Prerequisites

This course is an introduction to mathematical modelling with differential equations — both the theory and methods of solution, and the process of building a model in the first place. It follows directly on from your first-semester calculus, and assumes you’re comfortable with that material rather than re-teaching it.

What you need: you’ll constantly differentiate and integrate by hand throughout this course, so fluency here really matters. You covered these skills in MATH1036A: Calculus, and you should be confident with:

• differentiating and integrating all elementary functions;
• methods of integration, including substitution and integration by parts;
• the rules and laws of exponents and logarithms, particularly for the natural exponential \(f(x) = e^x\) and its inverse, the natural logarithm \(\ln x\), related by \(y = e^x \iff x = \ln y\); and
• trigonometric functions and their derivatives/integrals.

If any of this feels shaky, keep your MATH1036A notes close at hand — we won’t be re-teaching calculus, but you’ll be using it every week. Khan Academy and similar resources are also excellent for a quick refresher.

What you don’t need: this course does not assume any second-year linear algebra. Where the mathematics of interacting systems would normally call for matrices and eigenvalues, we’ll instead build genuine intuition using elimination methods and hand-sketched direction fields and phase portraits — tools built entirely from what you already know. You’ll be perfectly placed to revisit this material with the full machinery once you take linear algebra.