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1
Intro to Calculus: Zeno's Paradox
2
Definition of the Limit
3
Right- and Left-hand Limits
4
tan(x) & Vertical Asymptotes
5
More Vertical Asymptotes: sec^2(x)
6
Asymptotes of a Rational Function
7
A Nasty Rational Function
8
The Limit Laws
9
Limit Laws & Polynomials
10
Limit Laws & Rational Functions
11
Squeeze Theorem
12
Continuity: 3 ways it fails
13
Continuity: Two Examples
14
Continuity: Properties
15
Intermediate Value Theorem
16
Rate of Change & Tangent Line
17
Limit Definition of Derivative
18
The Derivative as a Function
19
Derivative of Square Root
20
Derivative: Power Rule
21
Derivative: Sum/Difference Rule
22
Derivative of e^x
23
Derivative: Product Rule
24
Derivative: Quotient Rule
25
Derivative Example Requiring Both Quotient and Product Rule
26
Derivative of sin(x)
27
17th derivative of sin(x)
28
Derivative of tan(x) -- and the other trig functions
29
Trig derivative example
30
Motivating Chain Rule
31
Justifying the Chain Rule
32
Chain Rule Examples
33
Derivative of a^x
34
Intro to Implicit Differentiation
35
Implicit Differentiation Example
36
Second Derivative Using Implicit Differentiation
37
Derivative of ln(x)
38
Logarithmic Differentiation
39
Derivative of Arcsine
40
Derivatives of Inverse Trig Functions
41
Extrema of Function
42
Extreme Value Theorem
43
First Derivative Test
44
Second Derivative and Concavity
45
Sketching the Graph of a Polynomial
46
Sketching Graph of Rational Function
47
L'Hospital's Rule: Zero Over Zero?
48
L'Hospital's Rule: Infinity Over Infinity?
49
L'Hospital's Rule: Infinity Minus Infinity?
50
L'Hospital's Rule: Zero To The Zero?
51
Optimization: Closest Point
52
Optimization: Largest Rectangle in Semicircle
53
Optimization: Largest Box
54
Optimization: Largest Cone Cup
Description:
Explore the fundamentals of calculus in this comprehensive 7-hour course. Begin with an introduction to Zeno's Paradox and delve into the definition of limits, including right- and left-hand limits. Examine vertical asymptotes, limit laws, and the Squeeze Theorem. Study continuity, the Intermediate Value Theorem, and rates of change. Master the limit definition of derivatives and learn various derivative rules, including power, sum/difference, product, and quotient rules. Investigate derivatives of trigonometric, exponential, and logarithmic functions. Tackle implicit differentiation, logarithmic differentiation, and derivatives of inverse trigonometric functions. Explore function extrema, concavity, and graph sketching techniques. Apply L'Hospital's Rule to various indeterminate forms and solve optimization problems involving closest points, largest rectangles, boxes, and cone cups.

Lit Calculus

Math at Andrews
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Intro to Calculus: Zeno's Paradox