units

MTH2015

Faculty of Science

18 September 2017 22 November 2024

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This unit entry is for students who completed this unit in 2016 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.

Monash University

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

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

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Yann Bernard

Offered

Clayton

  • Second semester 2016 (Day)

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.

Outcomes

On completion of this unit students will be able to:

  1. Understand and apply multivariable calculus to problems in the mathematical and physical sciences;

  1. Find and classify the extrema of functions of several variables;

  1. Compute Taylor series for functions of several variables;

  1. Compute line, surface and volume integrals in Cartesian, cylindrical and polar coordinates;

  1. Apply the integral theorems of Green, Gauss and Stokes;

  1. Use computer algebra packages to solve mathematical problems;

  1. Present a mathematical argument in written form;

  1. Understand and apply the formal definition of a limit to functions of several variables;

  1. Prove various identities between grad, div and curl;

  1. Develop and present rigorous mathematical proofs.

Assessment

Final examination (3 hours): 70%
Assignments and tests: 30%

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

Dr Simon Clarke

This unit applies to the following area(s) of study

Applied mathematics
Astrophysics
Atmospheric science
Financial and insurance mathematics
Mathematical statistics
Mathematics

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 Science Student Services office.

Prohibitions

ENG2005, ENG2006, ENG2091, MTH2010