Analysis of change

This unit develops critical thinking generally as well as a comprehensive understanding of several important areas of mathematics, equipping you with versatile techniques and skills applicable within specific disciplines, for example the natural sciences, engineering, computer science, and economics.

The unit is broken up into three areas. First, the focus is on logic and proofs, which are fundamental to mathematical reasoning. Topics covered include proof by induction and proof by contradiction. 

Second, vectors and complex numbers are covered. Topics covered include: definitions and properties of vectors; dot and cross product; lines and planes in 3-dimensional space; definitions and properties of complex numbers; Cartesian and exponential forms of complex numbers; powers and roots of complex numbers. 

Third, the unit delves into calculus. Topics covered include: rates of change and derivatives; local and global extrema; optimisation and related rates; anti-derivatives and integrals; applications of integrals to calculating areas and volumes.