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 need to be able to say how rapidly such a surface curves, and that immediately requires us to do calculus on functions of two (or more) variables.
We will 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 this material is fundamental to the study of all areas of Engineering and (continuum) Applied Mathematics, and it underpins modern continuum mechanics and electromagnetic theory.
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. Previously we have looked at power series as an infinite sum of terms involving increasing powers of a particular variable. A Fourier series is an infinite sum of terms involving sine and cosine functions. This is an important concept for solving problems in acoustics, signal processing, heat-flow theory, fluid mechanics, vibrations, electromagnetic field theory, and so on.
|Unit name||Calculus and Applications 2|
|College/School||College of Sciences and Engineering
School of Natural Sciences
|Coordinator||Doctor Michael Brideson|
|Available as an elective?||Yes|
|Delivered By||University of Tasmania|
|Location||Study period||Attendance options||Available to|
- International students
- Domestic students
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|Study Period||Start date||Census date||WW date||End date|
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- 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
|Field of Education||Commencing Student Contribution 1||Grandfathered Student Contribution 1||Approved Pathway Course Student Contribution 2||Domestic Full Fee|
1 Please refer to more information on student contribution amounts.
2 Please refer to more information on eligibility and Approved Pathway courses.
3 Please refer to more information on eligibility for HECS-HELP.
4 Please refer to more information on eligibility for FEE-HELP.
Please note: international students should refer to What is an indicative Fee? to get an indicative course cost.
Prerequisites(KMA152 OR JEE103) AND (KMA154 OR JEE104)
You cannot enrol in this unit as well as the following:KME771 AND KME271
3x1-hour workshops and 1-hour tutorial weekly.
|Assessment||Online Homeworks (20%)|Final Examination (40%)|Written Assignments (40%)|
|Timetable||View the lecture timetable | View the full unit timetable|
Required readings will be listed in the unit outline prior to the start of classes.
Students who completed KMA152 and KMA154 should have access to an online version of the text above.
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.
|Links||Booktopia textbook finder|
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