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Learn calculus with online courses and programs

Calculus is the gateway to advanced mathematics. As one of the foundations of modern scientific practice, it’s a vital tool for engineers of all kinds. Learn calculus with online courses delivered through edX.

What is calculus?

Calculus is a branch of mathematics that studies rates of change and areas around curves. From animations to software applications, calculus and its formulas can be found all around us.

Differential calculus involves derivatives, which measure a function’s rate of change at a specific point.Footnote 1 For example, stock analysts can use derivatives to speculate whether a certain stock will rise or fall in a specific time period. 

By contrast, integral calculus involves the measurement of infinitesimal quantities.Footnote 2 An integral represents an area under a curve on a graph. You can use integral calculus to determine the length of cable needed to connect two electrical substations, with distance represented by a certain function. In a sense, derivatives and integrals are opposites. Together, they form the field of calculus.

In the late 17th century, Isaac Newton and Gottfried Leibniz introduced the concept of calculus independently of one another. Newton’s laws of motion and gravitation are two popular examples of the earliest concepts that led to the development of calculus. Calculus was continually developed over the following centuries, laying the foundation for modern mathematical explorations and physics as we know it.

Today, calculus has countless applications across disciplines and is commonly used in the hard sciences and technical fields such as chemical or environmental engineering. Employers need candidates with strong calculus skills in a variety of industries, including:

  • Medicine: applies calculus formulas to understand relationships between patients and drug absorption, measure organ function, or analyze images. 

  • Biological research: relies on calculations to project the growth or decay of bacteria colonies, or to monitor how a patient’s temperature changes as a direct result of a particular medication.

  • Economics: helps lenders calculate the amount of interest to be paid on a loan, business owners increase profits, or manufacturers understand how work hours impact productivity.Footnote 3

  • Architecture: uses calculus to create scale models, design a symmetrical structure, or achieve balance.Footnote 4

If you want to work in a field that requires knowledge of this branch of mathematics, an online calculus course can help you expand your mathematical skills.

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Frequently asked questions

Calculus courses may cover both differential calculus (which concerns functions’ rates of change) and integral calculus (which concerns the area under curves). In a typical course, you will learn how to find the derivative and integral of an equation. A calculus course may also generally cover new types of functions you may not have encountered in algebra and geometry, such as trigonometric, exponential, and logarithmic functions. These may also be covered in pre-calculus courses.

Calculus is often a challenging course for many students. It involves learning many new formulas and applying them in increasingly complicated contexts. However, if you have a strong mathematical foundation and the dedication needed to learn calculus, you can succeed. Be prepared to spend a significant amount of time studying, practicing mathematical concepts, and completing coursework. If you plan to learn calculus online, it also helps to be self-directed and highly motivated.

Calculus can be applied to many different fields. For example, physicists use calculus. In fact, Isaac Newton developed calculus to describe his laws of motion. But calculus also has applications beyond the hard sciences. For example, the concepts of derivatives, integrals, and limits are essential in economics.Footnote 7 If you learn calculus, you’ll have foundational skills that can take you far in a number of different fields.

This depends on numerous factors, including whether you decide to learn calculus online or through an in-person course. It can take more than a year to learn calculus, depending on your level of mathematical knowledge and the amount of time you have to dedicate to your coursework. An individual online calculus course may require only a few months. Depending on the course, you may be able to move through the material at your own pace and complete the course sooner.

When debating whether to learn calculus online or in person, some students may think that an in-person course is the only opportunity for direct interaction with professors. However, many online courses offer office hours during which students can interact with instructional staff, asking questions and receiving valuable feedback. Additionally, being able to access recorded lectures can make it easier for students to review material as they learn calculus. It’s more than possible to learn through an online calculus course or program if you’re committed to attending all sessions and completing all coursework.

Chemical engineers use calculus for many purposes in their work. They deal with complex chemical processes, many of which can only be described using equations learned in a calculus course. For instance, multivariable differential calculus is crucial when monitoring the transformations of energy in a multiphasic system. Differential and integral calculus play roles in representing the accumulation of conserved quantities over time.Footnote 8 If you want to be a chemical engineer, it’s essential that you know how to do calculus. An online calculus class can be the first step.