Module Code - Title:
MA4601
-
SCIENCE MATHEMATICS 1
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
Rationale and Purpose of the Module:
* To introduce students to the fundamental concepts of calculus and linear algebra.
* To develop and integrate the basic mathematical skills relevant to science.
Syllabus:
[Vectors:] definition; addition; components, resultant, position vector; scalar product; dot product and angle between vectors; cross product; simple applications in mechanics.
[Trigonometry:] basic definitions and relation to unit circle; basic formulae and
identities; frequency, amplitude and phase.
[Linear equations:] solution of systems of linear equations by Gaussian elimination;
examples with a unique solution, an infinite number or no solutions.
[Matrices:] Addition and multiplication; matrix inversion; simple determinants.
[Functions:] graphs and functions; polynomial and algebraic functions; curve-fitting;
least-squares approximation (formula only); exponential and logarithm; inverse
function.
[Derivative and applications:] basic concepts: slope as rate of change;
differentiation of sum, product, quotient; chain rule; derivative of standard functions;
tangent and normal; higher derivatives; maxima and minima; applications to
optimisation in science.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
Construct and resolve vectors in two and three dimsensions, calculate dot products
and cross
Products and apply to simple mechanics probelsm.
Define trigonometric functions and use simple formulas and identities.
Add multiply and invert matrices and calculate simple determinants.
Solve systems of linear equations.
Define and graph elementary functions including polynomials, exponentials and
logarithms.
Fit line to data points using the method of least squares.
Differentiate elementary functions using the laws of differentiation and apply to
curve-sketching and to optimisation problems from science.
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Normal lecture/tutorial delivery. Examples used should be taken from all of the
various sciences as far as possible
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Stewart, J. (2007)
Calculus: Early Transcendentals
, Brooks Cole
Other Relevant Texts:
James, G (2007)
Modern Engineering Mathematics (4ed),
, Prentice Hall
Stroud, K.A. and Booth D.J (2007)
Engineering Mathematics 6th Edition,
, Palgrave
Macmillan
Programme(s) in which this Module is Offered:
BSEDBSUFA - Biological Science
BAJOHOUFA - JOINT HONOURS
BSELECUFA - Electronics
BSENERUFA - Energy
BSENSCUFA - ENVIRONMENTAL SCIENCE
BSFSHEUFA - FOOD SCIENCE AND HEALTH
BSEDPSUFA - Physical Science
BSINBIUFA - INDUSTRIAL BIOCHEMISTRY
BSMCSEUFA - Mobile Communications and Security
BSPICHUFA - PHARMACEUTICAL AND INDUSTRIAL CHEMISTRY
BSSCCHUFA - Science Choice
BSSESCUFA - SPORT AND EXERCISE SCIENCES
Semester(s) Module is Offered:
Autumn
Module Leader:
padraig.maccarron@ul.ie