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Calculus: Single Variable Part 4 - Applications
Course
en
English
30 h
This content is rated 4.5 out of 5
- Self-paced
- Free Access
- Fee-based Certificate
- 5 Sequences
- Introductive Level
Course details
Syllabus
- Week 1 - 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 ... - Week 2 - 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... - Week 3 - 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, ... - Week 4 - 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 average... - Week 5 - An Introduction to Probability
This capstone module gives a very brief introduction to probability, using what we know about integrals and differential elements. Beginning with common-sense uniform probabilities, we move on to define probability density functions and the corresponding proba...
Prerequisite
None.
Instructors
Robert Ghrist
Professor
Mathematics and Electrical & Systems Engineering
Editor
The University of Pennsylvania (commonly known as Penn), founded in 1740, is a private university located in Philadelphia, Pennsylvania, USA. A member of the Ivy League, Penn is the fourth oldest institution of higher learning in the United States and considers itself the first university in the United States to offer both undergraduate and graduate degrees.
Platform
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