# Mathematics 2 MT105b

## Half course

This half course develops further the basic mathematical methods introduced in MT105a Mathematics 1, and also demonstrates further applications in economics, finance and management.

### Prerequisites / Exclusions

Students can only take MT105b Mathematics 2 at the same time as or after MT105a Mathematics 1, not before.

This half course may not be taken with MT1173 Algebra, MT1174 Calculus, MT1186 Mathematical Methods.

### Topics covered

• 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.
• Linear Algebra: 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.
• Differential equations: 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.
• Difference 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.

### Learning outcomes

If you complete the course successfully, you should be able to:

• Used the concepts, terminology, methods and conventions covered in the half course to solve mathematical problems in this subject.
• The ability to solve unseen mathematical problems involving understanding of these concepts and application of these methods.
• Seen how mathematical techniques can be used to solve problems in economics and related subjects.

### Assessment

Unseen written examination (2 hrs).