Textbook
Introductory Mathematics for Engineering ApplicationsFebruary 2014, ©2015

Rattan and Klingbeil’s Introductory Mathematics for Engineering Applications is designed to help improve engineering student success through applicationdriven, justintime 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.
1.1 Vehicle during Braking 1
1.2 VoltageCurrent Relationship in a Resistive Circuit 3
1.3 ForceDisplacement 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 OneLink Planar Robot 60
3.2.1 Kinematics of OneLink Robot 60
3.2.2 Inverse Kinematics of OneLink Robot 68
3.3 TwoLink Planar Robot 72
3.3.1 Direct Kinematics of TwoLink Robot 73
3.3.2 Inverse Kinematics of TwoLink Robot 75
3.3.3 Further Examples of TwoLink Planar Robot 79
3.4 Further Examples of Trigonometry in Engineering 89
Problems 97
4 TWODIMENSIONAL 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 OneLink 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 OneLink Planar Robot as a Sinusoid 157
6.2 Angular Motion of the OneLink 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 TwoLoop 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 FirstOrder Differential Equations 348
10.5 SecondOrder Differential Equations 374
10.5.1 Free Vibration of a SpringMass System 374
10.5.2 Forced Vibration of a SpringMass System 379
10.5.3 SecondOrder LC Circuit 386
Problems 390
ANSWERS TO SELECTED PROBLEMS 401
INDEX 417
 Endof 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.
 Applicationsdriven presentation provides motivation for engineering math by using realistic engineering problems.
 Can serve as a primary text for a firstyear 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.
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