CLIP 13592

# Newton and the development of calculus

Key Info
• Newton and the development of calculus
• Calculus is introduced as the mathematics of change. In contrast to the static maths of algebra and arithmetic, it is stated that calculus can be used for the maths of any changing value, such as the speed of a car or changing heart-rate. It is stated that both Newton and Leibniz developed the concept of calculus. A sketch involving Sir Isaac Newton killing zombies is used to demonstrate how calculus works. The concept of using infinitesimals to work of the angle of the tangent to a curve or the area under a curve is set out. It is explained that calculus is now used in fields such as statistics and can be used to plot population changes.
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## Numbers

• Keywords: ApproximateHistoryofMaths, calculus, Newton, Leibniz, infinite, infinitesimal, change, curve, tangent, graph
Ideas for use in class
• This clip contains comedy cartoon violence with some blood shown. Discuss the history of calculus and look at the competing claims of Newton and Leibniz as the fathers of calculus. Consider their advances in relation to earlier moves towards calculus in ancient Egypt and Greece. Look at the ideas of Democritus related to breaking objects down into infinite cross-sections. Discuss with students why he was unable to rationalise this with the idea of a smooth-sided cone or pyramid. This could be further explored though presenting students with Zeno’s paradoxes. Also consider the work of Eudoxus and Archimedes and the method of exhaustion. Look further at the work of Newton and the links between his mathematical and scientific work. Explain to students the simplified nature of the examples shown in the clip and make clear the greater complexity of dealing with velocity and acceleration in its true sense.
Background details
• Clip language : English
• Aspect ratio : 16x9