1 Welcome to Calculus 1
2 1.1 Introduction to Limits
3 1.2 Estimating Limits
4 1.3 Limits that Fail to Exist [01] - |x|/x
5 1.3 Limit that Fails to Exist [02] - 1/x^2
6 1.3 Limits that Fail to Exist [03] - sin(1/x)
7 1.4 Properties of LImits
8 1.5 Solving Limits [01] (Factoring)
9 1.5 Solving Limits [02] (Rationalization)
10 1.5 Solving Limits [03] (Fractions)
11 1.6 Trig Limits [01] (1-cosx/x)
12 1.6 Trig Limits [02] (tanx/x & sin3x/x)
13 1.7 Limit Definition - Epsilon Delta [01] (NEW)
14 1.7 Limit Definition - Epsilon Delta [02]
15 1.7 Epsilon Delta Limit Definition [03] (example 1)
16 1.7 Proving a Limit: x^2 = 4 (advanced)
17 1.8 One Sided Limits
18 1.8 One Sided Limit (example 1)
19 1.8 Continuity
20 1.8 Continuity (example 1)
21 1.6 Trig Limits [03] Proof of sinx/x
22 1.9 Geometric Interpretation of sec(x) and tan(x)
23 1.9 Geometry of [1 - cos(x)/x]
24 1.9 Problem Solving [01]
25 1.9 Problem Solving [02]
26 2.1 - Definition of the Derivative
27 2.1 Finding the Slope of a Tangent Line - Example 1
28 2.1 Finding the Slope of Tangent Line - Example 2
29 2.1 Finding the Slope of a Tangent Line - Example 3
30 2.2 Function vs. Derivative - Example 1
31 2.2 Function vs. Derivative - Example 2
32 2.2 Function vs. Derivative - Example 3
33 2.3 Derivative of a Constant
34 2.3 Power Rule
35 2.4 Derivative of sin(x)
36 2.4 Derivatives - Trig Functions
37 2.5 Product Rule
38 2.6 Chain Rule (function notation)
39 2.6 Chain Rule (Leibniz notation)
40 2.6 Chain Rule - Example 1 - e^(2x)
41 2.6 Chain Rule - Example 2 - sin(x^2 + 1)
42 2.6 Chain Rule - Example 3 - Advanced
43 2.7 Quotient Rule 01
44 2.7 Quotient Rule 02
45 2.8 Introduction to Implicit Differentiation
46 2.8 Implicit Differentation (example 1)
47 2.8 Implicit Differentiation (example 2) - ln(x)
48 2.8 Derivative of arcsin(x)
49 2.8 Derivative of arcsec(x)
50 2.9 Related Rates Introduction
51 2.9 Relates Rates Example 01 (Filling a Pool)
52 2.9 Related Rates Example 02 (Filling a Trough)
53 2.9 Related Rates Example 03 (Security Laser Part 1)
54 2.9 Related Rates Example 03 (Security Laser Part 2)
55 2.9 Related Rates Example 04 (Man walking with his shadow)
56 3.1 Introduction to Extrema
57 3.1 Extrema Example
58 3.1 Critical Numbers
59 3.2 Finding Critical Numbers [Example 1]
60 3.2 Finding Critical Numbers [Example 2]
61 3.2 Finding Critical Numbers [Example 3]
62 3.2 Finding Critical Numbers [Example 4]
63 3.2 Finding Critical Numbers [Example 5]
64 3.3 Rolle's Theorem
65 3.3 Mean Value Theorem
66 3.3 Mean Value Thereom Example (prove a car was speeding)
67 3.4 First Derivative Test [Example 1]
68 3.4 First Derivative Test [Example 2] (Part 1)
69 3.4 First Derivative Test [Example 2] (Part 2)
70 3.5 Introduction to Concavity
71 3.5 Concavity and the Second Derivative [1]
72 3.5 Inflection Points
73 3.5 Concavity and the Second Derivative [2]
74 3.6 Optimization - Box with max volume (Part 1)
75 3.6 Optimization - Box with max volume (Part 2)
76 3.6 Optimization 02 (circle and square with maximum area)
77 3.7 Linear Approximation
78 4.1 Introduction to Antiderivatives
79 4.1 Antiderivative Power Rule
80 4.1 Basic Properties of Antiderivatives
81 4.1 Common Antiderivatives
82 4.2 Intro to Area Under a Curve
83 Summation Formulas and Sigma Notation (Part 1) Notation
84 Summation Formulas and Sigma Notation (Part 2) Formulas
85 Summation Formulas and Sigma Notation (Part 3) Advanced Properties
86 Summation Formulas and Sigma Notation (Part 4) Examples
87 4.2 Estimating the Area Under a Curve
88 4.3 Exact Area Under A Curve
89 4.3 Exact Area Under a Curve 02
90 4.3 Exact Area - Left Hand Sum
91 4.3 Exact Area Under a Curve 3
92 4.4 Riemann Sum and the Definite Integral
93 4.5 First Fundamental Thereom of Calculus
94 4.5 First Fundamental Theorem of Calculus (Examples)
95 4.6 Properties of Integrals
96 4.6 Area Under the x-axis
97 4.6 Average Value of a Function
98 5.1 Integration: Re-Writing an Integral - Ex.1
99 5.1 Integration: Re-Writing an Integral - Ex.2
100 5.1 Integration: Re-Writing an Integral - Ex.3
101 5.2 Integration: U-Substitution - Ex.1
102 5.2 Integration: U-Substitution - Ex.2
103 5.2 Integration: U-Substitution - Ex.3
104 5.2 Integration | U-Substitution - Ex. 4
105 5.2 Integration | U-Substitution - Ex. 5
106 5.2 Integration | U-Substitution - Ex.6
107 5.3 Integration | Natural Log (ln) - Ex.1
108 5.3 Integration | Natural Log (ln) - Ex.2
109 5.3 Integration | Natural Log (ln) - Ex.3
110 5.3 Integration | Natural Log (ln) - Ex. 4
111 5.4 Integration | Integral of secx
112 5.4 Integration | Integral of tanx