A Refresher Course in Mathematics - Talking Electronics

FRANK WERNER

A REFRESHER COURSE

IN MATHEMATICS

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A Refresher Course in Mathematics

1st edition

? 2016 Frank Werner &

ISBN 978-87-403-1319-2

Peer reviewed by Dr. Larysa Burtseva, The Engineering Institute of the

Autonomous University of Baja California, Mexicali, Mexico

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A REFRESHER COURSE IN MATHEMATICS

Contents

Contents

1 Some Mathematical Foundations

9

1.1

Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.2

Sum and Product Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

1.3

Proof by Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

2 Real Numbers and Arithmetic Operations

25

2.1

Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.2

Basic Arithmetic Rules and the Absolute Value . . . . . . . . . . . . . . . . . . .

26

2.3

Calculations with Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

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A REFRESHER COURSE IN MATHEMATICS

Contents

2

CONTENTS

2.4

Calculations with Powers and Roots . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.5

Calculations with Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

3 Equations

43

3.1

Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.2

Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

3.3

Root Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.4

Logarithmic and Exponential Equations . . . . . . . . . . . . . . . . . . . . . . .

59

3.5

Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

3.6

Approximate Solution of Equations . . . . . . . . . . . . . . . . . . . . . . . . . .

67

4 Inequalities

71

4.1

Basic Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

4.2

Linear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

4.3

Inequalities with Absolute Values . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

4.4

Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

4.5

Further Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

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