Module Identifier MA13610  
Academic Year 2006/2007  
Co-ordinator Professor V Mavron  
Semester Semester 2  
Other staff Mrs Glenda Roberts, Mr Gareth Daniel Edward Lanagan, Professor V Mavron  
Pre-Requisite MA12610 or MA10110 or MA12010.  
Mutually Exclusive May not be taken at the same time as MA11010.  
Course delivery Lecture   22 Hours. (22 x 1 hour lectures)  
  Seminars / Tutorials   10 Hours. (1 hour help-desk, weekly (optional))  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (multiple choice examination)  100%
Supplementary Assessment2 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.


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


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.

Reading Lists

** Recommended Text
G Renshaw (2005) Math for Economics 1st. Oxford University Press 0199267460
I.Jacques (2003) Mathematics for Economics and Business 4th. Prentice Hall 0273655647
V C Mavron, T N Phillips (2006) Elements of Mathematics for Economics and Finance 1st. Springer 1846285607
** Supplementary Text
E.T.Dowling (1992) Schaum's outline of theory and problems of introduction to mathematical economics. McGraw-Hill 0070176744
M.Wisniewski (1994) Introductory Mathematical Methods in Economics 2nd. McGraw-Hill 0077091094


This module is at CQFW Level 4