Registry

Module Specifications

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

Module Title	Calculus
Module Code	MS126
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Eugene O'Riordan Semester 2: Eugene O'Riordan Autumn: Eugene O'Riordan
Module Teacher	Eugene O'Riordan
NFQ level	8	Credit Rating	10
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This course concentrates on developing the algebraic skills of the student. The course reviews some foundational mathematics involving functions, inequalities, quadratic equations, trigonometric identities, exponential and logarithmic functions. The course also develops skills in the techniques of differentiation and integration. Enhancing the student's ability to solve mathematical problems lies at the heart of this module.

Learning Outcomes

1. Perform standard algebraic manipulations involving addition, subtraction, multiplication, division and exponents
2. Solve basic trigonometric equations
3. Differentiate logarithmic and exponential functions
4. Graph functions using the first and second derivatives
5. Use common integration techniques

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	72	lecture
Tutorial	24	No Description
Independent learning	154	No Description
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

Foundations.
Absolute value and inequalities; polynomials; functions and graphs; lines and parabolae; trigonometry; complex numbers including De Moivre's theorem.

Limits and continuity.
Informal treatment of limits of functions, infinite limits and continuous function..

Differential Calculus.
Tangents to curves and derivatives; rates of change; sum, product, quotient and chain rules; differentiation of polynomial and trigonometric functions; Mean Value theorem; critical points and extremum problems; curve sketching; rational functions.

Integral Calculus.
Area under a curve as motivation; the Riemann integral; antiderivative; fundamental theorem of calculus; applications involving area; methods of integration including substitution, integration by parts and partial fractions.

Transcendental Functions.
Inverse functions and their derivatives; inverse trigonometric functions and their derivatives, logarithmic and exponential functions; growth and decay problems;.

Other Topics in Calculus.
Limits and L'Hopital's rule, Taylor and Maclaurin series; first order differential equations; Newton's method.

Vectors.
Vectors in 2 and 3 dimensions, inner and vector products, lines and planes in R3, systems of 2 or 3 linear equations.

Assessment Breakdown
Continuous Assessment	30%	Examination Weight	70%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Short answer questions	n/a	6%	Week 6
Short answer questions	n/a	6%	Week 11
Short answer questions	n/a	6%	Week 21
Short answer questions	n/a	6%	Week 25
Short answer questions	n/a	6%	Week 30

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