units

MTH2021

Faculty of Science

18 September 2017 22 November 2024
Monash University

Undergraduate - Unit

This unit entry is for students who completed this unit in 2013 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

print version

6 points, SCA Band 2, 0.125 EFTSL

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LevelUndergraduate
FacultyFaculty of Science
Organisational UnitSchool of Mathematical Sciences
OfferedClayton First semester 2013 (Day)
Coordinator(s)Dr Tim Garoni

Synopsis

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Jacobi iteration, Gauss-Seidel iteration, least squares approximation, power method. Applications to coding, computer graphics, geometry, dynamical systems, Markov chains, differential equations.

Outcomes

On completion of this unit students will be able to:

  1. Understand basic concepts related to vector spaces, including subspace, span, linear independence and basis;

  1. Understand basic properties of linear transformations and identify their kernel and range;

  1. Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;

  1. Understand basic concepts related to inner product spaces and apply these to problems such as least-squares data fitting;

  1. Apply tools from linear algebra in a wide variety of relevant situations;

  1. Understand and apply relevant numerical methods and demonstrate computational skills in linear algebra;

  1. Present clear mathematical arguments in both written and oral forms.

Assessment

Examination (3 hours): 70%
Assignments: 20%
Laboratory work: 10%.

Chief examiner(s)

Dr Tim Garoni

Contact hours

Three 1-hour lectures and one 2-hour support class per week

Prerequisites

MAT1841, MTH1030, MTH1035, or equivalent

Prohibitions

MAT2912