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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