- This was the web site for 2016. The web site for 2017 will be updated in July 2017.
- I have arranged for a directory on the FIRGA system, so that you can access the D3 set of functions for displaying various objects in 3D. Start MATLAB and follow these instructions.
This module is about the extension of calculus (i.e. differentiation and integration) to multivariate functions, such as f(x,y,z) and is also about the extension of calculus to functions with more than one component (vector functions), such as F(x)=[f(x),g(x),h(x)]. Eventually you will also do calculus on multivariate vector functions, for example F(x,y,z) =[f(x,y,z), g(x,y,z), h(x,y,z)].
You will become acquainted with the vector operators, grad, div and curl and will learn how to apply them correctly. You will learn to integrate over a surface, on the boundary of a surface, through a volume and on the boundary of a volume, and you will find tangent planes to curves and directional derivatives in space. There will be ample opportunity for exercise and the development of technical skills in handling these operations.
The crux of this course consists of three important theorems in vector calculus, viz. Greenís theorem, Stokesí theorem and the divergence theorem of Gauss. Each of these theorems proves the equivalence between two types of integrals: one over a domain and the other on the boundary of the same domain. By applying these theorems, difficult integrals can sometimes be calculated in a much easier way. Furthermore, by studying the origin of these theorems specific insight into the behaviour of vector fields may be obtained.
Fundamental knowledge of vector analysis is required for the handling of concepts in electromagnetism, fluid dynamics, elasticity and every other application where physical quantities are represented as continuous vector functions of more than one variable.
The emphasis in this course will be on interpretation of results and in particular on the visual understanding of what each operation does and how each result is represented in physical space.
The software package MATLAB will be used in this course to illustrate concepts graphically. It is not expected of you to be acquainted with MATLAB, although a little knowledge of how it is used will be an advantage. Some class time will be allocated to present a short introduction in the use of the package.
Applied Mathematics B 242
2.00 lectures, 1.50 Tutorials (per week)
Mathematical Sciences:Applied Mathematics
Dr MF Maritz
|Computer Applications: |
Eng. Math. 145
|By requisites: |
Appl. Math. B224
|Formulae for the calculation of marks |
will be published in the Module info sheet only.
This assessment of this course is done according to the Flexible assessment method. Go to the relevant document in SunLearn ( click here ) to see how this type of evaluation is implemented.
The final mark conststs of three components: SM (the Semester Mark), A1 (the first test) and A2 (the second test). In some cases students are allowed to "Further assessment" and they will then write A3 (the third test).
Each week, you will also write a smaller test, called the Tut Test. This test is written at the end of the relevant tutorial session and covers the work done during that tutorial session. Do not waste time during any tutorial session, but start working immediately. Tutorial problems will be from Zill & Wright and the numbers of problems to be done will be put on this web site on the Monday preceding the tutorial session. You may therefore already start working on these problems at home.
Calculators as prescribed by the Faculty of Engineering may be used during all tests.
TimetableBelow is a 'screen shot' of the time table as published on the official university web site.
TestsBelow is a 'screen shot' of the test dates as published on the official university web site.
Date, time and venue information below is given by way of elucidation only (as copied from the screen shot above), however, no guarantee for its correctness is given here.
It remains the responsibility of the student to consult the official university web page.
|1st Test||Tuesday, 30 Aug 2016||8:00||A107 and A403A||Prep-page||Memo|
|2nd Test||Monday, 31 Oct 2016||9:00||t.b.a.||Prep-page|
|3rd Test||Monday, 21 Nov 2015||9:00||t.b.a.||Use previous 2 Prep-pages|
- Module Info Sheet
- Module Outcomes
- In order to link the set of D3-functions to MATLAB so that they are accessible, follow these instructions. If you want to download these functions directly, they are here.
- Cartesian, Cylindrical and Spherical Coordinates
- Here is an older repository of the MATLAB D3 set of functions for downloading.