units

MTH1035

Faculty of Science

25 November 2014
21 December 2014

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

Level | Undergraduate |

Faculty | Faculty of Science |

Organisational Unit | School of Mathematical Sciences |

Monash Passport category | Advanced Studies (Enhance Program) |

Offered | Clayton First semester 2015 (Day) |

Coordinator(s) | Mr Simon Teague |

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): 70%

Assignments and tests: 30%

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

See also Unit timetable information

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.