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1
Graphs and Limits
2
When Limits Fail to Exist
3
Limit Laws
4
The Squeeze Theorem
5
Limits using Algebraic Tricks
6
When the Limit of the Denominator is 0
7
Limits at Infinity and Graphs
8
Limits at Infinity and Algebraic Tricks
9
Continuity at a Point
10
Continuity Example with a Piecewise Defined Function
11
Continuity on Intervals
12
Continuity and Domains
13
Intermediate Value Theorem
14
Derivatives and Tangent Lines
15
Computing Derivatives from the Definition
16
Interpreting Derivatives
17
Derivatives as Functions and Graphs of Derivatives
18
Proof that Differentiable Functions are Continuous
19
Power Rule and Other Rules for Derivatives
20
Higher Order Derivatives and Notation
21
Derivative of e^x
22
Proof of the Power Rule and Other Derivative Rules
23
Product Rule and Quotient Rule
24
Proof of Product Rule and Quotient Rule
25
Special Trigonometric Limits
26
Derivatives of Trig Functions
27
Proof of Trigonometric Limits and Derivatives
28
Derivatives and Rates of Change (Rectilinear Motion)
29
Marginal Cost
30
The Chain Rule
31
More Chain Rule Examples and Justification
32
Justification of the Chain Rule
33
Implicit Differentiation
34
Derivatives of Exponential Functions
35
Derivatives of Log Functions
36
Logarithmic Differentiation
37
Inverse Trig Functions
38
Derivatives of Inverse Trigonometric Functions
39
Related Rates - Distances
40
Related Rates - Volume and Flow
41
Related Rates - Angle and Rotation
42
Maximums and Minimums
43
Mean Value Theorem
44
Proof of Mean Value Theorem
45
Derivatives and the Shape of the Graph
46
First Derivative Test and Second Derivative Test
47
Derivatives and the shape of the graph - example
48
Extreme Value Examples
49
Linear Approximation
50
The Differential
51
L'Hospital's Rule
52
L'Hospital's Rule on Other Indeterminate Forms
53
Newtons Method
54
Antiderivatives
55
Finding Antiderivatives Using Initial Conditions
56
Any Two Antiderivatives Differ by a Constant
57
Summation Notation
58
Approximating Area
59
The Fundamental Theorem of Calculus, Part 1
60
The Fundamental Theorem of Calculus, Part 2
61
Proof of the Fundamental Theorem of Calculus
62
The Substitution Method
63
Why U-Substitution Works
64
Average Value of a Function
65
Proof of the Mean Value Theorem for Integrals
66
Recitation 2 a solution and some hints
67
Limit as x goes to infinity recitation problem
Description:
Master the fundamentals of calculus in this comprehensive 9-hour course. Explore essential concepts including limits, continuity, derivatives, and integrals. Begin with graphs and limits, progressing through limit laws, the Squeeze Theorem, and continuity. Dive into derivatives, learning computation methods, rules, and applications. Study implicit differentiation, logarithmic differentiation, and inverse trigonometric functions. Analyze related rates, extrema, and the Mean Value Theorem. Investigate the shape of graphs using derivatives and apply techniques like linear approximation and Newton's Method. Conclude with antiderivatives, the Fundamental Theorem of Calculus, and integration techniques. Gain a solid foundation in calculus principles through detailed explanations, proofs, and practical examples.

Calculus 1

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Graphs and Limits