# SACE Stage 2 Specialist Mathematics – Rates of Change and Differential Equations

6.1 Implicit Differentiation
6.2 Differential Equations
6.3 Pairs of Varying Quantities - Polynomials
6.4 Related Rates, Velocity and Tangents
6.5 Trigonometric Parameterisations

A mathematical equation that relates a function to its derivatives is known as a differential equation. In applications, functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two.

This topic continues the study of differentiation and integration of functions. Calculus techniques are applied to vectors and simple differential equations. The study of rates of change and differential equations demonstrates applications of learning throughout this subject in a range of contexts.

This topic also highlights the fundamental theorem of calculus from the point of view of differential equations, intended to deepen students’ perspective on indefinite integrals.

Source – Subject Outline, South Australian Certificate of Education 2023

SACE Stage 2 Specialist Mathematics Courses

SACE Stage 2 Specialist Mathematics Syllabus

## Course Content

### Rates of Change

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Differential Equations
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