UNIT OVERVIEW

Differential calculus is the mathematics of change. It gives us tools to understand how things vary, how fast they change, and how to find the best possible outcomes.

When your car's speedometer shows 80 km/h, that number is a rate of change — how quickly your position changes over time. When engineers design fuel-efficient cars, they use calculus to find optimal shapes. This is the mathematics that transformed science and engineering.

In this unit, you will learn to:

• Understand limits and instantaneous rates of change
• Find the gradient of a curve at any point
• Calculate derivatives from first principles
• Apply efficient differentiation rules
• Find equations of tangent lines
• Use the second derivative to analyse curve shape
• Sketch cubic functions using calculus
• Solve optimisation problems
• Apply calculus to motion and rates of change