## Announcements

• For those who are going to write A3, a 'Preparation sheet' for A3 is available here. Note that A3 covers ALL THE WORK (i.e. it does not concentrate more on term 4, as was the case with A2).
• Marks for Tuttests are here , and Semester Marks and A1 Marks are 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.

## 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.

## Assessment

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 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).

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.

## Timetable

Below is a 'screen shot' of the time table as published on the official university web site.

## 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 t.b.a. Prep-page A1 Memo 2nd Test 16 Nov 2019 9:00 t.b.a. Prep-page 3rd Test 29 Nov 2019 14:00 t.b.a. Prep-page

## Textbook

Dennis G. Zill & Warren S. Wright,
Jones & Bartlett Learning (Any edition from 2 to 6 is OK.)

## Lecturer: 3rd term

Dr Andie de Villiers
Engineering Building A312
andiedevilliers 'at' sun.ac.za
(021) 808-9741

## Lecturer: 4th term

Dr Milton Maritz
Engineering Building A416
mfmaritz 'at' sun.ac.za
(021) 808-4228