Give your career the gift of Coursera Plus with $160 off, billed annually. Save today.

University of Pennsylvania

Single Variable Calculus

Robert Ghrist

Instructor: Robert Ghrist

43,858 already enrolled

Included with Coursera Plus

Gain insight into a topic and learn the fundamentals.
4.6

(314 reviews)

10 hours to complete
3 weeks at 3 hours a week
Flexible schedule
Learn at your own pace
Gain insight into a topic and learn the fundamentals.
4.6

(314 reviews)

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

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

19 assignments

Taught in English

See how employees at top companies are mastering in-demand skills

Placeholder
Placeholder

Earn a career certificate

Add this credential to your LinkedIn profile, resume, or CV

Share it on social media and in your performance review

Placeholder

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 assignments

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 assignment

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 assignments

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 assignments

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 assignments

Instructor

Instructor ratings
4.6 (52 ratings)
Robert Ghrist
University of Pennsylvania
5 Courses190,188 learners

Offered by

Recommended if you're interested in Math and Logic

Why people choose Coursera for their career

Felipe M.
Learner since 2018
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
Jennifer J.
Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
Larry W.
Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
Chaitanya A.
"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."

Learner reviews

Showing 3 of 314

4.6

314 reviews

  • 5 stars

    78.73%

  • 4 stars

    12.38%

  • 3 stars

    3.17%

  • 2 stars

    0.95%

  • 1 star

    4.76%

YZ
4

Reviewed on Dec 20, 2021

DK
4

Reviewed on Apr 10, 2021

XL
5

Reviewed on Dec 3, 2017

Placeholder

Open new doors with Coursera Plus

Unlimited access to 7,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription

Advance your career with an online degree

Earn a degree from world-class universities - 100% online

Join over 3,400 global companies that choose Coursera for Business

Upskill your employees to excel in the digital economy

Frequently asked questions