Introductory Mathematics for Engineering Applications
February 2014, ©2015
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.
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
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
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
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
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
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
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
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
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
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
ANSWERS TO SELECTED PROBLEMS 401
- 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.
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