# Introductory Mathematics for Engineering Applications, Preliminary Edition, Revised

# Introductory Mathematics for Engineering Applications, Preliminary Edition, Revised

ISBN: 978-1-118-46616-2

Sep 2012

460 pages

## Description

Rattan and Klingbeil’s ** Introductory Mathematics for Engineering Applications** is designed to help improve engineering student retention and success through application-driven, just-in-time engineering math instruction. It is intended to be taught by engineering faculty, not math faculty, so the emphasis is on using math to solve engineering problems, not on derivations and theory.

The book is a product of several major grants to develop and disseminate a new approach to engineering mathematics education. The authors have developed a course that does just this, and faculty at more than two dozen institutions have piloted aspects of this course in their own curricula. This approach covers only the salient math topics actually used in core engineering courses, including physics, statics, dynamics, electric circuits and computer programming. More importantly, the course replaces traditional math prerequisites for the above core courses, so that students can advance in the engineering curriculum without first completing the required calculus sequence. The result has shifted the traditional emphasis on math prerequisite requirements to an emphasis on engineering motivation for math, and has had an overwhelming impact on engineering student retention.

## Related Resources

**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

1.5 Problems 20

**2 Quadratic Equations in Engineering 31**

2.1 A Projectile in a Vertical Plane 31

2.2 Current in a Lamp 35

2.3 Equivalent Resistance 37

2.4 Further Examples of Quadratic Equations in Engineering 38

2.5 Problems 50

**3 Trigonometry in Engineering 61**

3.1 Introduction 61

3.2 One-Link Planar Robot 62

3.3 Two-Link Planar Robot 73

3.4 Further Examples of Trigonometry in Engineering 91

3.5 Problems 100

**4 Two-Dimensional Vectors in Engineering 109**

4.1 Introduction 109

4.2 Position Vector in Rectangular Form 110

4.3 Position Vector in Polar Form 111

4.4 Vector Addition 113

4.5 Problems 127

**5 Complex Numbers in Engineering 135**

5.1 Introduction 135

5.2 Position of One-Link Robot as a Complex Number 136

5.3 Impedance of *R, L*, and *C* as a Complex Number 137

5.4 Impedance of a Series RLC Circuit 139

5.5 Impedance of *R* and *L* Connected in Parallel 141

5.6 Armature Current in a DC Motor 143

5.7 Further Examples of Complex Numbers in Electric Circuits 145

5.8 Complex Conjugate 149

5.9 Problems 150

**6 Sinusoids in Engineering 161**

6.1 One-Link Planar Robot as a Sinusoid 161

6.2 Angular Motion of the One-Link Planar Robot 164

6.3 Phase Angle, Phase Shift, and Time Shift 167

6.4 General Form of a Sinusoid 168

6.5 Addition of Sinusoids of the Same Frequency 171

6.6 Problems 178

**7 Systems of Equations in Engineering 191**

7.1 Introduction 191

7.2 Solution of a Two-Loop Circuit 191

7.3 Tension in Cables 197

7.4 Further Examples of Systems of Equations in Engineering 200

7.5 Problems 215

**8 Derivatives in Engineering 225**

8.1 Introduction 225

8.2 Maxima and Minima 225

8.3 Applications of Derivatives in Dynamics 233

8.4 Applications of Derivatives in Electric Circuits 248

8.5 Applications of Derivatives in Strength of Materials 258

8.6 Further Examples of Derivatives in Engineering 269

8.7 Problems 276

**9 Integrals in Engineering 293**

9.1 Introduction: The Asphalt Problem 293

9.2 Concept of Work 299

9.3 Application of Integrals in Statics 302

9.4 Distributed Loads 312

9.5 Applications of Integrals in Dynamics 319

9.6 Applications of Integrals in Electric Circuits 331

9.7 Current and Voltage in an Inductor 340

9.8 Further Examples of Integrals in Engineering 345

9.9 Problems 353

**10 Differential Equations in Engineering 369**

10.1 Introduction: The Leaking Bucket 369

10.2 Differential Equations 370

10.3 Solution of Linear DEQ with Constant Coefficients 371

10.4 First-Order Differential Equations 372

10.5 Second-Order Differential Equations 399

10.6 Problems 415

ANSWERS TO SELECTED PROBLEMS 425

INDEX 437

- Just-in-time presentation of engineering math concepts.
- Applications-driven presentation provides motivation for engineering math by using realistic engineering problems.
- Designed to be taught by engineering faculty, not math faculty.
- 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.