PHILADELPHIA — Learning calculus is no easy feat. But beginning next month, the University of Pennsylvania’s Robert Ghrist will use a new, visually stimulating approach to engage tens of thousands of students in the task with a massive open online course, or MOOC, offered through Coursera’s online platform.

Ghrist is the Andrea Mitchell Penn Integrates Knowledge Professor, with appointments in the School of Engineering and Applied Science’s Department of Electrical and Systems Engineering and in the School of Arts and Sciences’ Department of Mathematics.

His course, Calculus: Single Variable, builds upon a high-school-level knowledge of calculus and will cover similar material to the Advanced Placement Calculus BC course.

Yet Ghrist’s course won’t look like a typical math class. Instead of relying on a textbook, calculators or chalkboards to teach students how to differentiate functions or determine the value of integrals, Ghrist will employ hand-drawn graphics and animations to emphasize conceptual understanding and applications.

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“This is a grand experiment that is going to enact several changes at once,” Ghrist said. “The platform and the openness and the size of the course are different from the way that any other calculus class has been taught.”

Penn entered into an agreement with Coursera earlier this year and has thus far offered 17 courses covering diverse subjects, from health-care economics and gamification to world music and poetry. A new slate of offerings, with repeats of a few popular courses, launches in 2013.

Ghrist has spent the last 10 years developing his calculus curriculum, testing some of his ideas in face-to-face classes at Penn. Freed from the bounds of a textbook, Ghrist’s version of the course aims to appeal to more “modern sensibilities” and includes applications related to economics, biology and data. Working professionals enrolled in the course can use it as an opportunity to brush up on old skills or gain new ones to advance in their jobs.

When the first iteration of Ghrist’s course ends after 13 weeks of instruction, the benefits to future students will just be getting started.

Edward Rock, Penn’s director of open course initiatives, envisions Ghrist’s course becoming a self-contained substitute for calculus textbooks and even whole courses taught far beyond Penn.

“My hope is that five years down the line, Ghrist’s course will be in widespread use both in high schools that teach Calculus BC as well as in many colleges, universities and community colleges,” Rock said.

To jump-start this dissemination, Rock is in discussions with selected high schools in the Philadelphia area and elsewhere to participate in a pilot program, which will begin in the fall of 2013. Teachers who sign up will have the opportunity to use Ghrist’s course on Coursera’s platform as a tool in their own Calculus BC courses. Some high school teachers will be taking the course in the spring of 2013 to become familiar with the material and lessons.

Ghrist noted that the course could also be a boon to gifted, driven high school students who have exhausted the mathematics offerings at their own schools.

“I see this future where some of the really talented and motivated students in high school can go as far as they want to, with no constraints,” Ghrist said. “That is an unambiguously good thing.”

As with Penn’s other offering through Coursera, students can take the calculus course free of charge; even purchasing a calculus textbook isn’t required.

“We’re interested in creating access to underserved populations, so our hope is that thousands of students will learn calculus from this course,” Rock said. “The idea that folks outside of Penn can get the really high-quality instruction that we offer here in a way that scales is really quite intoxicating.”