London School of Economics and Political Science (LSE)

Modules

05a/D05a Mathematics 1 (half unit)

This subject develops basic mathematical methods and will emphasise their applications to problems in economics, management and related areas.

Basics: Basic algebra; Sets, functions and graphs; Factorisation (including cubics); Inverse and composite functions; Exponential and logarithm functions; Trigonometrical functions.

Differentiation: The meaning of the derivative; Standard derivatives; Product rule, quotient rule and chain rule; Optimisation ; Curve sketching; Economic applications of the derivative: marginals and profit maximisation.

Integration: Indefinite integrals; Definite integrals; Standard integrals; Substitution method; Integration by parts; Partial fractions; Economic applications of integration: determination of total cost from marginal cost, and cumulative changes.

Functions of several variables: Partial differentiation; Implicit partial differentiation; Critical points and their natures; Optimisation; Economic applications of optimisation; Constrained optimisation and the Lagrange multiplier method; The meaning of the Lagrange multiplier; Economic applications of constrained optimisation.

Matrices and linear equations: Vectors and matrices, and their algebra; Systems of linear equations and their expression in matrix form; Solving systems of linear equations using row operations (in the case where there is a unique solution); Some economic/managerial applications of linear equations.

Sequences and series: Arithmetic and Geometric Progressions; Some Financial application of sequences and series.