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Start instantly and learn at your own schedule.

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#### Approx. 25 hours to complete

Suggested: 6-8 hours/week...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

#### Approx. 25 hours to complete

Suggested: 6-8 hours/week...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
3 hours to complete

## 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. ...
6 videos (Total 78 min), 2 readings, 8 quizzes
6 videos
Complex Areas15m
BONUS!8m
Volumes15m
BONUS!6m
Complex Volumes15m
How to Get Started in this Course10m
8 practice exercises
Core Homework: Simple Areas10m
Challenge Homework: Simple Areas4m
Core Homework: Complex Areas10m
Challenge Homework: Complex Areas6m
Core Homework: Simple Volumes10m
Challenge Homework: Simple Volumes6m
Core Homework: Complex Volumes12m
Challenge Homework: Complex Volumes2m
Week
2
2 hours to complete

## 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. ...
4 videos (Total 66 min), 6 quizzes
4 videos
BONUS13m
Arclength17m
Surface Area16m
6 practice exercises
Core Homework: Volume and Dimension6m
Challenge Homework: Volume and Dimension8m
Core Homework: Arclength10m
Challenge Homework: Arclength4m
Core Homework: Surface Area8m
Challenge Homework: Surface Area4m
Week
3
1 hour to complete

## 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. ...
3 videos (Total 36 min), 4 quizzes
3 videos
Work15m
Elements13m
BONUS!6m
4 practice exercises
Core Homework: Work8m
Challenge Homework: Work4m
Core Homework: Elements10m
Challenge Homework: Elements2m
Week
4
2 hours to complete

## 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. ...
5 videos (Total 65 min), 6 quizzes
5 videos
Centroids16m
BONUS!8m
Moments and Gyrations16m
BONUS!8m
6 practice exercises
Core Homework: Averages10m
Challenge Homework: Averages4m
Core Homework: Centroids10m
Challenge Homework: Centroids4m
Core Homework: Moments and Gyrations8m
Challenge Homework: Moments and Gyrations6m

## Instructor

### Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

## About 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. ...

## Frequently Asked Questions

• Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

More questions? Visit the Learner Help Center.