Module Information

Module Identifier
Module Title
Academic Year
Semester 2
Mutually Exclusive
May not be taken at the same time as MA11010.
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 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.


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 List

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


This module is at CQFW Level 4