Embed Size (px)
DESCRIPTION
Mathematical Methods 1 Unit Outline
Citation preview
Faculty of Engineering, Computing & Mathematics
Mathematics & Statistics
Unit Outline
Mathematical Methods 1
MATH1001
SEM-1, 2015
Campus: Crawley
Unit Coordinator: Prof Luchezar Stoyanov
All material reproduced herein has been copied in accordance with and pursuant to a statutory licence administered byCopyright Agency Limited (CAL), granted to the University of Western Australia pursuant to Part VB of the Copyright Act 1968
(Cth).
Copying of this material by students, except for fair dealing purposes under the Copyright Act, is prohibited. For the purposesof this fair dealing exception, students should be aware that the rule allowing copying, for fair dealing purposes, of 10% of thework, or one chapter/article, applies to the original work from which the excerpt in this course material was taken, and not to
the course material itself
© The University of Western Australia 2001
Page 1
Unit detailsUnit title Mathematical Methods 1Unit code MATH1001 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 Prof Luchezar StoyanovEmail [email protected] 6488-3393Consultation hours L. Stoyanov (Room 109 in Maths.): Mondays 4-5pm and Tuesdays 3-4pm; M. Giudici (Room 211 in Maths.):
2pmLecturers Name Position Email Telephone Number
Luchezar Stoyanov [email protected] 6488 3393Michael Giudici Associate Professor [email protected] 6488 3351Cheryl Praeger Winthrop Professor [email protected] 6488 3344
Unit contact hours Lectures: 3 hrs per week; tutorials: 2 hrs per week; labs: 1 hr per weekLecture capture system LCS is implemented for this unit.Online handbook http://units.handbooks.uwa.edu.au/units/MATH/MATH1001
Unit rulesPrerequisites WACE Mathematics: Specialist 3C/3D or MATH1722 Mathematics Foundations: Specialist or MATH1712
Intermediate Mathematics Specialist or MATH1035 Calculus and Matrices or TEE Calculus or equivalent. Studentswho commenced in 2011 may substitute MATH1038 Calculus and its Applications for MATH1035 Calculus andMatrices.
Incompatibility MATH2040 Engineering Mathematics
Unit descriptionThis unit is the first of two units that provide the essential foundation in the concepts and techniques of mathematics that form the basisof science, engineering and higher mathematics and statistics. It covers multivariable calculus, linear algebra and differential equations.Students who successfully complete this unit should be able to:
systematically solve systems of linear algebraic equations with up to 5 variables
identify when a system of linear algebraic equations has 0, 1 or infinitely many solutions.
determine when a set of vectors is a subspace.
determine when a set of vectors is linearly independent.
find a basis for a subspace, including the row space, column space and null space of a matrix, and hence determine its dimension.
understand the operations of matrix algebra and identify the similarities and differences between matrix algebra and the algebra ofreal numbers.
determine the inverse of an n x n matrix with n at most 5.
compute determinants and understand the relationship between determinants, rank and invertibility of matrices.
recognise linear functions and understand the relationship between linear transformations and matrix multiplication.
appreciate the rank-nullity theorem in the context of linear transformations.
demonstrate familiarity with vector functions and functions of several variables including determining level curves.
calculate limits of functions of one variable using the limit laws and squeeze theorem.
Page 2
demonstrate an understanding of the notion of a limit for vector functions and functions of several variables, and determine if suchlimits exist.
identify if a function is continuous.
determine partial derivatives of functions of several variables.
calculate and interpret the derivative of a vector function and a function of several variables.
demonstrate and apply an understanding of the chain rule for vector functions and functions of several variables.
find equations of normals and tangents to curves, and planes tangent to surfaces.
calculate the directional derivative and gradient vector of a function of several variables.
find Taylor polynomials of functions of one and several variables.
find and identify extrema of functions of several variables.
solve simple ordinary differential equations using a variety of standard techniques such as separation of variables, integrating factor,by solving the characteristic equation, and method of undetermined coefficients.appreciate how differential equations can be used to model physical systems and interpret the solutions in terms of the originalsystem.
determine eigenvalues, eigenvectors and eigenspaces of 2x2 and 3x3 matrices.
demonstrate a familiarity with the basic properties of eigenvalues, eigenvectors and eigenspaces.
use eigenvalues and eigenvectors to solve systems of two linear differential equations.
demonstrate an understanding of the concept of change of basis.
determine change of basis transition matrices (in the 2x2 and 3x3 case).
demonstrate an understanding of sequences and series, and use associated tests for convergence.
Learning outcomesStudents are able to (1) understand the basics of linear algebra, including the concepts of subspace, linear transformation anddeterminant; (2) understand and use the calculus and geometry of functions of more than one variable; (3) understand Taylor seriesand some of their uses; (4) use first and second order differential equations in applications; (5) understand the concepts of eigenvaluesand eigenvectors, and change of basis; and (6) understand the basic theory of sequences and series.
AssessmentAssessment overviewTypically this unit is assessed in the following way(s): (1) tutorials; (2) tests and assignments; (3) mid-semester test; and (4) finalexamination. Further information is available in the unit outline.
Assessment mechanism
# Component Weight Due Date1 End of semester examination 60 In official exam period2 Mid semester Test 10 Saturday 18th of April3 Three short computer based tests 15 In weeks 4, 8 and 124 Online computer assignments 10 weekly from week 25 Tutorial attendance 5 weekly from week 26
Page 3
Assessment items
Item Title Description Submission Procedure for AssignmentsEnd of semesterexamination
Summative assessment of all examinableaspects of the unit
Mid semester test written testTwo short computerbased testsOnline assignments Continuing formative assessment Automatic submission at due date and time by computer-
aided assessment programTutorial attendance
Textbooks and resourcesRecommended textsThe notes for this unit will be available in the LMS and hardcopies will be for sale in the Coop Bookshop. These form the primary sourceof material for the unit. In addition to these we recommend the following books and online notesM.D. Weir, J. Hass and F.R. Giordano, Thomas’ Calculus, 11th edition, Addison Wesley.James, G. Modern Engineering Mathematics, 4th edition, Pearson.Jim Hefferon, Linear Algebra available at http://joshua.smcvt.edu/linearalgebra/
Other important information
Page 4
