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【俄亥俄州立大学】 Calculus One #微积分基础（Coursera精选）

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转载于 ：www.coursera.com 如有侵权 联系删除！ 微积分是关于非常大，非常小，和事物如何变化。令人惊讶的是，似乎如此抽象的东西最终解释了现实世界。微积分在生物学、物理学和社会科学中扮演着重要的角色。通过在课堂外集中注意力，我们将看到日常生活中微积分的例子。
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视频选集
（1/193）
01_why-is-calculus-going-to-be-so-much-fun
02:25
02_how-is-this-course-structured
01:13
01_how-do-we-get-started-with-calculus
01:44
01_what-is-a-function
11:20
02_when-are-two-functions-the-same
05:59
03_how-can-more-functions-be-made
03:26
01_what-are-some-real-world-examples-of-functions
06:57
02_what-is-the-domain-of-square-root
15:57
01_morally-what-is-the-limit-of-a-sum
06:16
02_what-is-the-limit-of-sin-1-x
08:18
03_what-is-the-limit-of-sin-x-x
06:11
04_what-is-the-limit-of-x-2-1-x-1
08:49
01_what-is-the-limit-of-a-product
02:15
02_what-is-the-limit-of-a-quotient
09:18
01_how-fast-does-a-ball-move
16:43
01_what-else-is-there-to-study-about-functions-and-limits
01:34
01_what-is-a-one-sided-limit
03:46
02_what-does-continuous-mean
05:02
03_what-is-the-intermediate-value-theorem
02:25
04_how-can-i-approximate-root-two
10:21
01_why-is-there-an-x-so-that-f-x-x
05:13
02_what-does-lim-f-x-infinity-mean
05:25
03_what-is-the-limit-f-x-as-x-approaches-infinity
04:44
04_why-is-infinity-not-a-number
06:22
01_what-is-the-difference-between-potential-and-actual-infinity
02:51
02_what-is-the-slope-of-a-staircase
06:51
03_how-fast-does-water-drip-from-a-faucet
05:22
01_what-is-the-official-definition-of-limit
03:36
02_why-is-the-limit-of-x-2-as-x-approaches-2-equal-to-4
05:00
03_why-is-the-limit-of-2x-as-x-approaches-10-equal-to-20
02:19
01_what-comes-next-derivatives
01:09
01_what-is-the-definition-of-derivative
06:35
02_what-is-a-tangent-line
03:29
03_why-is-the-absolute-value-function-not-differentiable
02:39
04_how-does-wiggling-x-affect-f-x
03:31
01_why-is-sqrt-9999-so-close-to-99-995
05:44
02_what-information-is-recorded-in-the-sign-of-the-derivative
04:14
01_why-is-a-differentiable-function-necessarily-continuous
06:02
02_what-is-the-derivative-of-a-constant-multiple-of-f-x
04:54
01_why-is-the-derivative-of-x-2-equal-to-2x
12:22
02_what-is-the-derivative-of-x-n
07:32
03_what-is-the-derivative-of-x-3-x-2
05:09
04_why-is-the-derivative-of-a-sum-the-sum-of-derivatives
04:49
01_how-do-we-compute-derivatives
01:41
01_what-is-the-derivative-of-f-x-g-x
06:47
02_morally-why-is-the-product-rule-true
06:17
03_how-does-one-justify-the-product-rule
06:11
01_what-is-the-quotient-rule
04:11
02_how-can-i-remember-the-quotient-rule
05:58
01_what-is-the-meaning-of-the-derivative-of-the-derivative
11:04
02_what-does-the-sign-of-the-second-derivative-encode
04:27
03_what-does-d-dx-mean-by-itself
04:07
01_what-are-extreme-values
07:24
02_how-can-i-find-extreme-values
09:56
03_do-all-local-minimums-look-basically-the-same-when-you-zoom-in
03:56
04_how-can-i-sketch-a-graph-by-hand
07:29
01_what-is-a-function-which-is-its-own-derivative
09:02
01_is-there-anything-more-to-learn-about-derivatives
01:43
01_what-is-the-chain-rule
10:33
02_what-is-the-derivative-of-1-2x-5-and-sqrt-x-2-0-0001
07:05
01_what-is-implicit-differentiation
05:35
02_what-is-the-folium-of-descartes
04:42
01_how-does-the-derivative-of-the-inverse-function-relate-to-the-derivative-of-t
10:21
02_what-is-the-derivative-of-log
06:56
03_what-is-logarithmic-differentiation
04:26
01_how-can-we-multiply-quickly
08:49
01_how-do-we-justify-the-power-rule
11:18
02_how-can-logarithms-help-to-prove-the-product-rule
03:29
03_how-do-we-prove-the-quotient-rule
05:02
04_bonus-how-does-one-prove-the-chain-rule
06:49
01_what-are-derivatives-of-transcendental-functions
01:24
01_what-are-transcendental-functions
02:05
02_why-does-trigonometry-work
03:13
03_why-are-there-these-other-trigonometric-functions
04:49
01_what-is-the-derivative-of-sine-and-cosine
10:05
02_what-is-the-derivative-of-tan-x
09:26
03_what-is-the-derivative-of-sin-x-2
04:37
04_what-are-the-derivatives-of-the-other-trigonometric-functions
05:36
01_what-are-inverse-trigonometric-functions
04:33
02_what-are-the-derivatives-of-inverse-trig-functions
10:27
01_why-do-sine-and-cosine-oscillate
04:40
02_how-can-we-get-a-formula-for-sin-a-b
04:16
03_how-can-i-approximate-sin-1
03:26
01_how-can-we-multiply-numbers-with-trigonometry
04:12
01_why-would-i-ever-want-to-take-derivatives
02:06
01_how-can-derivatives-help-us-to-compute-limits
09:27
02_how-can-l-hopital-help-with-limits-not-of-the-form-0-0
14:44
03_why-shouldn-t-i-fall-in-love-with-l-hopital
08:16
01_how-long-until-the-gray-goo-destroys-earth
03:48
02_what-does-a-car-sound-like-as-it-drives-past
03:58
01_how-fast-does-the-shadow-move
05:12
02_how-fast-does-the-ladder-slide-down-the-building
03:52
03_how-quickly-does-a-bowl-fill-with-green-water
04:08
04_how-quickly-does-the-water-level-rise-in-a-cone
07:01
05_how-quickly-does-a-balloon-fill-with-air
03:46
01_why-is-optimization-part-of-this-course
01:55
01_what-is-the-extreme-value-theorem
08:58
02_what-sorts-of-optimization-problems-will-calculus-help-us-solve
01:40
01_how-do-i-find-the-maximum-and-minimum-values-of-f-on-a-given-domain
09:07
02_why-do-we-have-to-bother-checking-the-endpoints
04:16
03_why-bother-considering-points-where-the-function-is-not-differentiable
07:18
04_how-can-you-build-the-best-fence-for-your-sheep
08:50
01_how-large-can-xy-be-if-x-y-24
05:43
02_how-do-you-design-the-best-soup-can
10:33
01_where-do-three-bubbles-meet
12:46
02_how-large-of-an-object-can-you-carry-around-a-corner
10:33
03_how-short-of-a-ladder-will-clear-a-fence
04:04
01_why-are-we-thinking-about-linear-approximation
01:30
02_what-is-up-with-all-the-numerical-analysis-this-week
01:35
03_where-does-f-x-h-f-x-h-f-x-come-from
06:00
04_what-is-the-volume-of-an-orange-rind
06:42
01_what-happens-if-i-repeat-linear-approximation
10:34
02_why-is-log-3-base-2-approximately-19-12
10:22
01_what-does-dx-mean-by-itself
05:39
01_what-is-newtons-method
09:56
02_what-is-a-root-of-the-polynomial-x-5-x-2-1
06:56
03_how-can-newtons-method-help-me-to-divide-quickly
07:26
01_what-is-the-mean-value-theorem
06:52
02_why-does-f-x-0-imply-that-f-is-increasing
05:11
03_should-i-bother-to-find-the-point-c-in-the-mean-value-theorem
04:28
01_what-does-it-mean-to-antidifferentiate
02:49
01_how-do-we-handle-the-fact-that-there-are-many-antiderivatives
05:27
01_what-is-the-antiderivative-of-a-sum
03:44
02_what-is-an-antiderivative-for-x-n
07:37
03_what-is-the-most-general-antiderivative-of-1-x
04:15
04_what-are-antiderivatives-of-trigonometric-functions
05:45
05_what-are-antiderivatives-of-e-x-and-natural-log
02:46
01_what-is-the-antiderivative-of-f-mx-b
05:20
02_what-is-an-antiderivative-for-e-x-2
04:50
03_how-difficult-is-factoring-compared-to-multiplying
05:31
01_knowing-my-velocity-what-is-my-position
03:18
02_knowing-my-acceleration-what-is-my-position
04:25
03_what-is-the-antiderivative-of-sine-squared
03:19
04_what-is-a-slope-field
04:57
01_if-we-are-not-differentiating-what-are-we-going-to-do
02:28
01_how-can-i-write-sums-using-a-big-sigma
05:11
02_what-is-the-sum-1-2-k
06:12
03_what-is-the-sum-of-the-first-k-odd-numbers
04:16
04_what-is-the-sum-of-the-first-k-perfect-squares
06:48
05_what-is-the-sum-of-the-first-k-perfect-cubes
05:58
01_what-does-area-even-mean
07:10
01_how-can-i-approximate-the-area-of-a-curved-region
09:58
02_what-is-the-definition-of-the-integral-of-f-x-from-x-a-to-b
05:49
01_what-is-the-integral-of-x-2-from-x-0-to-1
08:10
02_what-is-the-integral-of-x-3-from-x-1-to-2
08:37
01_what-sorts-of-properties-does-the-integral-satisfy
04:43
02_when-is-the-accumulation-function-increasing-decreasing
04:45
01_what-is-the-integral-of-sin-x-dx-from-1-to-1
03:16
01_what-is-the-big-deal-about-the-fundamental-theorem-of-calculus
02:35
01_what-is-the-fundamental-theorem-of-calculus
05:33
01_how-can-i-use-the-fundamental-theorem-of-calculus-to-evaluate-integrals
06:08
02_what-is-the-integral-of-sin-x-dx-from-x-0-to-x-pi
03:33
03_what-is-the-integral-of-x-4-dx-from-x-0-to-x-1
04:16
01_what-is-the-area-between-the-graphs-of-y-sqrt-x-and-y-x-2
06:28
02_what-is-the-area-between-the-graphs-of-y-x-2-and-y-1-x-2
06:31
03_what-is-the-accumulation-function-for-sqrt-1-x-2
08:40
01_why-does-the-euler-method-resemble-a-riemann-sum
04:30
02_in-what-way-is-summation-like-integration
02:32
03_what-is-the-sum-of-n-4-for-n-1-to-n-k
09:25
04_physically-why-is-the-fundamental-theorem-of-calculus-true
04:01
05_what-is-d-da-integral-f-x-dx-from-x-a-to-x-b
05:07
01_how-can-we-compute-more-antiderivatives
01:36
01_how-does-the-chain-rule-help-with-antidifferentiation
05:32
02_when-i-do-u-substitution-what-should-u-be
07:10
03_how-should-i-handle-the-endpoints-when-doing-u-substitution
05:14
04_might-i-want-to-do-u-substitution-more-than-once
04:23
01_what-is-the-integral-of-dx-x-2-4x-7
09:05
02_what-is-the-integral-of-x-10-x-1-10-dx-from-x-0-to-x-1
05:37
03_what-is-the-integral-of-x-x-1-1-3-dx
03:55
04_what-is-the-integral-of-dx-1-cos-x
04:17
01_what-is-d-dx-integral-sin-t-dt-from-t-0-to-t-x-2
03:52
02_formally-why-is-the-fundamental-theorem-of-calculus-true
06:14
03_without-resorting-to-the-fundamental-theorem-why-does-substitution-work
03:49
01_how-will-we-find-antiderivatives-for-more-complicated-expressions
01:34
01_what-antidifferentiation-rule-corresponds-to-the-product-rule-in-reverse
05:05
02_what-is-an-antiderivative-of-x-e-x
04:14
03_how-does-parts-help-when-antidifferentiating-log-x
02:03
04_what-is-an-antiderivative-of-e-x-cos-x
06:13
01_what-is-an-antiderivative-of-e-sqrt-x
03:26
01_what-is-an-antiderivative-of-sin-2n-1-x-cos-2n-x-dx
05:51
02_what-is-the-integral-of-sin-2n-x-dx-from-x-0-to-x-pi
08:02
03_what-is-the-integral-of-sin-n-x-dx-in-terms-of-sin-n-2-x-dx
11:34
01_why-is-pi-22-7
08:26
01_what-can-we-do-with-integrals-besides-calculating-area
01:28
01_what-happens-when-i-use-thin-horizontal-rectangles-to-compute-area
06:38
02_when-should-i-use-horizontal-as-opposed-to-vertical-pieces
05:47
01_what-does-volume-even-mean
04:48
02_what-is-the-volume-of-a-sphere
06:05
03_how-do-washers-help-to-compute-the-volume-of-a-solid-of-revolution
05:20
04_what-is-the-volume-of-a-thin-shell
07:49
05_what-is-the-volume-of-a-sphere-with-a-hole-drilled-in-it
07:38
01_what-does-length-even-mean
04:17
02_on-the-graph-of-y-2-x-3-what-is-the-length-of-a-certain-arc
04:15

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