Module Identifier MA13610  
Academic Year 2000/2001  
Co-ordinator Dr V C Mavron  
Semester Semester 2  
Pre-Requisite MA12610 or MA10110 or MA12010.  
Mutually Exclusive May not be taken at the same time as MA13510.  
Course delivery Lecture   22 x 1 hour lectures  
  Seminars / Tutorials   6 x 1hour example classes  
Assessment Exam   2 Hours (written examination)   60%  
  Course work     20%  
  In-course assessment   Open book test   20%  
  Resit assessment   2 Hours (written examination)   100%  

General description
This module continues the thread of MA12610 with optimisation of functions of several variables and Lagrange Multipliers. It also includes basic matrix techniques and simple differential and difference equations. Like MA12610, it will be illustrated with applications to Economics.

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

Learning outcomes
On completion of this module, a student should be able to:

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 multiplica-tion, 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.
4. DYNAMICS: First-order differential equations, separation of variables, first-order difference equations, stability.

Reading Lists
** Should Be Purchased
I.B.Jacques. Mathematics for Economics and Business. Addison-Wesley
** Recommended Text
E.T.Dowling. Introduction to Mathematical Economics. Schaum?s Outline Series. McGraw-Hill
** Supplementary Text
M.Wisniewski. Introductory Mathematical Methods in Economics. McGraw-Hill
A.C.Chiang. Fundamental Methods of Mathematical Economics. McGraw-Hill
J Black & J F Bradley. Essential Mathematics for Economists. John Wiley