units

MTH1035

Faculty of Science

14 December 2016
20 January 2017

Undergraduate - Unit

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

Faculty

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Offered

- First semester 2017 (Day)

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.

On completion of this unit students will be able to:

- Understand the basic concepts of linear algebra, and recognise and manipulate elements of vector spaces;
- Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;
- Identify and evaluate improper integrals;
- Solve simple first and second order differential equations, and formulate them for applications to physical systems;
- Compute Taylor series expansions, with remainder, for functions of one variable;
- Apply Taylor series and l'Hopital's rule to compute limits;
- Understand and compute the convergence properties of infinite series;
- Provide written reports that contain complete mathematical arguments;
- Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;
- Prove elementary theorems by induction and by construction.

Final examination (3 hours): 65%

Assignments and tests: 30%

Participation in support classes: 5%

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

See also Unit timetable information

Applied mathematics

Astrophysics

Atmospheric science

Financial and insurance mathematics

Mathematical statistics

Mathematics

Pure mathematics

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 Science Student Services office.