University of Pennsylvania

Single Variable Calculus

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Robert Ghrist

Instructor: Robert Ghrist


(309 reviews)

14 hours to complete
3 weeks at 4 hours a week
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19 quizzes

Taught in English

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There are 5 modules in this course

It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>.

What's included

4 videos2 readings5 quizzes

That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations.

What's included

2 videos1 quiz

In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or <b>series</b>. The determination of convergence for such will occupy our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!

What's included

4 videos6 quizzes

This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series.

What's included

4 videos5 quizzes

Are we at the end? Yes, yes, we are. Standing on top of a high peak, looking back down on all that we have climbed together. Let's take one last look down and prepare for what lies above.

What's included

4 videos2 readings2 quizzes


Instructor ratings
4.6 (51 ratings)
Robert Ghrist
University of Pennsylvania
5 Courses184,938 learners

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Recommended if you're interested in Math and Logic

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