Before You Watch

This video introduces calculus. It presents the fundamental premise of calculus as well as some of the unique notation that is used in calculus in preparation for the other videos in this series.

You don’t have to know anything about calculus before watching this video, however, it is a good idea to be familiar with the general concepts of algebra first. If you’re not confident with rearranging algebraic equations or working with algebraic fractions, review the videos on those topics, then come back. You also need to be familiar with the linear equation before proceeding with calculus.

The Video

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Now What?

Now that you’ve been introduced to the fundamental concepts of calculus, you can explore further. As mentioned in the video, there are two main categories of calculus: differential calculus and integral calculus. Most commonly, differential calculus is taught first, followed by integral calculus.

So, when you’re familiar with the basic concepts in this video, watch Rates of Change and Differentiation next. Even if you already know how to differentiate, it will help you understand what differentiation means.

But When I am Going to Use This

Calculus is the mathematical study of how things change relative to one another. For instance, velocity (or speed) is a change of position over a change in time, and acceleration is a change in velocity over a change in time – so any motion is studied using calculus. Other examples include the flow of water through pipes over time, or changing commodity prices against demand. Because change is everywhere, the potential applications for calculus are endless, particularly in engineering and science. Calculus is necessary knowledge for any degree related to engineering or science.

Other Links

Maths Is Fun has a great page that takes you through a simple problem which highlights the need for calculus to discuss changes happening around us. It then continues to explore the main two areas of calculus, differentiation and integration, and provides regular questions to test your understanding.

IntMath gives some historical perspective to explain the sometimes confusing notation that is used in calculus, discussing how it is the mixed product of two mathematicians working independently. It also provides some excellent examples of applications of calculus that are in common use today, as well as helpful applets to understand both differential and integral calculus. 

The Khan Academy has a comprehensive set of video tutorials covering a wide range of mathematical topics, as well as questions to test your knowledge. This content explains the historical development of calculus, and is also an excellent introduction to differential calculus and the concepts it is based around. From here you can further investigate differential calculus.

Patrick JMT (Just Maths Tutorials) has an extensive set of video tutorials covering a large range of mathematical concepts. This video introduces and explains the concept of a limit to help develop your understanding of this idea.