MT105A Mathematics 1 (half course)
Graph paper will be provided.
May not be taken with MT1173 Algebra.
May not be taken with MT1174 Calculus.
This course develops basic mathematical methods and will emphasise their applications to problems in economics, management and related areas.
Basic algebra; Sets, functions and graphs; Factorisation (including cubics); Inverse and composite functions; Exponential and logarithm functions; Trigonometrical functions
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
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.