University of Pennsylvania
Calculus: Single Variable Part 4 - Applications
University of Pennsylvania

Calculus: Single Variable Part 4 - Applications

Taught in English

27,576 already enrolled

Course

Gain insight into a topic and learn the fundamentals

Robert Ghrist

Instructor: Robert Ghrist

4.9

(260 reviews)

20 hours to complete
3 weeks at 6 hours a week
Flexible schedule
Learn at your own pace

Details to know

Assessments

31 quizzes

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There are 5 modules in this course

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.

What's included

6 videos2 readings8 quizzes

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.

What's included

4 videos6 quizzes

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.

What's included

3 videos4 quizzes

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.

What's included

5 videos6 quizzes

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 probability element. Building on the physical intuition obtained from centers of mass and moments of inertia, we offer a unique perspective on expectation, variance, and standard deviation.

What's included

3 videos1 reading7 quizzes

Instructor

Instructor ratings
4.9 (37 ratings)
Robert Ghrist
University of Pennsylvania
5 Courses180,880 learners

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Recommended if you're interested in Math and Logic

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4.9

260 reviews

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