Department of Mathematics and Applied Mathematics, UCT
Introduction to
Complex Numbers
Contents:
Page
1. What are Complex Numbers?
1
2. A Formal approach to Complex Numbers
3
3. A geometric view of Complex Numbers
9
4. The exponential function
16
5. Findi

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Engineering Mathematics B (MAM1021S)
2015
Matrices
1. Linear equations
An equation such as
x + 2y = 7
(1)
is known as a linear equation because its graph is a straight line. It is easy to see
that this particular line cuts the coordinate axes at the point

APPENDIX C
C.4
A39
Differential Equations
Applications of Differential Equations
Use differential equations to model and solve real-life problems.
EXAMPLE 1
Modeling Advertising Awareness
The new cereal product from Example 3 in Section C.1 is introduced

Differential equations: some notes and
examples
MAM1018S
2013
July 31, 2013
Chapter 1
1.1
Introduction
Read these notes together with the section on d.e.s in Stewart. Separable
d.e.s are dealt with in the textbook and in these notes; the notes then
contin

Engineering Mathematics B (MAM1021S)
2015
Exercise Sheet 4
Vectors and the geometry of space.
1. A rectangular box has two of its vertices at (1, 3, 4) and (2, 1, 7). If the sides of the
box are parallel to the coordinate planes, where are the other verti

Engineering Mathematics B (MAM1021S)
2015
Exercise Sheet 1
All references are to the 4th Metric International Edition of Calculus : Concepts & Contexts
by James Stewart. Other editions of this textbook might differ.
Techniques of integration.
1. Stewart,

Engineering Mathematics B (MAM1021S)
2015
Exercise Sheet 3
Differential equations.
1. Stewart, Section 7.1: Exercises 1, 3, 5, 7, 9.
2. Sketch a few members of the following families of curves. By eliminating parameters, derive a differential equation whi

Engineering Mathematics B (MAM1021S)
2015
Exercise Sheet 5
The cross-product.
1. Stewart, Section 9.4: Exercises 1, 7, 13, 19, 23, 27, 29, 31, 33, 35, 39.
2. Let a = (1, 3, 4), b = (2, 2, 7) and c = (2, 1, 2). Calculate a (b c) and (a b) c.
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