課程信息
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100 個評分
21 個審閱
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完成時間(小時)

完成時間大約為25 小時

建議:6-8 hours/week...
可選語言

英語(English)

字幕:英語(English)...
100% online

100% online

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
完成時間(小時)

完成時間大約為25 小時

建議:6-8 hours/week...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 3 小時

Computing Areas and Volumes

Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and volume elements, we will see how to tackle tough geometry problems in a principled manner. ...
Reading
6 個視頻(共 78 分鐘), 2 個閱讀材料, 8 個測驗
Video6 個視頻
Simple Areas16分鐘
Complex Areas15分鐘
BONUS!8分鐘
Volumes15分鐘
BONUS!6分鐘
Complex Volumes15分鐘
Reading2 個閱讀材料
How to Get Started in this Course10分鐘
How Grading Works10分鐘
Quiz8 個練習
Core Homework: Simple Areas10分鐘
Challenge Homework: Simple Areas4分鐘
Core Homework: Complex Areas10分鐘
Challenge Homework: Complex Areas6分鐘
Core Homework: Simple Volumes10分鐘
Challenge Homework: Simple Volumes6分鐘
Core Homework: Complex Volumes12分鐘
Challenge Homework: Complex Volumes2分鐘
2
完成時間(小時)
完成時間為 2 小時

Other Geometric Applications

There's more to geometry than just area and volume! In this module, we will take things "to the next level", ascending to higher dimensions. Coming back to the 3-d world, we will return to problems of length and area, but this time in the context of curves and surfaces. As always, the emphasis will be on how to construct the appropriate differential element for integrating. ...
Reading
4 個視頻(共 66 分鐘), 6 個測驗
Video4 個視頻
BONUS13分鐘
Arclength17分鐘
Surface Area16分鐘
Quiz6 個練習
Core Homework: Volume and Dimension6分鐘
Challenge Homework: Volume and Dimension8分鐘
Core Homework: Arclength10分鐘
Challenge Homework: Arclength4分鐘
Core Homework: Surface Area8分鐘
Challenge Homework: Surface Area4分鐘
3
完成時間(小時)
完成時間為 1 小時

Physical Applications

There is so much more to applications of integrals than geometry! So many subjects, from physics to finance, have, at heart, the need for setting up and computing definite integrals. In this short but intense module, we will cover applications including work, force, torque, mass, and present & future value. ...
Reading
3 個視頻(共 36 分鐘), 4 個測驗
Video3 個視頻
Work15分鐘
Elements13分鐘
BONUS!6分鐘
Quiz4 個練習
Core Homework: Work8分鐘
Challenge Homework: Work4分鐘
Core Homework: Elements10分鐘
Challenge Homework: Elements2分鐘
4
完成時間(小時)
完成時間為 2 小時

Averages and Mass

There is a statistical aspect to integrals that has not yet been brought up in this course: integrals are ideal for computing averages. Motivated by physical problems of mass, centroid, and moments of inertia, we will cover applications of integrals to averages. ...
Reading
5 個視頻(共 65 分鐘), 6 個測驗
Video5 個視頻
Averages16分鐘
Centroids16分鐘
BONUS!8分鐘
Moments and Gyrations16分鐘
BONUS!8分鐘
Quiz6 個練習
Core Homework: Averages10分鐘
Challenge Homework: Averages4分鐘
Core Homework: Centroids10分鐘
Challenge Homework: Centroids4分鐘
Core Homework: Moments and Gyrations8分鐘
Challenge Homework: Moments and Gyrations6分鐘

講師

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Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

關於 University of Pennsylvania

The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies. ...

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