Differential Calculus

This presentation introduces students to the core idea of differential calculus by contrasting ordinary geometrical problems with calculus problems involving change, motion, and variation. It explains that calculus is needed when a quantity is not constant and we want to find an instantaneous rate of change, such as the gradient of a curve at a single point.

The slides then develop differentiation from first principles, showing how the gradient of a secant becomes the gradient of a tangent as the interval gets smaller and smaller. Students are guided through worked examples step by step, before completing independent practice questions and checking their understanding with detailed worked answers. The overall aim is to build both conceptual understanding and procedural confidence in the foundations of differentiation.