# Module Information

Module Identifier
MA13610
Module Title
MATHEMATICS FOR ECONOMICS AND FINANCE 2
2012/2013
Co-ordinator
Semester
Semester 2
Mutually Exclusive
May not be taken at the same time as MA11010.
Pre-Requisite
MA12610 or MA10110 or MA12010.
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 Hours. (22 x 1 hour lectures)
Seminars / Tutorials 5 Hours. (1 hour help-desk, weekly (optional))

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   100%
Supplementary Assessment 2 Hours   (multiple choice examination)  100%

### Learning Outcomes

On completion of this module, a student should be able to:
1. find the first and second order partial derivatives of a function of 2 or 3 variables;
2. optimize a function of 2 variables using either the substitution method or Lagrange multipliers;
3. perform basic matrix algebra, find the inverse of 2 by 2 or 3 by 3 matrices and use inverses to solve equations;
4. evaluate 2 by 2 and 3 by 3 determinants and apply Cramer's rule to solve equations;
5. reduce a matrix to echelon form, find its rank and solve associated systems of equations;
6. integrate simple polynomial, rational and exponential functions;
7. calculate the area under a curve;
8. find the total cost function given any marginal cost function;
9. find the total revenue function given any marginal revenue function;
10. find the consumption and savings functions given either the marginal propensity to consume or the marginal propensity to save.

### Brief description

This module continues the thread of MA12610 with optimisation of functions of several variables and Lagrange Multipliers. It also includes basic matrix techniques. Like MA12610, the mathematics will be illustrated with applications to Economics.

### Aims

To introduce the basic Mathematical techniques required for degrees involving Economics or Accounting.

### Content

1. FURTHER OPTIMIZATION: Constrained optimization in functions of one variable, the interpretation of Lagrange multipliers, unconstrained optimization in functions of more than one variable, constrained optimization in functions of more than one variable.
2. MATRIX ALGEBRA: Simultaneous linear equations, Gaussian reduction, laws of matrix algebra, identity and null matrices, matrix addition and subtraction, scalar multiplication, matrix multiplication, matrix inversion, determinants, determinants and matrix non-singularity, higher-order determinants, matrix inversion using determinants, Cramer's Rule, matrix rank.
3. INTEGRATION: The notion of an integral. Area under a curve. Integration of simple power and exponential functions. Integration of marginal functions.