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Intro to Precalculus
Precalculus - College Algebra/Trigonometry
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Professor Leonard
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Support: https://www.patreon.com/ProfessorLeonard Cool Mathy Merch: https://professor-leonard.myshopify.com/ How the Precalculus Series will be filmed and what it will entail.
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Course content
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75h 7m left
Intro to Precalculus
3:16
2
Introduction to Functions
41:45
3
How to Evaluate Functions
50:29
4
Finding the Domain of Functions
40:51
5
Operations of Functions
22:16
6
Using the Vertical Line Test
11:52
7
Features of Graphs, Domain, Range
49:23
8
Properties of Functions - Even vs Odd
29:08
9
Properties of Functions - Increasing vs Decreasing
15:15
10
Properties of Functions - Extrema
26:22
11
Average Rate of Change of a Function
10:32
12
How to Graph Piecewise Functions
45:29
13
Graphs You Must Know
19:11
14
Introduction to Graph Transformations
48:01
15
How to Graph with Transformations
33:09
16
Introduction to Solving Quadratics
12:34
17
The Square Root Method in Solving Quadratics
44:27
18
Using Factoring to Solve Quadratics
55:48
19
Completing the Square Made Easy
1:01:26
20
Proving the Quadratic Formula - Twice
19:08
21
Using the Quadratic Formula
46:04
22
Finding Intersections of Functions
19:51
23
Using Substitutions to Solve Equations
47:53
24
Graphing Quadratic Functions
54:57
25
Solving Quadratic Inequalities
37:25
26
Applications of Quadratic Functions
26:04
27
Introduction to Polynomial Functions
34:36
28
Power Functions
32:00
29
Multiplicity and End Behavior of Polynomials
37:44
30
Creating Polynomials from Real Zeros
58:08
31
How to Sketch Polynomial Functions
1:04:05
32
Synthetic Division and Long Division of Polynomials
52:49
33
Descartes Rule of Signs
30:37
34
How to Use the Rational Zeros Theorem
1:21:10
35
Introduction to Complex Solutions of Polynomials
17:32
36
Creating Polynomials from Complex Solutions
40:23
37
Finding ALL Solutions of Polynomials
1:09:18
38
Finding Vertical Asymptotes of Rational Functions
40:21
39
Graphing Rational Functions with Transformations
46:24
40
Finding a Horizontal Asymptote of a Rational Function
29:48
41
Finding an Oblique Asymptote of a Rational Function
15:46
42
Finding End Behavior of Rational Functions
7:49
43
Finding Asymptotes and Holes of Rational Functions
51:33
44
Graphing Rational Functions
1:45:45
45
Inequalities with Functions - Graphically
20:30
46
Inequalities with Polynomial Functions
34:05
47
Inequalities with Rational Functions
58:13
48
Composition of Functions
28:21
49
Finding Domain of Composite Functions
29:16
50
One to One Functions
14:55
51
Finding Inverse Functions
51:43
52
Graphs of Exponential Functions
23:51
53
Graphing Exponential Functions with Transformations
38:29
54
Solving Exponential Equations with Common Bases
37:06
55
Introduction to Logarithms and Their Graphs
1:01:13
56
Graphing Logarithms with Transformations
16:01
57
Introduction to Solving Logarithms and Exponentials
34:46
58
Properties of Logarithms
21:49
59
How to Expand Logarithms
28:42
60
How to Combine Logarithms
25:46
61
How to Change the Base of a Logarithm
9:55
62
Solving Logarithms with Common Bases
33:00
63
Solving Logarithmic Equations with Exponentials
1:03:43
64
Solving Exponential Equations with Logarithms
1:03:24
65
Review of Compound Interest
46:13
66
Exponential Growth and Decay
48:26
67
Introduction to Sequences
54:35
68
Introduction to Series and Summation Notation
42:41
69
Arithmetic Sequences
21:31
70
Arithmetic Series
15:11
71
Geometric Sequences
30:14
72
Geometric Series
42:02
73
Proof by Mathematical Induction
22:35
74
Introduction to Angles
26:59
75
Converting Degrees, Minutes, and Seconds
19:10
76
Introduction to Radians
17:26
77
Converting Radians and Degrees
38:45
78
Area of a Sector, Angular Velocity, Applications
36:57
79
Trigonometric Functions and the Unit Circle
39:59
80
How to Use the Unit Circle in Trigonometry
42:57
81
Basic Properties of Trigonometric Functions
1:10:54
82
Reciprocal Identities in Trigonometry
46:54
83
Pythagorean Identities for Trigonometric Functions
37:54
84
The Graphs of Sine and Cosine
34:34
85
Graphing Transformations with Sine and Cosine
1:06:48
86
How to Graph Tangent and Cotangent
26:14
87
Graphing Transformations with Tangent and Cotangent
40:39
88
How to Graph Cosecant and Secant
29:55
89
How to Graph Phase Shifts of Trigonometric Functions
37:52
90
Introduction to Inverse Trigonometric Functions
30:58
91
How to Use Inverse Trigonometric Functions
53:55
92
How to Find Inverse Trigonometric Functions
32:14
93
How to Solve Basic Inverse Trigonometric Functions
7:14
94
An Indepth Look at Using Inverse Trig Functions
1:18:27
95
How to Solve Trigonometric Equations
1:34:36
96
Introduction to Using Trigonometric Identities
23:44
97
How to Prove Trigonometric Identities
55:39
98
Introduction to Sum and Difference Formulas in Trigonometry
51:27
99
Using Sum and Difference Formulas in Trigonometry
58:07
100
Proving the Double and Half Angle Formulas for Trigonometry
27:17
101
How to Use the Double and Half Angle Formulas for Trigonometry
1:20:34
102
How to Use Product to Sum and Sum to Product Formulas in Trig
45:47
103
Introduction to Right Triangle Trigonometry
1:01:47
104
Finding Sides and Angles with Right Triangle Trigonometry
42:46
105
How to Use the Law of Sines in Trigonometry
1:27:46
106
How to Use the Law of Cosines in Trigonometry
56:36
107
How to Find the Area of a Triangle with Trigonometry
16:19
108
Simple Harmonic Motion in Trig
33:23
109
Introduction to Polar Coordinates
38:06
110
How to Convert From Polar Coordinates to Rectangular Coordinates
34:24
111
How to Convert From Rectangular Coordinates to Polar Coordinates
48:53
112
How to Convert From Rectangular Equations to Polar Equations
28:27
113
How to Convert From Polar Equations to Rectangular Equations
26:24
114
How to Graph Basic Polar Equations
24:48
115
How to Graph Advanced Polar Equations with Symmetry
46:38
