Announcements
- Student Feedback: A student feedback questionnaire has been activated for this module. You will receive an email request with the link to it. Please do the questionnaire and give your feedback on the module and how it was presented.
- Preparation page for A2: A preparation page to help you organize your preparation for the A2 test is available here. (Die Afrikaanse weergawe is hier.)
- Corrected Marks: The cumulative mark on the previously posted sheet was incorrect. The corrected marks list is here (under student number). All tuttest marks are included. The best 8 tuttests out of the ten tuttests (1,2, (there was no 3) , 4,5,6,7,8,9,10,11) count. The cumulative mark is "what you have at the moment".
- Screencasts: Some screencasts are available on this website above in the tab [SCREENCASTS]. I normally post the screencasts and recorded videos on SunLearn, because of the space needed for it, but SunLearn is very slow again. This temporary measure may help to alleviate the problem.
- Outcomes: A document with the Module Outcomes is available here, (or here for the Afrikaans version).
- D3-package: The MATLAB routines (such as D3axis, D3vector, ...) are available for download for those who are interested. Click on the tab 'DOWNLOAD' and then select 'D3-PACKAGE'. The files are all in one zipped folder. You may also download it from the SunLearn site. An instruction sheet on how to set the path so that MATLAB can find the routines is available here.
Introduction
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. Green’s theorem, Stokes’ 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.
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Module info
Module Code: 20753-B242(8) |
Module Name: Applied Mathematics B 242 |
Module Description: Vector Analysis |
US Credits: 8 |
Year: 2 Semester: 2 |
Lecturing load: 2.00 lectures, 1.50 Tutorials (per week) |
Home Department: Mathematical Sciences:Applied Mathematics |
|
Lecturer: Dr MF Maritz |
Office: A416 |
Telephone: 808-4228 |
Email: mfmaritz@sun.ac.za |
Classification: | Mathematics: 95% |
Basic Science: 5 % |
Computer Applications: 0 % |
Requirements: | Pass None |
Prerequisites: Eng. Math. 145 |
By requisites: Appl. Math. B224 |
Assessment: | Method: Flexible assessment |
Formulae for the calculation of marks will be published in the Module info sheet only. |
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Assessment
This assessment of this course is done according to the Flexible assessment method.
The final mark consists 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). Your final mark will be weighted: 10% of the semester mark, and 45% each of the best two marks of A1, A2 and A3.
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 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.
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Timetable
There are two lectures per week: Monday 9:00 in A303B, and Tuesday 12:00 in A303B. The tutorial session is on Wednesday 14:00 in S2001, and S2002.TO TOP
Tests
Below 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.
Event | Date | Time | Venue | Preparation | Memo |
1st Test | Wednesday, 6 Sep 2023 | 8:00 | S1018 | Prep-page, Voorb-blad (Afr.) | Memo |
2nd Test | Friday, 10 Nov 2023 | 9:00 | t.b.a. | Prep-page, Voorb-blad (Afr.) | |
3rd Test | Thursday, 30 Nov 2023 | 9:00 | t.b.a. | Use previous 2 Prep-pages |
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Download
- Module Info Sheet, Module Inligtingstuk (Afr.)
- Module Outcomes, Module-uitkomste (Afr.)
- The set of D3 functions for displaying various objects in 3D is available. Start MATLAB and follow these instructions. If you want to download these functions directly, click here an then the fille will download to you download folder as 'D3package.zip'.
- Cartesian, Cylindrical and Spherical Coordinates