Faculty of Engineering, Computing & Mathematics

Mathematics & Statistics

Unit Outline

Mathematical Methods 2

MATH1002

SEM-1, 2015

Campus: Crawley

Unit Coordinator: Dr Alice Devillers

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Unit detailsUnit title Mathematical Methods 2Unit code MATH1002 Credit points 6Availability SEM-1, 2015 (23/02/2015 - 20/06/2015)Location Crawley Mode Face to face

Contact detailsFaculty Faculty of Engineering, Computing & MathematicsSchool Mathematics & StatisticsSchool website http://www.maths.uwa.edu.auUnit coordinator Dr Alice DevillersEmail alice.devillers@uwa.edu.auTelephone 6488 3228Consultation hours Wed 3-4 Room 2.08 Maths BuildingUnit contact hours Lectures: 3 hrs per week; tutorials: 2 hrs per weekLecture capture system LCS is implemented for this unit.Online handbook http://units.handbooks.uwa.edu.au/units/MATH/MATH1002Unit website Http://www.maths.uwa.edu.au/students/units

Unit rulesPrerequisites MATH1001 Mathematical Methods 1Incompatibility MATH2040 Engineering Mathematics

Unit descriptionThis unit is the second of two units that provide the essential foundation in the concepts and techniques of mathematics that form thebasis of science, engineering and higher mathematics and statistics. It covers multidimensional integration, Laplace transforms andFourier series, and statistics.

1 understand the idea of an antiderivative2 appreciate Riemann sums as a method of approximating area3 be able to find area by evaluating definite integrals4 be able to employ a number of techniques of integration5 appreciate improper integrals6 understand numerical quadrature7 understand the Fundamental Theorem of Calculus and its significance8 understand the use of Riemann sums to approximate volume of a solid9 evaluate integrals over regions10 employ the technique of reversing the order of integration11 evaluate volumes/masses of solids using triple integrals12 use change of variables to evaluate multiple integrals13 evaluate double integrals using polar coordinates14 evaluate triple integrals using cylindrical and spherical coordinates15 evaluate path and surface integrals16 understand circulation around a closed curve17 understand flux across a curve in the plane or across a surface in space18 understand path independence and conservative fields19 understand the gradient of a scalar function20 be able to find potentials for conservative fields21 Understand the concept of periodic functions22 Be able to determine Fourier series for a given periodic function23 Understand the concept of odd and even functions and sine and cosine series24 understand Laplace transforms25 understand the shifting theorems26 understand derivatives and integrals of Laplace transforms27 use Laplace transforms to solve differential equations28 understand convolutions and their applications29 understand and recognise analytic functions30 understand the Cauchy-Riemann equations

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31 understand the Laplace equation32 understand random variables, such as normal, exponential, binomial33 understand hypothesis testing34 understand quantiles

Learning outcomesStudents are able to (1) understand and employ integration theory and technique; (2) integrate over objects in more than onedimension; (3) understand the concepts of work, path independence, conservative fields and potentials; (4) understand the basic theoryof complex functions; (5) understand and employ Fourier series and Laplace transforms; and (6) understand the basics of probabilitytheory.

Unit structureLectures: three hours per weekTutorials: two hours per week (starting week 2)

AssessmentAssessment overviewTypically this unit is assessed in the following way(s): (1) continuing assessment; and (2) a final examination. Further information isavailable in the unit outline.

Assessment mechanism

# Component Weight Due Date1 On-line Assignments 10 weekly from week 2 to 132 Mid-semester test 10 Sat April 18th at 9:30am3 Three computer based tests 15 weeks 4, 8, 124 Tutorial active participation 5 weekly from week 2 to 13, at least 10 for maximal marks5 End of semester examination 60

Assessment items

Item Title Description Submission Procedure for AssignmentsOn-lineAssignments

Continuing assessment Automatic submission at due date and time by computer-aided assessment program

Mid-semester Test Assessment of relevant parts of the unitThree computerbased tests

Assessment of relevant part of the unit;continuing assessment

in the MCL during assigned lab time in week 4,8,12

End of semesterexamination

Summative assessment of all examinableaspects of the unit

Tutorial activeparticipation

continuing assessment

Textbooks and resourcesRecommended textsThe notes for this unit will be available in the LMS. These form the primary source of material for the unit.

Suggested alternate textsIn addition to these notes we recommend the following books:

M.D. Weir, J. Hass and F.R. Giordano, Thomas' Calculus, 11th edition, Addison Wesley.

G. James, Modern Engineering Mathematics, 4th edition, Pearson.

Other important information

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