MT105B Mathematics 2 (half course)
Graph paper will be provided.
May not be taken with MT1173 Algebra.
May not be taken with MT1174 Calculus.
May not be taken with MT2076 Management Mathematics.
MT105B Mathematics 2 must be taken after, or at the same time as, MT105A Mathematics 1
This course develops further the basic mathematical methods introduced in Mathematics 1, and also demonstrates further applications in economics, finance and management. New techniques are also developed, particularly for linear algebra, differential equations and difference equations, and applications of these techniques are investigated.
Further differentiation and integration:
Mathematics 1 material on differentiation and integration; Using derivatives for approximations; Elasticities; Taylor's theorem; the effects of taxation. Definite integrals and the calculation of areas; Further economic applications of integration: includes consumer and producer surplus
Functions of several variables:
Mathematics 1 material on functions of several variables; Homogeneous functions and Euler's theorem; Review of constrained optimisation; Constrained optimisation for more than 2 variables; Further applications of constrained optimisation
Mathematics 1 material on matrices and linear equations; Supply and demand, and the imposition of excise and percentage tax; Consistency of linear systems; Solving systems of linear equations using row operations, in the case where there are infinitely many solutions; Determinants and Cramer's rule; Calculation of inverse matrices by row operations; Economic applications of systems of linear equations, including input-output analysis; Eigenvalues and eigenvectors; Diagonalisation of matrices
Exponential growth; Separable equations; Linear differential equations and integrating factors; Second-order differential equations; Coupled equations, including the use of matrix diagonalisation; Economic applications of differential equations
Solving first-order difference equations; Application of first-order difference equations to financial problems; The cobweb model; Second-order difference equations; Coupled first-order difference equations, including the use of matrix diagonalisation; Economic applications of second-order difference equations.