Hobart, Online
Introduction
This unit is a continuation of KMA152 and KMA154, with emphasis on the application of multivariable calculus and Fourier Series to problems in mathematics, the physical and biological sciences, economics, and engineering. The calculus section of this unit is focussed on dealing with functions of several variables, of which the typical case is z = f(x,y). Functions like this are important because they describe many of the situations we encounter when applying mathematics to models of the real world. The graph of the function z = f(x,y) is a surface, so it might be used to describe building structures; aeroplane wings; temperature, stress, and pressure distributions; income as a function of various expenses; and so on. We may need to say how rapidly such a surface curves, and that immediately requires us to do calculus on functions of two (or more) variables. We also need to consider vectors that are functions of several variables. Some obvious examples of these are the velocity vector in a moving fluid, the heat-flow vector in a solid, and the electric and magnetic fields produced by an antenna. This will lead us to consider more advanced concepts such as circulation, compressibility, divergence, and curl. Understanding these concepts is fundamental to the study of all areas of Engineering, Physics, and (continuum) Applied Mathematics. Topics will be introduced in the Cartesian (rectangular) coordinate system but we will also investigate functions, regions, and vectors defined in cylindrical and spherical coordinates. The Fourier-Series section of this unit is concerned with how to represent periodic functions as an infinite sum of the standard trigonometric functions, sine and cosine. This is an important concept for solving problems in acoustics, signal processing, heat-flow theory, fluid mechanics, vibrations, electromagnetic field theory, and so on.
Summary
| Unit name | Calculus and Applications 2 |
| Unit code | KMA252 |
| Credit points | 12.5 |
| College/School | Sciences and Engineering School of Natural Sciences |
| Discipline | Mathematics |
| Coordinator | Doctor Michael Brideson |
| Available as an elective? | Yes |
| Delivered By | University of Tasmania |
| Level | Intermediate |
Availability
Specific information on 2027 unit availability will be available in August
Key Dates
| Study Period | Start date | Census date | WW date | End date |
|---|---|---|---|---|
| Semester 1 | 21/2/2027 | 15/3/2027 | 18/4/2027 | 12/6/2027 |
* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (refer to How do I withdraw from a unit? for more information).
Unit census dates currently displaying for 2027 are indicative and subject to change. Finalised census dates for 2027 will be available from the 1st October 2026. Note census date cutoff is 11.59pm AEST (AEDT during October to March).
Learning Outcomes
- interrogate the behaviour of multivariable functions using a variety of analytical techniques
- manipulate functions, operations, and problems into different coordinate systems and solve problems accordingly
- solve unconstrained and constrained optimisation problems involving several variables
- construct and solve double and triple integrals, as well as line, surface, and volume integrals
- develop and use vector calculus techniques to solve problems involving scalar fields and vector fields
- develop and use Fourier Series techniques for periodic functions
Fee Information
2027 fee information will be available in August.
Requisites
Prerequisites
(KMA152 OR JEE103) AND (KMA154 OR JEE104)Mutual Exclusions
You cannot enrol in this unit as well as the following:
KME771 AND KME271Teaching
| Teaching Pattern | Weekly commitment: 3x1-hour lectures and 1x1-hour tutorial. |
|---|---|
| Assessment | Online Homeworks (20%)|Final Examination (40%)|Written Assignments (40%) |
| Timetable | View the lecture timetable | View the full unit timetable |
Textbooks
| Required |
Required readings will be listed in the unit outline prior to the start of classes. |
|---|---|
| Recommended |
Students who completed KMA152 and KMA154 have access to the e-text above - subscription paid by the Discipline of Mathematics.
The Advanced Engineering Mathematics texts are excellent reference books, covering a plethora of applied mathematics topics including linear algebra, vector calculus, differential equations (ordinary and partial), Fourier analysis, complex analysis, numerical analysis, optimisation, and probability and statistics. There are many topics that you will meet in other units in Mathematics, Physics, and Engineering. |
The University reserves the right to amend or remove courses and unit availabilities, as appropriate.