课程信息
4.9
100 个评分
21 个审阅
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
完成时间(小时)

完成时间大约为25 小时

建议:6-8 hours/week...
可选语言

英语(English)

字幕:英语(English)...
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
完成时间(小时)

完成时间大约为25 小时

建议:6-8 hours/week...
可选语言

英语(English)

字幕:英语(English)...

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 3 小时

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 个视频(共 78 分钟), 2 个阅读材料, 8 个测验
Video6 个视频
Simple Areas16分钟
Complex Areas15分钟
BONUS!8分钟
Volumes15分钟
BONUS!6分钟
Complex Volumes15分钟
Reading2 个阅读材料
How to Get Started in this Course10分钟
How Grading Works10分钟
Quiz8 个练习
Core Homework: Simple Areas10分钟
Challenge Homework: Simple Areas4分钟
Core Homework: Complex Areas10分钟
Challenge Homework: Complex Areas6分钟
Core Homework: Simple Volumes10分钟
Challenge Homework: Simple Volumes6分钟
Core Homework: Complex Volumes12分钟
Challenge Homework: Complex Volumes2分钟
2
完成时间(小时)
完成时间为 2 小时

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 个视频(共 66 分钟), 6 个测验
Video4 个视频
BONUS13分钟
Arclength17分钟
Surface Area16分钟
Quiz6 个练习
Core Homework: Volume and Dimension6分钟
Challenge Homework: Volume and Dimension8分钟
Core Homework: Arclength10分钟
Challenge Homework: Arclength4分钟
Core Homework: Surface Area8分钟
Challenge Homework: Surface Area4分钟
3
完成时间(小时)
完成时间为 1 小时

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 个视频(共 36 分钟), 4 个测验
Video3 个视频
Work15分钟
Elements13分钟
BONUS!6分钟
Quiz4 个练习
Core Homework: Work8分钟
Challenge Homework: Work4分钟
Core Homework: Elements10分钟
Challenge Homework: Elements2分钟
4
完成时间(小时)
完成时间为 2 小时

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 个视频(共 65 分钟), 6 个测验
Video5 个视频
Averages16分钟
Centroids16分钟
BONUS!8分钟
Moments and Gyrations16分钟
BONUS!8分钟
Quiz6 个练习
Core Homework: Averages10分钟
Challenge Homework: Averages4分钟
Core Homework: Centroids10分钟
Challenge Homework: Centroids4分钟
Core Homework: Moments and Gyrations8分钟
Challenge Homework: Moments and Gyrations6分钟

讲师

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

关于 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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