units

MTH2015

Faculty of Science

18 September 2017 24 April 2024
Monash University

Undergraduate - Unit

This unit entry is for students who completed this unit in 2012 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.

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6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

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

LevelUndergraduate
FacultyFaculty of Science
Monash Passport categoryAdvanced Studies (Enhance Program)
OfferedClayton Second semester 2012 (Day)
Coordinator(s)Mr John McCloughan

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. 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)

Mr John McCloughan

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