Overview

This course builds upon Calculus 1 and introduces students to advanced concepts in analysis, approximation, multivariable calculus, and optimisation. In the first week, students explore infinite series, power series, and Taylor series. The second week introduces multivariable concepts, including partial derivatives, gradients, and double integrals, with applications to areas, volumes, and averages. The final week focuses on modelling and decision-making, involving the solution of simple differential equations, such as exponential and logistic growth, and the application of optimisation techniques, both with and without constraints.

The course emphasises both proof and practice. Each week highlights one key theorem. By the end of the course, students will be able to approximate functions, analyse multivariable systems, and construct or optimise simple models, while also developing confidence in presenting their mathematical reasoning.