Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Calculus
Module Code	MS105
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Thomas Brady Semester 2: Thomas Brady Autumn: Thomas Brady
Module Teacher	Thomas Brady
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module is aimed at students, starting with knowledge of higher level leaving certificate mathematics, to gain a sound grasp of calculus. Students on the module are expected to master fundamental techniques of calculus through doing a substantial number of exercises. It also exposes students to applications of calculus in economics and finance, and lays the foundations for further courses in calculus, probability and statistics.

Learning Outcomes

1. Analyse and manipulate inequalities, basic algebraic expressions, functions of one variable and their inverses
2. Analyse important properties of quadratic and polynomial functions, and apply these to real-world problems
3. Differentiate important elementary functions, and be able to apply rules and theory of differentiation to analyse differentiable functions
4. Sketch the graphs of scalar differentiable functions
5. Prove important results about the logarithm, exponential, and trigonometric functions
6. Integrate important elementary functions, using the rules of integration
7. Apply their knowledge of differentiation and integration to solve real world problems in economics and finance

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	30	Lecture
Tutorial	18	Whole group tutorial
Independent learning time	202	Self study
Total Workload: 250

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Review (1 week).
real-valued functions, composition of functions, invertibility of functions; basic algebra.

Differentiation (5 weeks).
differentiation of polynomials andtrigonometric functions, rules for differentiating products,quotients, compositions and inverses; differentiation of inversetrigonometric; extremum problems and curve sketching. Rigorous introduction to trigonometric functions. Applications to economics: producer/ consumer surplus, firms with single product; costminimization; profit and revenue maximization, elasticity ofdemand/supply; marginal and total costs/revenue; economic order quantity for stocks; utility or production maximisation subject to budget constraints.

Integration (4 weeks).
idea of definite integrals and fundamental theorem,techniques of integration including change of variables, integrationby parts, partial fractions and reduction formula; naturallogarithms and exponential function. Applications to economics: continuously compounded interest, present values, relationship between flow and stock variables.

Limits (2 weeks).
Limits and continuity, L'Hospital's rule, Taylor series..

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	Class test	25%	Week 10

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List

K. Binmore and J. Davies: 2001, Calculus, 4th ed, Cambridge,
I. Jacques: 2001, Mathematics for Economics and Business, Addison Wesley,
R. A. Adams: 2003, Calculus, 5th ed, Addison Wesley Longman,
M. Pemberton and N. Rao: 2001, Mathematics for Economists, Manchester University Press,

Other Resources

None

Array

Programme or List of Programmes

ACM

BSc Actuarial Mathematics

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

CAFM

Common Entry into Mathematical Sciences