Courses & Units

Computational Techniques 3 KMA350

Note:

Introduction

Numerical methods are necessary in science and engineering, because most problems of practical interest are just too difficult to be solved in “closed form”. While many important problems, such as the motion of a mass on a spring etc., have “exact” solutions in terms of known functions such as sin or cos, these are nevertheless “simple” problems. Making these problems just a little more complicated leads very quickly to equations that have no easy solutions. Numerical techniques are therefore needed.

Often the approach that is needed to solve a problem numerically is quite unlike the way that you would solve the same problem by hand (eigenvalues are a good example of this). In addition, the numerical solution of some problems can have its own behaviour, which may not be an accurate reflection of the behaviour of the true solution. For that reason, it is important to keep a check on how accurate a method is, and whether it converges (in some sense) to the true solution.

This unit gives an introduction to using numerical methods to solve some of the key problems in science and engineering. We first consider how computers represent numbers and functions, then consider how to solve algebraic equations. A problem of major importance concerns the solution of linear (matrix) equations. Eigenvalues of a matrix are very important in applications, since they tell us the vibrational frequencies of a structure for example, and we will consider how to calculate the eigenvalues and eigenvectors of a matrix. Approximate methods for integrating and differentiating functions will be discussed. Finally, we will look at solving ordinary differential equations using the computer.

Numerical principles will be demonstrated and explored with the scientific software Matlab.

Summary

Unit name Computational Techniques 3
Unit code KMA350
Credit points 12.5
College/School College of Sciences and Engineering
School of Natural Sciences
Discipline Mathematics
Coordinator Doctor Michael Brideson
Available as an elective? Yes
Delivered By University of Tasmania
Level Advanced

Availability

Location Study period Attendance options Available to
Hobart Semester 1 On-Campus International Domestic

Key

On-campus
Off-Campus
International students
Domestic students
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Key Dates

Study Period Start date Census date WW date End date
Semester 1 20/2/2023 21/3/2023 10/4/2023 28/5/2023

* 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 2023 are indicative and subject to change. Finalised census dates for 2023 will be available from the 1st October 2022. Note census date cutoff is 11.59pm AEST (AEDT during October to March).

About Census Dates

Learning Outcomes

  • Examine numerical methods from theoretical and practical perspectives.
  • Analyse the propagation of errors in numerical methods.
  • construct appropriate numerical schemes to approximate mathematical models or operations
  • design and run code to solve problems numerically
Field of Education Commencing Student Contribution 1 Grandfathered Student Contribution 1 Approved Pathway Course Student Contribution 2 Domestic Full Fee
$1,037.00 $1,037.00 not applicable $2,938.00

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.

If you have any questions in relation to the fees, please contact UConnect or more information is available on StudyAssist.

Please note: international students should refer to What is an indicative Fee? to get an indicative course cost.

Requisites

Prerequisites

(KMA152 Mathematics 1A OR JEE103 Mathematics I) AND (KMA154 Mathematics 1B OR JEE104 Mathematics II)

Teaching

Teaching Pattern

3 x 1-hr workshops and 1 x 1-hr tutorial/practical weekly

AssessmentFinal Examination (40%)|Fortnightly Assignments (42%)|Matlab Assignments (6%)|Large Assignment (12%)
TimetableView 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

 

You will find a significant amount of material for this unit in books such as: 

  • Advanced Engineering Mathematics, 9th edition, E. Kreyszig (Wiley 2006)
  • Advanced Engineering Mathematics, 3rd edition, D Zill and M Cullen (Jones and Bartlett 2006)
  • Advanced Engineering Mathematics, 8th edition, P O’Neil (Cengage 2018)
  • Elementary Numerical Analysis, K. Atkinson (Wiley 1985)
  • Numerical Analysis, 4th edition, R.L. Burden and J.D. Faires (PWS-Kent 1989)
  • Numerical Methods Using MATLAB, 4th ed., J.H. Mathews and K.D. Fink (Pearson 2004)

 

There are many books with the title “Numerical Analysis” or something similar, and these ought to be helpful too.

LinksBooktopia textbook finder

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