To provide foundational knowledge and skills in core calculus topics, including applications of integration, infinite series, multivariable differentiation, and double integrals, that serve as essential prerequisites for progression into later stages of study and support Y1LO5 (Foundational academic capability); To develop students' ability to apply mathematical concepts to real-world contexts, such as business, economics, and the arts, supporting Y1LO5 and Y1LO2 through practical reasoning and discipline-aware communication; To strengthen independent learning, problem-solving, academic communication and literacy (Y1LO2), including the ability to interpret, explain, and present mathematical arguments clearly while preparing students for Year 2 study.
A Determine convergence and divergence of sequences and series using appropriate tests. B Use differentials for linear approximations and apply Taylor/Maclaurin series for higher-accuracy approximations of functions. C Use vector operations, including dot and cross products, to analyse lines and planes in three-dimensional space. D Apply partial derivatives, directional derivatives and gradients to solve multivariable optimisation problems, including constrained optimisation using Lagrange multipliers. E Solve separable differential equations related to exponential growth and decay. F Use single integrals and double integrals (over rectangular and general regions, in Cartesian and polar coordinates) to compute geometric measures such as plane areas and volumes of revolution, as well as to solve probability problems involving continuous random variables and probability density functions.
Students will be expected to attend three hours of lectures and one hour of tutorial each teaching week. Lectures introduce core ideas and techniques through worked examples and applications to business, economics, and the arts. Tutorials provide guided practice, feedback, and opportunities for students to explain solutions using appropriate mathematical notation and academic language, supporting Y1LO2 (Academic communication and literacy). Private study is used to complete problem sets, review feedback, and consolidate foundational skills for Year 2 readiness, supporting Y1LO5 (Foundational academic capability).