source: Jim Fowler 2013年5月2日 / list compiled by CosmoLearning

https://zh-tw.coursera.org/learn/calculus1

https://math.osu.edu/people/fowler.291

This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems.

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Who will help me? - Week 1 Introduction 1:48

What is a function? - Week 1 - Lecture 1 11:20

When are two functions the same? - Week 1 - Lecture 2 5:58

How can more functions be made? - Week 1 - Lecture 3 3:26

What are some real-world examples of functions? - Week 1 - Lecture 4 6:57

What is the domain of square root? - Week 1 - Lecture 5 15:57

What is the limit of (x^2 - 1)/(x-1)? - Week 1 - Lecture 6 8:49

What is the limit of (sin x)/x? - Week 1 - Lecture 7 6:11

What is the limit of sin (1/x)? - Week 1 - Lecture 8 8:18

Morally, what is the limit of a sum? - Week 1 - Lecture 9 6:15

What is the limit of a product? - Week 1 - Lecture 10 2:14

What is the limit of a quotient? - Week 1 - Lecture 11 9:18

How fast does a ball move? - Week 1 - Lecture 12 16:43

Where are we in the course? - Week 2 Introduction 1:23

What is a one-sided limit? - Week 2 - Lecture 1 3:46

What does "continuous" mean? - Week 2 - Lecture 2 5:02

What is the intermediate value theorem? - Week 2 - Lecture 3 2:25

How can I approximate root two? - Week 2 - Lecture 4 10:21

Why is there an x so that f(x) = x? - Week 2 - Lecture 5 5:13

What does lim f(x) = infinity mean? - Week 2 - Lecture 6 5:25

What is the limit f(x) as x approaches infinity? - Week 2 - Lecture 7 4:44

Why is infinity not a real number? - Week 2 - Lecture 8 6:22

What is the difference between potential and actual infinity? - Week 2 - Lecture 9 2:50

What is the slope of a staircase? - Week 2 - Lecture 10 6:51

How fast does water drip from a faucet? - Week 2 - Lecture 11 5:22

What is the official definition of limit? - Week 2 - Lecture 12 3:35

Why is the limit of x^2 as x approaches 2 equal to 4? - Week 2 - Lecture 13 5:00

Why is the limit of 2x as x approaches 10 equal to 20? - Week 2 - Lecture 14 2:19

What comes next? Derivatives? - Week 3 Introduction 1:38

What is the definition of derivative? - Week 3 - Lecture 1 6:35

What is a tangent line? - Week 3 - Lecture 2 3:29

Why is the absolute value function not differentiable? - Week 3 - Lecture 3 2:39

How does wiggling x affect f(x)? - Week 3 - Lecture 4 3:30

Why is sqrt(9999) so close to 99.995? - Week 3 - Lecture 5 5:44

What information is recorded in the sign of the derivative? - Week 3 - Lecture 6 4:14

Why is a differentiable function necessarily continuous? - Week 3 - Lecture 7 6:02

What is the derivative of a constant multiple of f(x)? - Week 3 - Lecture 8 4:54

Why is the derivative of x^2 equal to 2x? - Week 3 - Lecture 9 12:22

What is the derivative of x^n? - Week 3 - Lecture 10 7:32

What is the derivative of x^3 + x^2? - Week 3 - Lecture 11 5:09

Why is the derivative of a sum the sum of derivatives? - Week 3 - Lecture 12 4:49

What will Week 4 bring us? - Week 4 Introduction 1:22

What is the derivative of f(x) g(x)? - Week 4 - Lecture 1 6:47

Morally, why is the product rule true? - Week 4 - Lecture 2 6:17

How does one justify the product rule? - Week 4 - Lecture 3 6:11

What is the quotient rule? - Week 4 - Lecture 4 4:11

How can I remember the quotient rule? - Week 4 - Lecture 5 5:58

What is the meaning of the derivative of the derivative? - Week 4 - Lecture 6 11:04

What does the sign of the second derivative encode? - Week 4 - Lecture 7 4:27

What does d/dx mean by itself? - Week 4 - Lecture 8 4:06

What are extreme values? - Week 4 - Lecture 9 7:24

How can I find extreme values? - Week 4 - Lecture 10 9:56

Do all local minimums look basically the same when you zoom in? - Week 4 - Lecture 11 3:56

How can I sketch a graph by hand? - Week 4 - Lecture 12 7:29

What is a function which is its own derivative? - Week 4 - Lecture 13 9:02

Is there anything more to learn about derivatives? - Week 5 Introduction 1:01

What is the chain rule? - Week 5 - Lecture 1 10:33

What is the derivative of (1+2x)^5 and sqrt(x^2 + 0.0001)? - Week 5 - Lecture 2 7:05

What is implicit differentiation? - Week 5 - Lecture 3 5:35

What is the folium of Descartes? - Week 5 - Lecture 4 4:42

How does the derivative of the inverse relate to the original? - Week 5 - Lecture 5 10:21

What is the derivative of log? - Week 5 - Lecture 6 6:56

What is logarithmic differentiation? - Week 5 - Lecture 7 4:26

How can we multiply quickly? - Week 5 - Lecture 8 8:49

How do we justify the power rule? - Week 5 - Lecture 9 11:18

How can logarithms help to prove the product rule? - Week 5 - Lecture 10 3:29

How do we prove the quotient rule? - Week 5 - Lecture 11 5:02

How does one prove the chain rule? - Week 5 - Lecture 12 6:49

What are transcendental functions? - Week 6 Introduction 2:05

Why does trigonometry work? - Week 6 - Lecture 1 3:13

Why are there these other trigonometric functions? - Week 6 - Lecture 2 4:49

What is the derivative of sine and cosine? - Week 6 - Lecture 3 10:05

What is the derivative of tan x? - Week 6 - Lecture 4 9:26

What are the derivatives of the other trigonometric functions? - Week 6 - Lecture 5 5:36

What is the derivative of sin(x^2)? - Week 6 - Lecture 6 4:37

What are inverse trigonometric functions? - Week 6 - Lecture 7 4:33

What are the derivatives of inverse trig functions? - Week 6 - Lecture 8 10:27

Why do sine and cosine oscillate? - Week 6 - Lecture 9 4:40

How can we get a formula for sin(a+b)? - Week 6 - Lecture 10 4:16

How can I approximate sin 1? - Week 6 - Lecture 11 3:27

How can we multiply numbers with trigonometry? - Week 6 - Lecture 12 4:12

What applications of the derivative will we do this week? - Week 7 Introduction 1:23

How can derivatives help us to compute limits? - Week 7 - Lecture 1 9:27

How can l'Hôpital help with limits not of the form 0/0? - Week 7 - Lecture 2 14:44

Why shouldn't I fall in love with l'Hôpital? - Week 7 - Lecture 3 8:16

How long until the gray goo destroys Earth? - Week 7 - Lecture 4 3:47

What does a car sound like as it drives past? - Week 7 - Lecture 5 3:58

How fast does the shadow move? - Week 7 - Lecture 6 5:12

How fast does the ladder slide down the building? - Week 7 - Lecture 7 3:52

How quickly does a bowl fill with green water? - Week 7 - Lecture 8 4:08

How quickly does the water level rise in a cone? - Week 7 - Lecture 9 7:01

How quickly does a balloon fill with air? - Week 7 - Lecture 10 3:46

What sorts of optimization problems will calculus help us solve? - Week 8 Introduction 1:39

What is the extreme value theorem? - Week 8 - Lecture 1 8:57

How do I find the maximum and minimum values of f on a given domain? - Week 8 - Lecture 2 9:07

Why do we have to bother checking the endpoints? - Week 8 - Lecture 3 4:16

Why bother considering where the function is not differentiable? - Week 8 - Lecture 4 7:18

How can you build the best fence for your sheep? - Week 8 - Lecture 5 8:50

How large can xy be if x + y = 24? - Week 8 - Lecture 6 5:43

How do you design the best soup can? - Week 8 - Lecture 7 10:33

Where do three bubbles meet? - Week 8 - Lecture 8 12:46

How large of an object can you carry around a corner? - Week 8 - Lecture 9 10:33

How short of a ladder will clear a fence? - Week 8 - Lecture 10 4:04

What is up with all the numerical analysis this week? - Week 9 Introduction 1:35

Where does f(x+h) = f(x) + h f'(x) come from? - Week 9 - Lecture 1 6:00

What is the volume of an orange rind? - Week 9 - Lecture 2 6:42

What happens if I repeat linear approximation? - Week 9 - Lecture 3 10:34

Why is log 3 base 2 approximately 19/12? - Week 9 - Lecture 4 10:22

What does dx mean by itself? - Week 9 - Lecture 5 5:39

What is Newton's method? - Week 9 - Lecture 6 9:56

What is a root of the polynomial x^5 + x^2 - 1? - Week 9 - Lecture 7 6:56

How can Newton's method help me to divide quickly? - Week 9 - Lecture 8 7:26

What is the mean value theorem? - Week 9 - Lecture 9 6:52

Why does f'(x) positive imply that f is increasing? - Week 9 - Lecture 10 5:11

Should I bother to find the point c in the mean value theorem? - Week 9 - Lecture 11 4:28

What does it mean to antidifferentiate? - Week 10 Introduction 2:21

How do we handle the fact that there are many antiderivatives? - Week 10 - Lecture 1 5:27

What is the antiderivative of a sum? - Week 10 - Lecture 2 3:44

What is an antiderivative for x^n? - Week 10 - Lecture 3 7:37

What is the most general antiderivative of 1/x? - Week 10 - Lecture 4 4:15

What are antiderivatives of trigonometric functions? - Week 10 - Lecture 5 5:45

What are antiderivatives of e^x and natural log? - Week 10 - Lecture 6 2:46

How difficult is factoring compared to multiplying? - Week 10 - Lecture 7 5:31

What is an antiderivative for e^(-x^2)? - Week 10 - Lecture 8 4:50

What is the antiderivative of f(mx+b)? - Week 10 - Lecture 9 5:20

Knowing my velocity, what is my position? - Week 10 - Lecture 10 3:18

Knowing my acceleration, what is my position? - Week 10 - Lecture 11 4:25

What is the antiderivative of sine squared? - Week 10 - Lecture 12 3:19

What is a slope field? - Week 10 - Lecture 13 4:57

If we are not differentiating, what are we going to do? - Week 11 Introduction 2:58

How can I write sums using a big Sigma? - Week 11 - Lecture 1 5:11

What is the sum 1 + 2 + ... + k? - Week 11 - Lecture 2 6:12

What is the sum of the first k odd numbers? - Week 11 - Lecture 3 4:16

What is the sum of the first k perfect squares? - Week 11 - Lecture 4 6:48

What is the sum of the first k perfect cubes? - Week 11 - Lecture 5 5:58

What does area even mean? - Week 11 - Lecture 6 7:10

How can I approximate the area of a curved region? - Week 11 - Lecture 7 9:58

What is the definition of the integral of f(x) from x = a to b? - Week 11 5:49

What is the integral of x^2 from x = 0 to 1? - Week 11 - Lecture 9 8:10

What is the integral of x^3 from x = 1 to 2? - Week 11 - Lecture 10 8:37

When is the accumulation function increasing? Decreasing? - Week 11 4:45

What sorts of properties does the integral satisfy? - Week 11 - Lecture 12 4:43

What is the integral of sin x dx from -1 to 1? - Week 11 - Lecture 13 3:16

What is the big deal about the fundamental theorem of calculus? - Week 12 Introduction 2:14

What is the fundamental theorem of calculus? - Week 12 - Lecture 1 5:33

How can I use the fundamental theorem of calculus to integrate? - Week 12 - Lecture 2 6:08

What is the integral of sin x dx from x = 0 to x = pi? - Week 12 - Lecture 3 3:33

What is the integral of x^4 dx from x = 0 to x = 1? - Week 12 - Lecture 4 4:16

What is the area between the graphs of y = sqrt(x) and y = x^2? - Week 12 - Lecture 5 6:27

What is the area between the graphs of y = x^2 and y = 1 - x^2? - Week 12 - Lecture 6 6:31

What is the accumulation function for sqrt(1-x^2)? - Week 12 - Lecture 7 8:40

Why does the Euler method resemble a Riemann sum? - Week 12 - Lecture 8 4:30

In what way is summation like integration? - Week 12 - Lecture 9 2:32

What is the sum of n^4 for n = 1 to n = k? - Week 12 - Lecture 10 9:25

Physically, why is the fundamental theorem of calculus true? - Week 12 - Lecture 11 4:01

What is d/da integral f(x) dx from x = a to x = b? - Week 12 - Lecture 12 5:07

How is this course structured? - Week 13 Introduction 2:16

How does the chain rule help with antidifferentiation? - Week 13 - Lecture 1 5:32

When I do u-substitution, what should u be? - Week 13 - Lecture 2 7:11

How should I handle the endpoints when doing u-substitution? - Week 13 - Lecture 3 5:14

Might I want to do u-substitution more than once? - Week 13 - Lecture 4 4:23

What is the integral of dx / (x^2 + 4x + 7)? - Week 13 - Lecture 5 9:05

What is the integral of (x+10)(x-1)^10 dx from x = 0 to x = 1? - Week 13 - Lecture 6 5:37

What is the integral of x / (x+1)^(1/3) dx? - Week 13 - Lecture 7 3:55

What is the integral of dx / (1 + cos x) ? - Week 13 - Lecture 8 4:17

What is d/dx integral sin t dt from t = 0 to t = x^2? - Week 13 - Lecture 9 3:52

Formally, why is the fundamental theorem of calculus true? - Week 13 - Lecture 10 6:14

Without resorting to the FTC, why does substitution work? - Week 13 - Lecture 11 3:49

What remains to be done? - Week 14 Introduction 1:30

What antidifferentiation rule is the product rule in reverse? - Week 14 - Lecture 1 5:06

What is an antiderivative of x e^x? - Week 14 - Lecture 2 4:14

How does parts help when antidifferentiating log x? - Week 14 - Lecture 3 2:03

What is an antiderivative of e^x cos x? - Week 14 - Lecture 4 6:13

What is an antiderivative of e^(sqrt(x))? - Week 14 - Lecture 5 3:26

What is an antiderivative of sin^(2n+1) x cos^(2n) x dx? - Week 14 - Lecture 6 5:51

What is the integral of sin^(2n) x dx from x = 0 to x = pi? - Week 14 - Lecture 7 8:02

What is the integral of sin^n x dx in terms of sin^(n-2) x dx? - Week 14 - Lecture 8 11:34

Why is pi less than 22/7? - Week 14 - Lecture 9 8:26

What application of integration will we consider? - Week 15 Introduction 1:46

What happens when I use thin horizontal rectangles to compute area? - Week 15 - Lecture 1 6:38

When should I use horizontal as opposed to vertical pieces? - Week 15 - Lecture 2 5:47

What does "volume" even mean? - Week 15 - Lecture 3 4:48

What is the volume of a sphere? - Week 15 - Lecture 4 6:04

How do washers help to compute the volume of a solid of revolution? - Week 15 - Lecture 5 5:20

What is the volume of a thin shell? - Week 15 - Lecture 6 7:49

What is the volume of a sphere with a hole drilled in it? - Week 15 - Lecture 7 7:39

What does "length" even mean? - Week 15 - Lecture 8 4:17

On the graph of y^2 = x^3, what is the length of a certain arc? - Week 15 - Lecture 9 4:16

This title is missing a question mark. - Week 15 - Lecture 10 1:16

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