the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. — John Maynard Keynes
This is a pre-sessional resource to refresh mathematical skills and techniques in preparation for an undergraduate degree in economics.
Refresh the essential mathematical skills that you will need throughout an economics course.
Refresh your knowledge about differentiation and integration of functions of one variable and how to use derivatives to understand the behaviour of functions, such as when they are increasing or decreasing, convex or concave, and where they might have local or global extremes.
2.1. Functions & inverses 2.2. Definition of derivative 2.3. Rules of differentiation 2.4. Slope, curvature and optimisation 2.5. IntegralsRefresh your knowledge about differentiation of functions of more than one variable and how to find partial derivatives or slopes of tangents to level curves.
3.1. Partial derivatives 3.2. Implicit differentiationRefresh your knowledge about sequences and series (sums) of numbers. In particular, how to deal with arithmetic and geometric sequences and series.
4.1. Sequences 4.2. SeriesRefresh your knowledge about matrix arithmetic, determinants, inverses, and the relationship between matrices and systems of simultaneous linear equations.
5.1. Matrix arithmetic 5.2. Determinants & inverses 5.3. Matrices & simultaneous linear equations