Registry

Module Specifications

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

Module Title	Mathematics for Scientists
Module Code	MS125
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Angela Murphy Semester 2: Angela Murphy Autumn: Angela Murphy
NFQ level	8	Credit Rating	10
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module focuses on the reasoning and technical skills necessary for students to become proficient in applying the mathematical concepts and tools of calculus. This module reviews foundation mathematics and develops the computational skills and techniques of differential and integral calculus.Students will participate in the following learning activities:Lectures; Students will attend three one-hour lectures per week. These lectures are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module.Tutorials; Each student will attend one one-hour tutorial per week. Problem sheets based on lecture content are distributed to the students and they are strongly advised to attempt all tutorial questions in advance of the tutorial. Reading; Students are expected to fully utilise the textbooks recommended below to enhance the learning experience.

Learning Outcomes

1. Find limits of functions and determine continuity of functions.
2. Compute derivatives of algebraic, trigonometric, logarithmic and exponential functions, and use derivatives to solve related rates and optimization problems.
3. Integrate algebraic, trigonemetric, logarithmic and exponential functions, and use integrals to solve applied problems.
4. Perform elementary calculations involving matrices and complex numbers.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	72	3 lectures per week
Tutorial	20	1 tutorial per week
Examination	2	end of year exam
Directed learning	40	Solving tutorial questions
Independent learning	116	Study over 2 semesters including exam period
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

Preliminaries:.
Lines, circles and parabolae: functions and their graphs: Combining functions, shifting and scaling graphs: trigonometric functions..

Limits and Continuity:.
Rates of change and limits; Calculating limits using the limit laws; one-sided limits and limits at infinity; continuity..

Differentiation:.
The derivative as a function; Differentiation rules; the derivative as a rate of change; derivatives of trigonometric functions; the chain rule and parametric equations; implicit differentiation; related rates..

Applications of derivatives:.
Extreme values of functions; monotonic functions and the first derivative test; concavity and curve sketching; applied optimization problems; indeterminate forms and L'Hopital's rule; antiderivatives..

Integration:.
Estimating with finite sums; sigma notation and limits of finite sums; the definite integral; the fundamental theorem of calculus; indefinite integrals and the substitution rule; substitution and area between curves..

Transcendental functions:.
Inverse functions and their derivatives: natural logarithms; the exponential function; exponential growth and decay; inverse trigonometric functions..

Techniques of Integration:.
Basic integration formulas; integration by parts; integration of rational functions by partial fractions..

Matrices:.
Matrix operations- multiplication of matrices; transpose of a matrix; the identity matrix..

Complex Numbers:.
Basic operations- modulus, absolute value; complex roots of polynomials with real coefficients..

Assessment Breakdown
Continuous Assessment	30%	Examination Weight	70%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	n/a	7%	Week 6
In Class Test	n/a	8%	Sem 1 End
In Class Test	n/a	7%	Week 24
In Class Test	n/a	8%	Sem 2 End

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

Elliott Mendelson,: 2008, Schaum's Outline of Beginning Calculus, Third Edition Schaum's Outline Series, McGrawHill, 978-0-07-163535-60071635351
George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano,: 0, Thomas' Calculus, Media Upgrade, Part One, Eleventh, Pearson/Addison Wesley, 0-321-49875-5

Other Resources

2581, 0, Math Learning Centre,

Array

Programme or List of Programmes

BSc in Chemical and Pharmaceutical Sc.

BSc in Analytical Science

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

BSc in Biotechnology

CES