Monash University Handbook 2011 Undergraduate - Unit

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

Synopsis

This unit is an alternative to MTH2010 for students with a strong mathematical foundation.
Functions of several variables, partial derivatives, extreme values, Lagrange multipliers. Multiple integrals, line integrals, surface integrals. Vector differential calculus; grad, div and curl. Integral theorems of Gauss and Stokes. Use of a computer algebra package.

Objectives

On completion of this unit students will be able to:

1. demonstrate understanding of fundamental concepts in multivariable calculus and its applications in a number of areas of mathematics and science;
2. test the formal definition of limits and continuity of functions of several variables;
3. develop higher order expansion of the Taylor series in multivariable calculus;
4. determine extreme values of multivariable functions;
5. differential the determinant of a square matrix;
6. evaluate line, double, triple and surface integrals;
7. comprehend the concepts of gradient, divergence and curl;
8. prove identities of grad, div and curl;
9. apply the Gauss divergence theorem and the Stokes' theorem;
10. have developed skills in the effective use of computer algebra software as an aid for modelling and in the production of scientific reports; and
11. be able to apply rigorous mathematical reasoning to problem solving, and to develop simple mathematical proofs.

Assessment

Continuous assessments: 40%
Final Examination: 60%

Chief examiner(s)

Dr Simon Clarke

Contact hours

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

Prerequisites

A High Distinction in VCE Enhancement Mathematics or MTH1030; a Distinction in MTH1035; 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

MTH2010