Before You Watch
Some Practice Questions
By now you will be familiar the basics of calculus, the meaning of rates of change, and why we are interested in rates of change. You should also understand the concept of differentiation, which is the mathematical process of going from one formula that relates two variables (such as position and time) to another formula that gives the rate of change between those two variables (such as the rate of change between position and time, also known as speed).
The next step is to learn how to differentiate. In the next video, Differentiation of Polynomials, you’ll be shown how to differentiate the group of equations known as polynomials.
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.
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.