MTH2015 - Multivariable calculus (advanced)

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Overview

This unit is an alternative to MTH2010 for students with a strong mathematical foundation. Students enrolled in MTH2015 will follow the same curriculum as students in MTH2010 and will cover additional more advanced material. Functions of several variables, partial derivatives, extreme values, Lagrange multipliers. Multiple integrals, line integrals, surface integrals. … For more content click the Read More button below.

This unit is an alternative to MTH2010 for students with a strong mathematical foundation.

Students enrolled in MTH2015 will follow the same curriculum as students in MTH2010 and will cover additional more advanced material.

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. Curves in 3-space, notions of torsion and curvature. Introductory notions of topology and geometry (stereographic projection). Basic introduction to real analysis: pointwise versus uniform convergence of functions of one variable. Introduction to complex analysis: holomorphic functions, harmonic functions, complex integration, Cauchy's integral formula, the fundamental theorem of Algebra.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Norm Do

Unit Coordinator(s)

Dr Yann Bernard

Learning outcomes

On successful completion of this unit, you should be able to:

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

Find and classify the extrema of functions of several variables;

Compute Taylor series for functions of several variables;

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

Apply the integral theorems of Green, Gauss and Stokes;

Use computer algebra packages to solve mathematical problems;

Present a mathematical argument in written form;

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

Prove various identities between grad, div and curl;

10.

Develop and present rigorous mathematical proofs.

11.

Demonstrate an understanding of the notions of torsion and curvature and be able to compute them;

12.

Apply stereographic projection and its properties;

13.

Articulate the difference between pointwise and uniform convergence for functions of one variable;

14.

Use the properties of analytic functions to prove fundamental results.

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workshops

Workload requirements

Workload

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Unit course reader, Printing, Stationery) - $120.

Availability in areas of study

This unit applies to the following areas of study:
Applied mathematics
Astrophysics
Atmospheric science
Financial and insurance mathematics
Mathematical statistics
Mathematics