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.
|Unit name||Computational Techniques 3|
|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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- 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|
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Prerequisites(KMA152 Mathematics 1A OR JEE103 Mathematics I) AND (KMA154 Mathematics 1B OR JEE104 Mathematics II)
3 x 1-hr workshops and 1 x 1-hr tutorial/practical weekly
|Assessment||Final Examination (40%)|Fortnightly Assignments (42%)|Matlab Assignments (6%)|Large Assignment (12%)|
|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.
You will find a significant amount of material for this unit in books such as:
There are many books with the title “Numerical Analysis” or something similar, and these ought to be helpful too.
|Links||Booktopia textbook finder|
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