
 
Extra Example 2: Tangent and Cotangent of Angles 
5:02  

Secant and Cosecant Functions 
27:18 
 
Intro 
0:00  
 
Secant and Cosecant Definitions 
0:17  
 
 Secant Definition 
0:18  
 
 Cosecant Definition 
0:33  
 
Example 1: Graph Secant Function 
0:48  
 
Example 2: Values of Secant and Cosecant 
6:49  
 
Example 3: Odd, Even, or Neither 
12:49  
 
Extra Example 1: Graph of Cosecant Function 
4:58  
 
Extra Example 2: Values of Secant and Cosecant 
5:19  

Inverse Trigonometric Functions 
32:58 
 
Intro 
0:00  
 
Arcsine Function 
0:24  
 
 Restrictions between 1 and 1 
0:43  
 
 Arcsine Notation 
1:26  
 
Arccosine Function 
3:07  
 
 Restrictions between 1 and 1 
3:36  
 
 Cosine Notation 
3:53  
 
Arctangent Function 
4:30  
 
 Between Pi/2 and Pi/2 
4:44  
 
 Tangent Notation 
5:02  
 
Example 1: Domain/Range/Graph of Arcsine 
5:45  
 
Example 2: Arcsin/Arccos/Arctan Values 
10:46  
 
Example 3: Domain/Range/Graph of Arctangent 
17:14  
 
Extra Example 1: Domain/Range/Graph of Arccosine 
4:30  
 
Extra Example 2: Arcsin/Arccos/Arctan Values 
5:40  

Computations of Inverse Trigonometric Functions 
31:08 
 
Intro 
0:00  
 
Inverse Trigonometric Function Domains and Ranges 
0:31  
 
 Arcsine 
0:41  
 
 Arccosine 
1:14  
 
 Arctangent 
1:41  
 
Example 1: Arcsines of Common Values 
2:44  
 
Example 2: Odd, Even, or Neither 
5:57  
 
Example 3: Arccosines of Common Values 
12:24  
 
Extra Example 1: Arctangents of Common Values 
5:50  
 
Extra Example 2: Arcsin/Arccos/Arctan Values 
8:51  
IV. Trigonometry (Identities) 

Pythagorean Identity 
19:11 
 
Intro 
0:00  
 
Pythagorean Identity 
0:17  
 
 Pythagorean Triangle 
0:27  
 
 Pythagorean Identity 
0:45  
 
Example 1: Use Pythagorean Theorem to Prove Pythagorean Identity 
1:14  
 
Example 2: Find Angle Given Cosine and Quadrant 
4:18  
 
Example 3: Verify Trigonometric Identity 
8:00  
 
Extra Example 1: Use Pythagorean Identity to Prove Pythagorean Theorem 
3:32  
 
Extra Example 2: Find Angle Given Cosine and Quadrant 
3:55  

Identity Tan(squared)x+1=Sec(squared)x 
23:16 
 
Intro 
0:00  
 
Main Formulas 
0:19  
 
 Companion to Pythagorean Identity 
0:27  
 
 For Cotangents and Cosecants 
0:52  
 
 How to Remember 
0:58  
 
Example 1: Prove the Identity 
1:40  
 
Example 2: Given Tan Find Sec 
3:42  
 
Example 3: Prove the Identity 
7:45  
 
Extra Example 1: Prove the Identity 
2:22  
 
Extra Example 2: Given Sec Find Tan 
4:34  

Addition and Subtraction Formulas 
52:52 
 
Intro 
0:00  
 
Addition and Subtraction Formulas 
0:09  
 
 How to Remember 
0:48  
 
Cofunction Identities 
1:31  
 
 How to Remember Graphically 
1:44  
 
 Where to Use Cofunction Identities 
2:52  
 
Example 1: Derive the Formula for cos(AB) 
3:08  
 
Example 2: Use Addition and Subtraction Formulas 
16:03  
 
Example 3: Use Addition and Subtraction Formulas to Prove Identity 
25:11  
 
Extra Example 1: Use cos(AB) and Cofunction Identities 
7:54  
 
Extra Example 2: Convert to Radians and use Formulas 
11:32  

Double Angle Formulas 
29:05 
 
Intro 
0:00  
 
Main Formula 
0:07  
 
 How to Remember from Addition Formula 
0:18  
 
 Two Other Forms 
1:35  
 
Example 1: Find Sine and Cosine of Angle using Double Angle 
3:16  
 
Example 2: Prove Trigonometric Identity using Double Angle 
9:37  
 
Example 3: Use Addition and Subtraction Formulas 
12:38  
 
Extra Example 1: Find Sine and Cosine of Angle using Double Angle 
6:10  
 
Extra Example 2: Prove Trigonometric Identity using Double Angle 
3:18  

HalfAngle Formulas 
43:55 
 
Intro 
0:00  
 
Main Formulas 
0:09  
 
 Confusing Part 
0:34  
 
Example 1: Find Sine and Cosine of Angle using HalfAngle 
0:54  
 
Example 2: Prove Trigonometric Identity using HalfAngle 
11:51  
 
Example 3: Prove the HalfAngle Formula for Tangents 
18:39  
 
Extra Example 1: Find Sine and Cosine of Angle using HalfAngle 
7:16  
 
Extra Example 2: Prove Trigonometric Identity using HalfAngle 
3:34  
V. Trigonometry (Applications) 

Trigonometry in Right Angles 
25:43 
 
Intro 
0:00  
 
Master Formula for Right Angles 
0:11  
 
 SOHCAHTOA 
0:15  
 
 Only for Right Triangles 
1:26  
 
Example 1: Find All Angles in a Triangle 
2:19  
 
Example 2: Find Lengths of All Sides of Triangle 
7:39  
 
Example 3: Find All Angles in a Triangle 
11:00  
 
Extra Example 1: Find All Angles in a Triangle 
5:10  
 
Extra Example 2: Find Lengths of All Sides of Triangle 
4:18  

Law of Sines 
56:40 
 
Intro 
0:00  
 
Law of Sines Formula 
0:18  
 
 SOHCAHTOA 
0:27  
 
 Any Triangle 
0:59  
 
 Graphical Representation 
1:25  
 
 Solving Triangle Completely 
2:37  
 
When to Use Law of Sines 
2:55  
 
 ASA, SAA, SSA, AAA 
2:59  
 
 SAS, SSS for Law of Cosines 
7:11  
 
Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
8:44  
 
Example 2: How Many Triangles Satisfy Conditions, Solve Completely 
15:30  
 
Example 3: How Many Triangles Satisfy Conditions, Solve Completely 
28:32  
 
Extra Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
8:01  
 
Extra Example 2: How Many Triangles Satisfy Conditions, Solve Completely 
15:11  

Law of Cosines 
49:05 
 
Intro 
0:00  
 
Law of Cosines Formula 
0:23  
 
 Graphical Representation 
0:34  
 
 Relates Sides to Angles 
1:00  
 
 Any Triangle 
1:20  
 
 Generalization of Pythagorean Theorem 
1:32  
 
When to Use Law of Cosines 
2:26  
 
 SAS, SSS 
2:30  
 
Heron's Formula 
4:49  
 
 Semiperimeter S 
5:11  
 
Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
5:53  
 
Example 2: How Many Triangles Satisfy Conditions, Solve Completely 
15:19  
 
Example 3: Find Area of a Triangle Given All Side Lengths 
26:33  
 
Extra Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
11:05  
 
Extra Example 2: Length of Third Side and Area of Triangle 
9:17  

Finding the Area of a Triangle 
27:37 
 
Intro 
0:00  
 
Master Right Triangle Formula and Law of Cosines 
0:19  
 
 SOHCAHTOA 
0:27  
 
 Law of Cosines 
1:23  
 
Heron's Formula 
2:22  
 
 Semiperimeter S 
2:37  
 
Example 1: Area of Triangle with Two Sides and One Angle 
3:12  
 
Example 2: Area of Triangle with Three Sides 
6:11  
 
Example 3: Area of Triangle with Three Sides, No Heron's Formula 
8:50  
 
Extra Example 1: Area of Triangle with Two Sides and One Angle 
2:54  
 
Extra Example 2: Area of Triangle with Two Sides and One Angle 
6:48  

Word Problems and Applications of Trigonometry 
34:25 
 
Intro 
0:00  
 
Formulas to Remember 
0:11  
 
 SOHCAHTOA 
0:15  
 
 Law of Sines 
0:55  
 
 Law of Cosines 
1:48  
 
 Heron's Formula 
2:46  
 
Example 1: Telephone Pole Height 
4:01  
 
Example 2: Bridge Length 
7:48  
 
Example 3: Area of Triangular Field 
14:20  
 
Extra Example 1: Kite Height 
4:36  
 
Extra Example 2: Roads to a Town 
10:34  

DeMoivre's Theorem 
57:37 
 
Intro 
0:00  
 
Introduction to DeMoivre's Theorem 
0:10  
 
 n nth Roots 
3:06  
 
DeMoivre's Theorem: Finding nth Roots 
3:52  
 
 Relation to Unit Circle 
6:29  
 
 One nth Root for Each Value of k 
7:11  
 
Example 1: Convert to Polar Form and Use DeMoivre's Theorem 
8:24  
 
Example 2: Find Complex Eighth Roots 
15:27  
 
Example 3: Find Complex Roots 
27:49  
 
Extra Example 1: Convert to Polar Form and Use DeMoivre's Theorem 
7:41  
 
Extra Example 2: Find Complex Fourth Roots 
14:36  
VI. Vectors and Parametric Equations 

Geometric Vectors 
40:10 
 
Intro 
0:00  
 
Magnitude and Direction 
0:07  
 
 Describing Quantities 
0:12  
 
 William Rowan Hamilton 
1:42  
 
 James Maxwell 
2:04  
 
Vector Representation 
2:43  
 
 Scalar 
3:50  
 
 2 Vectors may not be Collinear 
4:30  
 
Algebraically or Geometrically 
5:44  
 
 Representing Vectors 
5:45  
 
Adding and Subtracting Vectors 
7:58  
 
 Addition: u + v 
8:15  
 
 Subtraction: u  v 
10:16  
 
Multiplying Vectors 
12:57  
 
 Scalar Multiplication: 2u + (1/3)v 
12:58  
 
Unit Vectors 
15:28  
 
 Standard Vectors Along x and y Axis 
15:29  
 
Extra Example 1: Sketch 3u  (1/2)v 
17:58  
 
Extra Example 2: Sketch the Vector 
20:31  
 
Extra Example 3: Resultant Velocity of a Plane 
22:57  
 
Extra Example 4: Add the Scalar Multiples 
35:33  

Algebraic Representation of Vectors 
54:36 
 
Intro 
0:00  
 
Component Form 
0:08  
 
 Component Form 
0:29  
 
 Using Standard Unit Vector i, j 
1:31  
 
Vector Operations 
3:21  
 
 Addition 
3:30  
 
 Subtraction 
4:24  
 
 Scalar Multiplication 
5:40  
 
Unit Vectors 
6:17  
 
 Example: Find the Unit Vector 
6:36  
 
 Example: Find the Angle 
9:42  
 
Dot Product 
12:27  
 
 Example: Dot Product 
12:28  
 
Determining Orthogonality 
22:28  
 
 Example: Orthogonal 
22:29  
 
 Parallel 
26:07  
 
Projections 
28:52  
 
 Finding Vector Components (Projection) 
28:54  
 
Extra Example 1: Calculate u  v 
35:40  
 
Extra Example 2: Find the Unit Vector 
36:41  
 
Extra Example 3: Find the Angle 
39:32  
 
Extra Example 4: Find the Direction and Magnitude of the Resultant Force 
42:25  

Vectors in 3D Space 
50:08 
 
Intro 
0:00  
 
Algebraic Vector Operations in 3D 
0:07  
 
 Addition 
1:11  
 
 Subtraction 
3:10  
 
 Scalar Multiplication 
4:30  
 
 Magnitude (Distance Formula) 
4:55  
 
Algebraic Vector Operations in 3D 
7:54  
 
 Equation of a Sphere 
8:07  
 
 Midpoint Formula 
8:56  
 
 Dot Product 
9:55  
 
 Angle Between 2 Vectors 
11:00  
 
 Quadrants/Octants 
14:24  
 
Cross Product 
16:13  
 
 Cross Product/ Determinant 
16:17  
 
Vector and Planes 
21:01  
 
 Example: x +3y + 6z = 12 
21:02  
 
Cartesian Equation 
24:39  
 
 Cartesian Equation 
24:41  
 
Equation of the Plane 
31:16  
 
 Example: Find the Equation of the Plane 
31:17  
 
Extra Example 1: Find u  v 
33:34  
 
Extra Example 2: Are the Vectors Perpendicular? 
35:20  
 
Extra Example 3: Find the Equation of the Plane 
37:32  
 
Extra Example 4: Nonzero Vector, Equation of a Plane, and Area 
40:16  

Vectors and Parametric Equations 
34:10 
 
Intro 
0:00  
 
Rectangular and Parametric Equations 
0:08  
 
 Introduction to Rectangular and Parametric Equations 
0:18  
 
Converting Parametric to Rectangular 
2:35  
 
 Example: Converting Parametric to Rectangular 
2:36  
 
Trigonometric Functions 
7:12  
 
 Example: Trigonometric Functions 
7:13  
 
Converting Rectangular to Parametric 
10:08  
 
 Example: Converting Rectangular to Parametric 
10:09  
 
Extra Example 1: Parametric Equations 
11:43  
 
Extra Example 2: Rectangular Equations 
15:05  
 
Extra Example 3: Rectangular Equation 
18:24  
 
Extra Example 4: Describe the Cycloid 
22:17  

Using Parametric Equations to Model Motion 
31:13 
 
Intro 
0:00  
 
Vector Equations 
0:23  
 
 Linear Motion 
1:06  
 
 Parametric Equations 
3:56  
 
Vector Equations 
5:17  
 
 Parametric Equations 
5:18  
 
Parametric Equations on Curves 
7:41  
 
 Example: Parametric Equations on Curves 
7:42  
 
Lissajous Curve 
12:17  
 
 Examples: Lissajous Curve 
12:18  
 
Extra Example 1: Vector Equation 
16:55  
 
Extra Example 2: Velocity, Vector Equation, and Parametric Equations 
18:34  
 
Extra Example 3: Velocity and Speed 
22:27  
 
Extra Example 4: Hyperbola 
22:52  
VII. Linear Algebra (Matrices) 

Basic Matrix Concepts 
11:34 
 
Intro 
0:00  
 
What is a Matrix 
0:26  
 
 Brackets 
0:46  
 
 Designation 
1:21  
 
 Element 
1:47  
 
 Matrix Equations 
1:59  
 
Dimensions 
2:27  
 
 Rows (m) and Columns (n) 
2:37  
 
 Examples: Dimensions 
2:43  
 
Special Matrices 
4:22  
 
 Row Matrix 
4:32  
 
 Column Matrix 
5:00  
 
 Zero Matrix 
6:00  
 
Equal Matrices 
6:30  
 
 Example: Corresponding Elements 
6:36  
 
Example 1: Matrix Dimension 
8:12  
 
Example 2: Matrix Dimension 
9:03  
 
Example 3: Zero Matrix 
9:38  
 
Example 4: Row and Column Matrix 
10:26  

Matrix Operations 
21:36 
 
Intro 
0:00  
 
Matrix Addition 
0:18  
 
 Same Dimensions 
0:25  
 
 Example: Adding Matrices 
1:04  
 
Matrix Subtraction 
3:42  
 
 Same Dimensions 
3:48  
 
 Example: Subtracting Matrices 
4:04  
 
Scalar Multiplication 
6:08  
 
 Scalar Constant 
6:24  
 
 Example: Multiplying Matrices 
6:32  
 
Properties of Matrix Operations 
8:23  
 
 Commutative Property 
8:41  
 
 Associative Property 
9:08  
 
 Distributive Property 
9:44  
 
Example 1: Matrix Addition 
10:24  
 
Example 2: Matrix Subtraction 
11:58  
 
Example 3: Scalar Multiplication 
14:23  
 
Example 4: Matrix Properties 
16:09  

Matrix Multiplication 
29:36 
 
Intro 
0:00  
 
Dimension Requirement 
0:17  
 
 n = p 
0:24  
 
 Resulting Product Matrix (m x q) 
1:21  
 
 Example: Multiplication 
1:54  
 
Matrix Multiplication 
3:38  
 
 Example: Matrix Multiplication 
4:07  
 
Properties of Matrix Multiplication 
10:46  
 
 Associative Property 
11:00  
 
 Associative Property (Scalar) 
11:28  
 
 Distributive Property 
12:06  
 
 Distributive Property (Scalar) 
12:30  
 
Example 1: Possible Matrices 
13:31  
 
Example 2: Multiplying Matrices 
17:08  
 
Example 3: Multiplying Matrices 
20:41  
 
Example 4: Matrix Properties 
24:41  

Determinants 
33:13 
 
Intro 
0:00  
 
What is a Determinant 
0:13  
 
 Square Matrices 
0:23  
 
 Vertical Bars 
0:41  
 
Determinant of a 2x2 Matrix 
1:21  
 
 Second Order Determinant 
1:37  
 
 Formula 
1:45  
 
 Example: 2x2 Determinant 
1:58  
 
Determinant of a 3x3 Matrix 
2:50  
 
 Expansion by Minors 
3:08  
 
 Third Order Determinant 
3:19  
 
 Expanding Row One 
4:06  
 
 Example: 3x3 Determinant 
6:40  
 
Diagonal Method for 3x3 Matrices 
13:24  
 
 Example: Diagonal Method 
13:36  
 
Example 1: Determinant of 2x2 
18:59  
 
Example 2: Determinant of 3x3 
20:03  
 
Example 3: Determinant of 3x3 
25:35  
 
Example 4: Determinant of 3x3 
29:22  

Cramer's Rule 
28:25 
 
Intro 
0:00  
 
System of Two Equations in Two Variables 
0:16  
 
 One Variable 
0:50  
 
 Determinant of Denominator 
1:14  
 
 Determinants of Numerators 
2:23  
 
 Example: System of Equations 
3:34  
 
System of Three Equations in Three Variables 
7:06  
 
 Determinant of Denominator 
7:17  
 
 Determinants of Numerators 
7:52  
 
Example 1: Two Equations 
8:57  
 
Example 2: Two Equations 
13:21  
 
Example 3: Three Equations 
17:11  
 
Example 4: Three Equations 
23:43  

Identity and Inverse Matrices 
22:25 
 
Intro 
0:00  
 
Identity Matrix 
0:13  
 
 Example: 2x2 Identity Matrix 
0:30  
 
 Example: 4x4 Identity Matrix 
0:50  
 
 Properties of Identity Matrices 
1:24  
 
 Example: Multiplying Identity Matrix 
2:52  
 
Matrix Inverses 
5:30  
 
 Writing Matrix Inverse 
6:07  
 
Inverse of a 2x2 Matrix 
6:39  
 
 Example: 2x2 Matrix 
7:31  
 
Example 1: Inverse Matrix 
10:18  
 
Example 2: Find the Inverse Matrix 
13:04  
 
Example 3: Find the Inverse Matrix 
17:53  
 
Example 4: Find the Inverse Matrix 
20:44  

Gauss Jordan Method 
58:48 
 
Intro 
0:00  
 
Two Equations 
0:13  
 
 Example: Using Substitution/ Elimination 
0:14  
 
Three Equations or Higher 
2:39  
 
 History 
2:40  
 
Row Echelon Form and Back Substitution 
3:58  
 
 RowEchelon Form 
5:01  
 
 Back Substitution 
10:49  
 
Gaussian Elimination 
12:32  
 
 Steps in Gaussian Elimination 
12:33  
 
Augmented Matrix 
15:17  
 
 Example: Augmented Matrix 
15:18  
 
 More Example: Augmented Matrix 
17:14  
 
GaussJordan Elimination 
26:19  
 
 Example: GaussJordan Elimination 
26:20  
 
Extra Example 1: Augmented Matrix 
34:21  
 
Extra Example 2: Augmented Matrix and RowEchelon Form 
40:58  
 
Extra Example 3: Gaussian Elimination and Back Substitution 
49:21  
 
Extra Example 4: GaussJordan Elimination 
52:34  
VIII. Sequences and Series 

Arithmetic Sequences 
21:16 
 
Intro 
0:00  
 
Sequences 
0:10  
 
 General Form of Sequence 
0:16  
 
 Example: Finite/Infinite Sequences 
0:33  
 
Arithmetic Sequences 
0:28  
 
 Common Difference 
2:41  
 
 Example: Arithmetic Sequence 
2:50  
 
Formula for the nth Term 
3:51  
 
 Example: nth Term 
4:32  
 
Equation for the nth Term 
6:37  
 
 Example: Using Formula 
6:56  
 
Arithmetic Means 
9:47  
 
 Example: Arithmetic Means 
10:16  
 
Example 1: nth Term 
12:38  
 
Example 2: Arithmetic Means 
13:49  
 
Example 3: Arithmetic Means 
16:12  
 
Example 4: nth Term 
18:26  

Arithmetic Series 
21:36 
 
Intro 
0:00  
 
What are Arithmetic Series? 
0:11  
 
 Common Difference 
0:28  
 
 Example: Arithmetic Sequence 
0:43  
 
 Example: Arithmetic Series 
1:09  
 
 Finite/Infinite Series 
1:36  
 
Sum of Arithmetic Series 
2:27  
 
 Example: Sum 
3:21  
 
Sigma Notation 
5:53  
 
 Index 
6:14  
 
 Example: Sigma Notation 
7:14  
 
Example 1: First Term 
9:00  
 
Example 2: Three Terms 
10:52  
 
Example 3: Sum of Series 
14:14  
 
Example 4: Sum of Series 
18:13  

Geometric Sequences 
23:03 
 
Intro 
0:00  
 
Geometric Sequences 
0:11  
 
 Common Difference 
0:38  
 
 Common Ratio 
1:08  
 
 Example: Geometric Sequence 
2:38  
 
nth Term of a Geometric Sequence 
4:41  
 
 Example: nth Term 
4:56  
 
Geometric Means 
6:51  
 
 Example: Geometric Mean 
7:09  
 
Example 1: 9th Term 
12:04  
 
Example 2: Geometric Means 
15:18  
 
Example 3: nth Term 
18:32  
 
Example 4: Three Terms 
20:59  

Geometric Series 
22:43 
 
Intro 
0:00  
 
What are Geometric Series? 
0:11  
 
 List of Numbers 
0:24  
 
 Example: Geometric Series 
1:12  
 
Sum of Geometric Series 
2:16  
 
 Example: Sum of Geometric Series 
2:41  
 
Sigma Notation 
4:21  
 
 Lower Index, Upper Index 
4:38  
 
 Example: Sigma Notation 
4:57  
 
Another Sum Formula 
6:08  
 
 Example: n Unknown 
6:28  
 
Specific Terms 
7:41  
 
 Sum Formula 
7:56  
 
 Example: Specific Term 
8:11  
 
Example 1: Sum of Geometric Series 
10:02  
 
Example 2: Sum of 8 Terms 
14:15  
 
Example 3: Sum of Geometric Series 
18:23  
 
Example 4: First Term 
20:16  

Infinite Geometric Series 
18:32 
 
Intro 
0:00  
 
What are Infinite Geometric Series 
0:10  
 
 Example: Finite 
0:29  
 
 Example: Infinite 
0:51  
 
 Partial Sums 
1:09  
 
 Formula 
1:37  
 
Sum of an Infinite Geometric Series 
2:39  
 
 Convergent Series 
2:58  
 
 Example: Sum of Convergent Series 
3:28  
 
Sigma Notation 
7:31  
 
 Example: Sigma 
8:17  
 
Repeating Decimals 
8:42  
 
 Example: Repeating Decimal 
8:53  
 
Example 1: Sum of Infinite Geometric Series 
12:15  
 
Example 2: Repeating Decimal 
13:24  
 
Example 3: Sum of Infinite Geometric Series 
15:14  
 
Example 4: Repeating Decimal 
16:48  

Recursion and Special Sequences 
14:34 
 
Intro 
0:00  
 
Fibonacci Sequence 
0:05  
 
 Background of Fibonacci 
0:23  
 
 Recursive Formula 
0:37  
 
 Fibonacci Sequence 
0:52  
 
 Example: Recursive Formula 
2:18  
 
Iteration 
3:49  
 
 Example: Iteration 
4:30  
 
Example 1: Five Terms 
7:08  
 
Example 2: Three Terms 
9:00  
 
Example 3: Five Terms 
10:38  
 
Example 4: Three Iterates 
12:41  

Binomial Theorem 
48:30 
 
Intro 
0:00  
 
Pascal's Triangle 
0:06  
 
 Expand Binomial 
0:13  
 
 Pascal's Triangle 
4:26  
 
Properties 
6:52  
 
 Example: Properties of Binomials 
6:58  
 
Factorials 
9:11  
 
 Product 
9:28  
 
 Example: Factorial 
9:45  
 
Binomial Theorem 
11:08  
 
 Example: Binomial Theorem 
13:48  
 
Finding a Specific Term 
18:36  
 
 Example: Specific Term 
19:26  
 
Example 1: Expand 
24:39  
 
Example 2: Fourth Term 
30:26  
 
Example 3: Five Terms 
36:13  
 
Example 4: Three Iterates 
45:07  
IX. Analytic Geometry (Conic Sections) 

Midpoint and Distance Formulas 
32:42 
 
Intro 
0:00  
 
Midpoint Formula 
0:15  
 
 Example: Midpoint 
0:30  
 
Distance Formula 
2:30  
 
 Example: Distance 
2:52  
 
Example 1: Midpoint and Distance 
4:58  
 
Example 2: Midpoint and Distance 
8:07  
 
Example 3: Median Length 
18:51  
 
Example 4: Perimeter and Area 
23:36  

Parabolas 
41:27 
 
Intro 
0:00  
 
What is a Parabola? 
0:20  
 
 Definition of a Parabola 
0:29  
 
 Focus 
0:59  
 
 Directrix 
1:15  
 
 Axis of Symmetry 
3:08  
 
Vertex 
3:33  
 
 Minimum or Maximum 
3:44  
 
Standard Form 
4:59  
 
 Horizontal Parabolas 
5:08  
 
 Vertex Form 
5:19  
 
 Upward or Downward 
5:41  
 
 Example: Standard Form 
6:06  
 
Graphing Parabolas 
8:31  
 
 Shifting 
8:51  
 
 Example: Completing the Square 
9:22  
 
 Symmetry and Translation 
12:18  
 
 Example: Graph Parabola 
12:40  
 
Latus Rectum 
17:13  
 
 Length 
18:15  
 
 Example: Latus Rectum 
18:35  
 
Horizontal Parabolas 
18:57  
 
 Not Functions 
20:08  
 
 Example: Horizontal Parabola 
21:21  
 
Focus and Directrix 
24:11  
 
 Horizontal 
24:48  
 
Example 1: Parabola Standard Form 
25:12  
 
Example 2: Graph Parabola 
30:00  
 
Example 3: Graph Parabola 
33:13  
 
Example 4: Parabola Equation 
37:28  

Circles 
21:03 
 
Intro 
0:00  
 
What are Circles? 
0:08  
 
 Example: Equidistant 
0:17  
 
 Radius 
0:32  
 
Equation of a Circle 
0:44  
 
 Example: Standard Form 
1:11  
 
Graphing Circles 
1:47  
 
 Example: Circle 
1:56  
 
Center Not at Origin 
3:07  
 
 Example: Completing the Square 
3:51  
 
Example 1: Equation of Circle 
6:44  
 
Example 2: Center and Radius 
11:51  
 
Example 3: Radius 
15:08  
 
Example 4: Equation of Circle 
16:57  

Ellipses 
46:51 
 
Intro 
0:00  
 
What Are Ellipses? 
0:11  
 
 Foci 
0:23  
 
Properties of Ellipses 
1:43  
 
 Major Axis, Minor Axis 
1:47  
 
 Center 
1:54  
 
 Length of Major Axis and Minor Axis 
3:21  
 
Standard Form 
5:33  
 
 Example: Standard Form of Ellipse 
6:09  
 
Vertical Major Axis 
9:14  
 
 Example: Vertical Major Axis 
9:46  
 
Graphing Ellipses 
12:51  
 
 Complete the Square and Symmetry 
13:00  
 
 Example: Graphing Ellipse 
13:16  
 
Equation with Center at (h, k) 
19:57  
 
 Horizontal and Vertical 
20:14  
 
 Difference 
20:27  
 
 Example: Center at (h, k) 
20:55  
 
Example 1: Equation of Ellipse 
24:05  
 
Example 2: Equation of Ellipse 
27:57  
 
Example 3: Equation of Ellipse 
32:32  
 
Example 4: Graph Ellipse 
38:27  

Hyperbolas 
38:15 
 
Intro 
0:00  
 
What are Hyperbolas? 
0:12  
 
 Two Branches 
0:18  
 
 Foci 
0:38  
 
Properties 
2:00  
 
 Transverse Axis and Conjugate Axis 
2:06  
 
 Vertices 
2:46  
 
 Length of Transverse Axis 
3:14  
 
 Distance Between Foci 
3:31  
 
 Length of Conjugate Axis 
3:38  
 
Standard Form 
5:45  
 
 Vertex Location 
6:36  
 
 Known Points 
6:52  
 
Vertical Transverse Axis 
7:26  
 
 Vertex Location 
7:50  
 
Asymptotes 
8:36  
 
 Vertex Location 
8:56  
 
 Rectangle 
9:28  
 
 Diagonals 
10:29  
 
Graphing Hyperbolas 
12:58  
 
 Example: Hyperbola 
13:16  
 
Equation with Center at (h, k) 
16:32  
 
 Example: Center at (h, k) 
17:21  
 
Example 1: Equation of Hyperbola 
19:20  
 
Example 2: Equation of Hyperbola 
22:48  
 
Example 3: Graph Hyperbola 
26:05  
 
Example 4: Equation of Hyperbola 
36:29  

Conic Sections 
18:43 
 
Intro 
0:00  
 
Conic Sections 
0:16  
 
 Double Cone Sections 
0:24  
 
Standard Form 
1:27  
 
 General Form 
1:37  
 
Identify Conic Sections 
2:16  
 
 B = 0 
2:50  
 
 X and Y 
3:22  
 
Identify Conic Sections, Cont. 
4:46  
 
 Parabola 
5:17  
 
 Circle 
5:51  
 
 Ellipse 
6:31  
 
 Hyperbola 
7:10  
 
Example 1: Identify Conic Section 
8:01  
 
Example 2: Identify Conic Section 
11:03  
 
Example 3: Identify Conic Section 
11:38  
 
Example 4: Identify Conic Section 
14:50  

Solving Quadratic Systems 
47:04 
 
Intro 
0:00  
 
Linear Quadratic Systems 
0:22  
 
 Example: Linear Quadratic System 
0:45  
 
Solutions 
2:49  
 
 Graphs of Possible Solutions 
3:10  
 
Quadratic Quadratic System 
4:10  
 
 Example: Elimination 
4:21  
 
Solutions 
11:39  
 
 Example: 0, 1, 2, 3, 4 Solutions 
11:50  
 
Systems of Quadratic Inequalities 
12:48  
 
 Example: Quadratic Inequality 
13:09  
 
Example 1: Solve Quadratic System 
21:42  
 
Example 2: Solve Quadratic System 
29:13  
 
Example 3: Solve Quadratic System 
35:02  
 
Example 4: Solve Quadratic Inequality 
40:29  
X. Probability 

Experiment, Outcomes, and Sample Space 
14:54 
 
Intro 
0:00  
 
Basic Definitions 
0:29  
 
 Experiment 
0:35  
 
 Outcomes 
0:55  
 
 Sample Space 
1:04  
 
Examples 
1:34  
 
 Roll a Die 
1:39  
 
 Flip a Coin 
2:33  
 
Simple and Compound Events 
3:30  
 
 Event 
3:43  
 
 Simple Event 
3:58  
 
 Compound Event 
4:27  
 
Example 
5:14  
 
Extra Example 1 
0:59  
 
Extra Example 2 
4:21  

Calculating Probability 
14:13 
 
Intro 
0:00  
 
What is Probability 
0:27  
 
 Range 
0:53  
 
 Sum of Probabilities 
1:26  
 
 Example: Football Game 
2:05  
 
Classical Probability 
2:53  
 
 Equally Likely Outcomes 
3:05  
 
 Example: Coin Flip 
4:08  
 
 Example: Die Roll 
5:12  
 
Relative Frequency 
6:44  
 
 Example 
7:22  
 
Subjective Probability 
9:38  
 
 Example 
10:06  
 
Extra Example 1 
1:04  
 
Extra Example 2 
1:33  

Probability and Events 
22:08 
 
Intro 
0:00  
 
Mutually Exclusive Events 
0:17  
 
 Example: Coin Flip 
0:27  
 
 Example: Die Roll 
3:03  
 
Independent Events 
5:13  
 
 Notation 
3:31  
 
 Example: Coin 
6:01  
 
Independent Events, cont. 
9:19  
 
 Example: Coffee Drinkers 
9:23  
 
Mutually Exclusive vs Independent 
13:03  
 
Complementary Events 
14:08  
 
 Example: Coffee Drinkers 
15:37  
 
Extra Example 1 
1:16  
 
Extra Example 2 
3:32  

Intersection of Events and the Multiplication Rule 
19:58 
 
Intro 
0:00  
 
Intersection of Events 
0:08  
 
 Venn Diagram 
1:20  
 
Multiplication Rule 
2:22  
 
 Joint Probability 
2:23  
 
 Example 
3:23  
 
Example 
6:30  
 
Multiplication Rule for Independent Events 
10:30  
 
 Example 
11:39  
 
Joint Probability of Mutually Exclusive Events 
15:24  
 
Extra Example 1 
1:24  
 
Extra Example 2 
2:09  

Union of Events and the Addition Rule 
18:28 
 
Intro 
0:00  
 
Union of Events 
0:06  
 
 Venn Diagram 
0:52  
 
Addition Rule 
2:01  
 
 Example: Coffee Drinkers 
3:25  
 
Example 
6:26  
 
Addition Rule for Mutually Exclusive Events 
9:11  
 
Example 
10:27  
 
Extra Example 1 
2:41  
 
Extra Example 2 
1:15  

Bayes' Rule 
16:59 
 
Intro 
0:00  
 
Partition of Events 
0:07  
 
 Venn Diagram 
0:17  
 
Law of Total Probability 
3:12  
 
Bayes' Rule 
6:11  
 
Example 
9:09  
 
Extra Example 1 
4:07  

Probability II 
77:39 
 
Intro 
0:00  
 
What is Probability 
0:06  
 
 Foundation of Probability 
0:31  
 
 What is Probability? 
1:34  
 
Terms 
5:12  
 
 Common Probability Terms 
5:13  
 
Types of Probability Problems 
13:41  
 
 Probability of Either of 2 Events 
13:44  
 
Types of Probability Problems 
16:53  
 
 Probability of Either of 2 Mutually Exclusive Events 
17:08  
 
'At Least' Problems 
18:29  
 
 Example: 'At Least' Problem 
18:30  
 
Likely Scenarios 
24:16  
 
 Cards, Dice, Flipping Coins, and Colored Marbles 
24:17  
 
 Example: 'and ' Scenario 
24:54  
 
 Example: 'or' Scenario 
25:57  
 
Events Occurring Together 
30:29  
 
 Example: Conditional Probability 
30:30  
 
Conditional Probability 
37:10  
 
 Problems Involving Conditional Probability 
37:11  
 
Conditional Probability 
44:48  
 
 Example: Binomial Probability Theorem 
44:57  
 
Combinations 
51:00  
 
 Examples: Combinations 
51:14  
 
Expected Value 
54:08  
 
 Definition of Expected Value 
54:09  
 
 Example: Expected Value 
54:27  
 
Extra Example 1: Conditional Probability 
58:33  
 
Extra Example 2: Expected Value 
63:39  
 
Extra Example 3: Marbles 
72:52  