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1
Area Between Curves
2
Volumes of Solids of Revolution
3
Volumes Using Cross-Sections
4
Arclength
5
Work as an Integral
6
Average Value of a Function
7
Proof of the Mean Value Theorem for Integrals
8
Integration by Parts
9
Table Method For Integration By Parts by Morgan Goetz
10
Trig Identities
11
Proof of the Angle Sum Formulas
12
Integrals Involving Odd Powers of Sine and Cosine
13
Integrals Involving Even Powers of Sine and Cosine
14
Special Trig Integrals
15
Integration Using Trig Substitution
16
Integrals of Rational Functions
17
Improper Integrals - Type 1
18
Improper Integrals - Type 2
19
The Comparison Theorem for Integrals
20
Sequences - Definitions and Notation
21
Series Definitions
22
Sequences - More Definitions
23
Monotonic and Bounded Sequences Extra
24
L'Hospital's Rule
25
L'Hospital's Rule on Other Indeterminate Forms
26
Convergence of Sequences
27
Geometric Series
28
Koch’s snowflake problem
29
The Integral Test
30
Comparison Test for Series
31
The Limit Comparison Test
32
Proof of the Limit Comparison Test
33
Absolute Convergence
34
The Ratio Test
35
Proof of the Ratio Test
36
Series Convergence Test Strategy
37
Taylor Series Introduction
38
Power Series
39
Convergence of Power Series
40
Power Series Interval of Convergence Example
41
Proofs of Facts about Convergence of Power Series
42
Power Series as Functions
43
Representing Functions with Power Series
44
Using Taylor Series to find Sums of Series
45
Taylor Series Theory and Remainder
46
Parametric Equations
47
Slopes of Parametric Curves
48
Area under a Parametric Curve
49
Arclength of Parametric Curves
50
Polar Coordinates
Description:
Dive into advanced calculus concepts through a comprehensive 7-hour course covering integral calculus, sequences, series, and parametric equations. Master techniques for calculating volumes, arclengths, and areas between curves. Learn integration methods including parts, trig substitution, and improper integrals. Explore convergence tests for sequences and series, and delve into power series and Taylor series. Conclude with an introduction to parametric equations and polar coordinates. Enhance problem-solving skills with proofs and real-world applications throughout the course.

Calculus 2

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Area Between Curves