Introductory Mathematics for Engineering Applications

Contents

1 STRAIGHT LINES IN ENGINEERING

1.1 Vehicle during Braking

1.2 Voltage-Current Relationship in a Resistive Circuit

1.3 Force-Displacement in a Preloaded Tension Spring

1.4 Further Examples of Lines in Engineering

Problems

2 QUADRATIC EQUATIONS IN ENGINEERING

2.1 A Projectile in a Vertical Plane

2.2 Current in a Lamp

2.3 Equivalent Resistance

2.4 Further Examples of Quadratic Equations in Engineering

Problems

3 TRIGONOMETRY IN ENGINEERING

3.1 Introduction

3.2 One-Link Planar Robot

3.2.1 Kinematics of One-Link Robot

3.2.2 Inverse Kinematics of One-Link Robot

3.3 Two-Link Planar Robot

3.3.1 Direct Kinematics of Two-Link Robot

3.3.2 Inverse Kinematics of Two-Link Robot

3.3.3 Further Examples of Two-Link Planar Robot

3.4 Further Examples of Trigonometry in Engineering

Problems

4 TWO-DIMENSIONAL VECTORS IN ENGINEERING

4.1 Introduction

4.2 Position Vector in Rectangular Form

4.3 Position Vector in Polar Form

4.4 Vector Addition

4.4.1 Examples of Vector Addition in Engineering

Problems

5 COMPLEX NUMBERS IN ENGINEERING

5.1 Introduction

5.2 Position of One-Link Robot as a Complex Number

5.3 Impedance of R, L, and C as a Complex Number

5.3.1 Impedance of a Resistor R

5.3.2 Impedance of an Inductor L

5.3.3 Impedance of a Capacitor C

5.4 Impedance of a Series RLC Circuit

5.5 Impedance of R and L Connected in Parallel

5.6 Armature Current in a DC Motor

5.7 Further Examples of Complex Numbers in Electric Circuits

5.8 Complex Conjugate

Problems

6 SINUSOIDS IN ENGINEERING

6.1 One-Link ...