source: Jim Fowler 2013年11月22日 / list compiled by CosmoLearning

https://stemoutreach.osu.edu/events/mooc-calculus-two-sequences-and-series...

https://www.coursera.org/learn/advanced-calculus

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How can I succeed in this course? - Week 1 Introduction 1:08

What is a sequence? - Week 1 - Lecture 1 4:06

How is a sequence presented? - Week 1 - Lecture 2 5:46

Can the same sequence be presented in different ways? - Week 1 - Lecture 3 3:40

How can we build new sequences from old sequences? - Week 1 - Lecture 4 3:25

What is an arithmetic progression? - Week 1 - Lecture 5 2:19

What is a geometric progression? - Week 1 - Lecture 6 4:27

What is the limit of a sequence? - Week 1 - Lecture 7 4:43

Visually, what is the limit of a sequence? - Week 1 - Lecture 8 1:44

Is it easy to find the limit of a sequence? - Week 1 - Lecture 9 8:04

For some epsilon, how large need N be? - Week 1 - Lecture 10 4:10

How do sequences help with the square root of two? - Week 1 - Lecture 11 3:03

When is a sequence bounded? - Week 1 - Lecture 12 8:28

When is a sequence increasing? - Week 1 - Lecture 13 4:48

What is the Monotone Convergence Theorem? - Week 1 - Lecture 14 1:48

How can the Monotone Convergence Theorem help? - Week 1 - Lecture 15 5:45

Is there a sequence that includes every integer? - Week 1 - Lecture 16 4:47

Is there a sequence that includes every real number? - Week 1 - Lecture 17 5:21

What happens in Week 2? - Week 2 Introduction 1:21

What does sum a_k = L mean? - Week 2 - Lecture 1 3:54

Why does sum (1/2)^k = 2? - Week 2 - Lecture 2 5:21

What is the value of sum r^k for k = m to infinity? - Week 2 - Lecture 3 9:31

What is the value of sum r^k for k = m to infinity? - Week 2 - Lecture 4 7:06

What is sum 1/((k+1) * k)? - Week 2 - Lecture 5 10:11

Why does sum n/(n+1) diverge? - Week 2 - Lecture 6 10:15

Does sum 1/n converge or diverge? - Week 2 - Lecture 7 6:40

Does the series sum (sin^2 k)/(2^k) converge or diverge? - Week 2 - Lecture 8 3:52

What is the comparison test? - Week 2 - Lecture 9 8:27

How can grouping make the comparison test even better? - Week 2 - Lecture 10 6:20

Does sum 1/n^2 converge? - Week 2 - Lecture 11 9:01

In what sense does sum 9 * 10^(-n) equal one? - Week 2 - Lecture 12 5:06

In what sense is sum 9 + 90 + 900 + ... meaningful? - Week 2 - Lecture 13 9:41

What will happen in Week 3? - Week 3 Introduction 1:23

Does sum (n^5)/(4^n) converge? - Week 3 - Lecture 1 13:39

What does the ratio test say? - Week 3 - Lecture 2 7:52

Does the ratio test always work? - Week 3 - Lecture 3 5:35

Does sum (n!)/(n^n) converge? - Week 3 - Lecture 4 9:06

How does n! compare to n^n? - Week 3 - Lecture 5 6:13

Why don't I love the root test? - Week 3 - Lecture 6 3:41

How can integrating help us to address convergence? - Week 3 - Lecture 7 12:27

How else can I show sum 1/n diverges? - Week 3 - Lecture 8 5:06

Does sum 1/n^p converge? - Week 3 - Lecture 9 8:08

Does sum 1/(n log n) converge? - Week 3 - Lecture 10 7:40

How far out can you build a one-sided bridge? - Week 3 - Lecture 11 10:45

What is Week 4 all about? - Week 4 Introduction 1:15

Why have we been assuming the terms are positive? - Week 4 - Lecture 1 3:36

Why do absolutely convergent series just plain converge? - Week 4 - Lecture 2 5:21

Why is absolute convergence an important concept? - Week 4 - Lecture 3 3:38

What is conditional convergence? - Week 4 - Lecture 4 2:52

What is an alternating series? - Week 4 - Lecture 5 4:10

What is the alternating series test? - Week 4 - Lecture 6 11:04

How should I go about checking convergence? - Week 4 - Lecture 7 1:43

Why is monotonicity important for the AST? - Week 4 - Lecture 8 5:44

Why are alternating series important? - Week 4 - Lecture 9 6:10

Why is e irrational? - Week 4 - Lecture 10 8:42

When do two series share the same fate? - Week 4 - Lecture 11 5:54

Why can people get away with writing sum_n a_n? - Week 4 - Lecture 12 4:32

Why is this all so vague\ldots or coarse? - Week 4 - Lecture 13 6:06

What happens when I rearrange the terms in a series? - Week 4 - Lecture 14 7:19

What are power series? - Week 5 Introduction 3:04

For which values does a power series converge? - Week 5 - Lecture 1 3:48

Why does a power series converge absolutely? - Week 5 - Lecture 2 4:54

How complicated might the interval of convergence be? - Week 5 - Lecture 3 5:16

How do I find the radius of convergence? - Week 5 - Lecture 4 3:27

What if the radius of convergence is infinity? - Week 5 - Lecture 5 4:03

What if the radius of convergence is zero? - Week 5 - Lecture 6 3:27

What is a power series centered around a? - Week 5 - Lecture 7 4:07

Can I differentiate a power series? - Week 5 - Lecture 8 3:31

Can I integrate a power series? - Week 5 - Lecture 9 6:19

Why might I believe that sum (x^n)/(n!) is e^x? - Week 5 - Lecture 10 4:14

What happens if I multiply two power series? - Week 5 - Lecture 11 9:28

What happens if I transform 1/(1-x)? - Week 5 - Lecture 12 7:00

What is a formula for the Fibonacci numbers? - Week 5 - Lecture 13 12:13

What is this last week about? - Week 6 Introduction 2:11

What is better than a linear approximation? - Week 6 - Lecture 1 14:13

What is the Taylor series of f around zero? - Week 6 - Lecture 2 10:13

What is the Taylor series of f centered around a? - Week 6 - Lecture 3 4:40

What is the Taylor series for sin x around zero? - Week 6 - Lecture 4 4:37

What is Taylor's theorem? - Week 6 - Lecture 5 11:43

Why is the radius of convergence of 1/(1+x^2) so small? - Week 6 - Lecture 6 9:53

How is Taylor's theorem like the mean value theorem? - Week 6 - Lecture 7 8:05

Approximately, what is cos x when x is near zero? - Week 6 - Lecture 8 8:15

How do Taylor series provide intuition for limits? - Week 6 - Lecture 9 11:04

What is a real analytic function? - Week 6 - Lecture 10 4:55

How are real analytic functions like holograms? - Week 6 - Lecture 11 4:25

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