# Introductory Mathematics for Engineering Applications

# Introductory Mathematics for Engineering Applications

ISBN: 978-1-118-14180-9

Feb 2014

432 pages

## Description

Rattan and Klingbeil’s *Introductory Mathematics for Engineering Applications* is designed to help improve engineering student success through application-driven, just-in-time engineering math instruction. Intended to be taught by engineering faculty rather than math faculty, the text emphasizes using math to solve engineering problems instead of focusing on derivations and theory. This text implements an applied approach to teaching math concepts that are essential to introductory engineering courses that has been proven to improve the retention of students in engineering majors from the first to second year and beyond.

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**1 STRAIGHT LINES IN ENGINEERING 1**

1.1 Vehicle during Braking 1

1.2 Voltage-Current Relationship in a Resistive Circuit 3

1.3 Force-Displacement in a Preloaded Tension Spring 6

1.4 Further Examples of Lines in Engineering 8

Problems 19

**2 QUADRATIC EQUATIONS IN ENGINEERING 32**

2.1 A Projectile in a Vertical Plane 32

2.2 Current in a Lamp 36

2.3 Equivalent Resistance 37

2.4 Further Examples of Quadratic Equations in Engineering 38

Problems 50

**3 TRIGONOMETRY IN ENGINEERING 60**

3.1 Introduction 60

3.2 One-Link Planar Robot 60

3.2.1 Kinematics of One-Link Robot 60

3.2.2 Inverse Kinematics of One-Link Robot 68

3.3 Two-Link Planar Robot 72

3.3.1 Direct Kinematics of Two-Link Robot 73

3.3.2 Inverse Kinematics of Two-Link Robot 75

3.3.3 Further Examples of Two-Link Planar Robot 79

3.4 Further Examples of Trigonometry in Engineering 89

Problems 97

**4 TWO-DIMENSIONAL VECTORS IN ENGINEERING 106**

4.1 Introduction 106

4.2 Position Vector in Rectangular Form 107

4.3 Position Vector in Polar Form 107

4.4 Vector Addition 110

4.4.1 Examples of Vector Addition in Engineering 111

Problems 123

**5 COMPLEX NUMBERS IN ENGINEERING 132**

5.1 Introduction 132

5.2 Position of One-Link Robot as a Complex Number 133

5.3 Impedance of R, L, and C as a Complex Number 134

5.3.1 Impedance of a Resistor R 134

5.3.2 Impedance of an Inductor L 134

5.3.3 Impedance of a Capacitor C 135

5.4 Impedance of a Series RLC Circuit 136

5.5 Impedance of R and L Connected in Parallel 137

5.6 Armature Current in a DC Motor 140

5.7 Further Examples of Complex Numbers in Electric Circuits 141

5.8 Complex Conjugate 145

Problems 147

**6 SINUSOIDS IN ENGINEERING 157**

6.1 One-Link Planar Robot as a Sinusoid 157

6.2 Angular Motion of the One-Link Planar Robot 159

6.2.1 Relations between Frequency and Period 160

6.3 Phase Angle, Phase Shift, and Time Shift 162

6.4 General Form of a Sinusoid 164

6.5 Addition of Sinusoids of the Same Frequency 166

Problems 173

**7 SYSTEMS OF EQUATIONS IN ENGINEERING 184**

7.1 Introduction 184

7.2 Solution of a Two-Loop Circuit 184

7.3 Tension in Cables 190

7.4 Further Examples of Systems of Equations in Engineering 193

Problems 206

**8 DERIVATIVES IN ENGINEERING 218**

8.1 Introduction 218

8.1.1 What Is a Derivative? 218

8.2 Maxima and Minima 221

8.3 Applications of Derivatives in Dynamics 225

8.3.1 Position, Velocity, and Acceleration 226

8.4 Applications of Derivatives in Electric Circuits 240

8.4.1 Current and Voltage in an Inductor 243

8.4.2 Current and Voltage in a Capacitor 247

8.5 Applications of Derivatives in Strength of Materials 250

8.5.1 Maximum Stress under Axial Loading 256

8.6 Further Examples of Derivatives in Engineering 261

Problems 266

**9 INTEGRALS IN ENGINEERING 278**

9.1 Introduction: The Asphalt Problem 278

9.2 Concept ofWork 283

9.3 Application of Integrals in Statics 286

9.3.1 Center of Gravity (Centroid) 286

9.3.2 Alternate Definition of the Centroid 293

9.4 Distributed Loads 296

9.4.1 Hydrostatic Pressure on a Retaining Wall 296

9.4.2 Distributed Loads on Beams: Statically Equivalent Loading 298

9.5 Applications of Integrals in Dynamics 302

9.5.1 Graphical Interpretation 309

9.6 Applications of Integrals in Electric Circuits 314

9.6.1 Current, Voltage, and Energy Stored in a Capacitor 314

9.7 Current and Voltage in an Inductor 322

9.8 Further Examples of Integrals in Engineering 327

Problems 334

**10 DIFFERENTIAL EQUATIONS IN ENGINEERING 345**

10.1 Introduction: The Leaking Bucket 345

10.2 Differential Equations 346

10.3 Solution of Linear DEQ with Constant Coefficients 347

10.4 First-Order Differential Equations 348

10.5 Second-Order Differential Equations 374

10.5.1 Free Vibration of a Spring-Mass System 374

10.5.2 Forced Vibration of a Spring-Mass System 379

10.5.3 Second-Order LC Circuit 386

Problems 390

ANSWERS TO SELECTED PROBLEMS 401

INDEX 417

- End-of Chapter problem sets have been expanded to include
**more applications drawn from chemical and biological engineering**in addition to existing problems from mechanical, civil, and electrical engineering.

- This text is designed for use in a course that complements traditional math prerequisites for introductory engineering courses so that students can advance in the curriculum without first completing calculus requirements.
- Showing students the engineering applications of the math concepts they are learning provides them with more motivation to persist and has been proven to positively impact engineering student retention.
- Applications-driven presentation provides motivation for engineering math by using realistic engineering problems.
- Can serve as a primary text for a first-year engineering math course, allowing students to advance without first completing the required calculus sequence.
- This course doesn't replace calculus. It simply allows students to advance through introductory engineering courses while they gain the maturity and motivation to succeed in calculus at a slower pace.