essential engineering mathematics

EssentialEngineering
Mathematics
MichaelBatty

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Michael Batty

Essential Engineering Mathematics

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Essential Engineering Mathematics
© 2011 Michael Batty & Ventus Publishing ApS
ISBN 978-87-7681-735-0

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Contents

Essential Engineering Mathematics

Contents
0.

Introduction

8

1.
1.1
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
1.3.2
1.3.3
1.3.4

Preliminaries
Number Systems: The Integers, Rationals and Reals
Working with the Real Numbers
Intervals
Solving Inequalities
Absolute Value
Inequalities Involving Absolute Value
Complex Numbers
Imaginary Numbers
The Complex Number System and its Arithmetic
Solving Polynomial Equations Using Complex Numbers
Geometry of Complex Numbers

10

10
13
13
13
14
16
17
17
18
19
20

2.
2.1
2.2
2.2.1
2.2.2
2.2.3
2.3

Vectors and Matrices
Vectors
Matrices and Determinants
Arithmetic of Matrices
Inverse Matrices and Determinants
The Cross Product
Systems of Linear Equations and Row Reduction

23
23

26
26
27
28
30

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Contents

Essential Engineering Mathematics

2.3.1
2.3.2
2.3.3
2.4
2.5

Systems of Linear Equations
Row Reduction
Finding the Inverse of a Matrix using Row Reduction
Bases
Eigenvalues and Eigenvectors

30
30
32
34
35

3.
3.1
3.1.1
3.1.2
3.1.3
3.2
3.3

Functions and Limits
Functions
Denition of a Function
Piping Functions Together
Inverse Functions
Limits
Continuity

39
39
39
41
42
43
48

4.
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9

Calculus of One Variable Part 1: Differentiation
Derivatives
The Chain Rule

Some Standard Derivatives
Dierentiating Inverse Functions
Implicit Differentiation
Logarithmic Differentiation
Higher Derivatives
L’Hôpital’s Rule
Taylor Series

51
51
56
58
59
61
63
66
67
69

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