units

MTH1035

Faculty of Science

12 April 2013 26 May 2013

Undergraduate - Unit

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6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered, or view unit timetables.

LevelUndergraduate
FacultyFaculty of Science
Organisational UnitSchool of Mathematical Sciences
Monash Passport categoryAdvanced Studies (Enhance Program)
OfferedClayton First semester 2013 (Day)
Coordinator(s)Mr Simon Teague

Synopsis

Solution of systems of linear equations using Gaussian elimination; matrices and determinants, eigenvalues and eigenvectors; introduction to vectors; parametric curves; methods of integration - substitutions and integration by parts; solution of first-order ordinary differential equations - separable, use of integrating factor; solution of second-order linear ordinary differential equations with constant coefficients and applications; Sequences and series, Taylor series and series convergence, the remainder term.

Outcomes

On completion of this unit students will be able to:

  1. Understand the basic concepts of linear algebra, and recognise and manipulate elements of vector spaces;

  1. Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;

  1. Identify and evaluate improper integrals;

  1. Solve simple first and second order differential equations, and formulate them for applications to physical systems;

  1. Compute Taylor series expansions, with remainder, for functions of one variable;

  1. Apply Taylor series and l'Hopital's rule to compute limits;

  1. Understand and compute the convergence properties of infinite series;

  1. Provide written reports that contain complete mathematical arguments;

  1. Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;

  1. Prove elementary theorems by induction and by construction.

Assessment

Continuous assessments: 40%
Final Examination: 60%

Chief examiner(s)

Mr Simon Teague

Contact hours

Three 1-hour lectures plus one 2-hour tutorial/computer laboratory per week.

Prerequisites

VCE Specialist Mathematics with an ATAR/ENTER score of 95 or above; a VCE study score of 35 or above in Specialist Mathematics; a High Distinction in MTH1020; or by approval of the Head of School of Mathematical Sciences. In order to enrol in this unit students will need to apply via the Faculty of Science office.

Prohibitions

MTH1030, MTH1085