Numerical methods 1
All those maths modules that you've taken over the years... ever wondered how the theory is used in practice, or how it's probably been implemented in packages like MatLab/Maxima/Octave? Or, ever wondered how your calculator does the computations it performs? The microprocessor in a calculator can only add (the cheaper versions) and using a few other tricks to subtract, multiply and divide. Using the add function, it is able to perform complex calculations. Some of the later models can even do Calculus (Differentiation and Integration), all by adding, subtracting, multiplying and dividing, using the techniques in this module.
Numerical Methods / Analysis is all about finding the most efficient algorithms for implementing the various mathematical methods on a computer, and where that's not possible, how best to approximate the results. Because results are almost always approximated a significant part of the course involves determining the approximate error of your initial approximation.
The Unisa syllabus
- Solving Nonlinear Equations
- Solving Sets of Equations
- Interpolation and Curve Fitting
- Numerical Differentiation and Integration
The COS2633 textbook
- Richard L. Burden, J. Douglas Faires: Numerical Analysis
Where the the prescribed texbook by Gerald & Wheadly is full of errors and very poor on examples, this book has plenty of worked out examples and there are no apparent errors. It might be an expensive texbook, but you will not look back after purchasing it.
The COS2633 exam
Past exam papers
The exam in Oct/Nov 2009
How to pass COS2633
- Learn how to use your normal scientific calculator's storage function extensively. The exams on these modules tend to have lots and lots of calculations in them. They do not only test your knowledge of the subject, but also your ability to do a lot of these calculations in a short period of time.
- A must for this module is the purchase of a Student Edition of Matlab. The nice thing about this program is that you can actually write nice programs in a C like environment, which will do all the work for you, and this program is very easy to use, once you learn how.
- While Matlab is not a prerequisite for this course, you'll find the prescribed textbook and assignment solutions refer to Matlab code to the point of you being annoyed that it hasn't been prescribed. So instead of shelling out about R1500 for a student copy get hold of an open-source Matlab-compatible CAS such as Gnu Octave. To wrap your head around the root-finding methods described in chapter 1 by exerting yourself trying to pick up a numerical methods-specific skill such as learning the Matlab language, you could use a general purpose (but very powerful) language such as Python to implement the example code.
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Pros of COS2633
- You will learn a lot of new mathematical cool things.
- If your aim is to go into the Engineering field, especially Electronic Engineering as a programmer for an Engineering company, this module will help you with the math needed for programming Digital Signal Processing (DSP) functions on DSP microcontrollers.
- If you have done Statistics, you will learn how and where those formulas come from for doing those statistical calculations.
- Following the Study tips on this page, you will learn how to use Matlab and be amazed with what it can do for you.
Cons of COS2633
- This subject is incredibly tough. When you do assignments, you will find you have to read several 10s of pages to find out what the question requires.
- The textbook contains very limited examples and the supplementary material supplied by Unisa is not helpful.
- If you are taking maths as a major, then this subject might not be so difficult, but if you have only done first year maths, it may be best to steer clear of this one.