Introduction to Engineering Modeling and Problem Solving

by Brockman, Jay

• ISBN13: 9780471431602
• ISBN10: 0471431605
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-04-29
• Publisher: WILEY

Summary

Written through the eyes of an engineer, this book offers readers an introduction to the field that looks at how engineers apply science and technology to solve problems facing society. It first focuses on how engineers represent and solve engineering problems and then describes some of the different kinds of mathematical models that are used. Readers will also find a whole section dedicated to MATLAB, an integrated environment for technical computing.

Author Biography

Dr. Jay Brockman is concurrently serving as an Associate Professor in the Department of Computer Science and Engineering and in the Department of Electrical Engineering at the University of Notre Dame.

Table of Contents

The Engineering Mindset	p. 1
Engineering and Society	p. 3
Introduction	p. 3
The Engineering Method	p. 5
Science, Mathematics, and Engineering	p. 5
Ingenuity: From Lifting Weights to Microelectronics	p. 6
Engineering Models	p. 9
Networks and Systems	p. 10
Everything is Connected to Everything	p. 10
A Web of Innovation	p. 11
Systems	p. 15
Engineering Disciplines and Majors	p. 18
Introduction	p. 18
Overview of Engineering Disciplines	p. 19
Professional Organizations	p. 27
Innovation at the Interfaces Between Disciplines	p. 27
Engineering and Computing	p. 31
Programming and Logical Thinking	p. 31
Number Crunching	p. 32
Problems	p. 36
Organization and Representation of Engineering Systems	p. 38
What We Think About How We Think	p. 38
Example: Doing Math in Your Head	p. 39
A Model for Cognitive Processing	p. 40
"How To" Knowledge and Problem Solving	p. 42
Mind and Brain	p. 46
Concept Maps	p. 48
What Is a Concept Map?	p. 48
How to Build a Good Concept Map	p. 50
Hierarchies	p. 54
Representation and Design	p. 58
Purpose, Environment, and Form	p. 58
Requirements, Specifications, and the Forces That Shape a Design	p. 62
Design Hierarchies	p. 65
Example: What Supply for Rural Communities in Developing Nations	p. 72
The Top-Level Problem: Meeting Community Needs	p. 74
A Lower-Level Problem: Design of a Handpump	p. 77
Even Lower-Level Design Details: Seals and Bearings	p. 82
Problems	p. 85
Learning and Problem Solving	p. 88
Introduction	p. 88
Expertise and The Learning Process	p. 89
What Do You Know? Levels of Understanding	p. 90
Knowledge: Recalling Facts from Memory	p. 92
Comprehension: Understanding Meaning	p. 93
Application: Using in New Situations	p. 93
Analysis: Breaking Down into Parts	p. 93
Synthesis: Constructing a New Integrated Whole	p. 94
Evaluation: Using Judgment to Make Decisions	p. 95
Social and Societal Responsibilities of Decision Making	p. 96
Getting Good Results from Your Learning Efforts	p. 96
Get Ready to Learn	p. 97
Building a Good Structure for Knowledge	p. 97
Metacognition: Monitoring Your Own Understanding	p. 101
A Framework for Problem Solving	p. 102
Problem Solving Step 0: I Can	p. 104
Problem Solving Step 1: Define	p. 104
Problem Solving Step 2: Explore	p. 105
Problem Solving Step 3: Plan	p. 106
Problem Solving Step 4: Implement	p. 109
Problem Solving Step 5: Check	p. 109
Problem Solving Step 6: Generalize	p. 111
Problem Solving Step 7: Present the Results	p. 111
How Much CO Does a Typical Passenger Car Produce?	p. 113
Define	p. 113
Explore	p. 114
Plan	p. 115
Do It	p. 115
Check	p. 117
Generalize	p. 117
Present the Results	p. 118
Planning Larger Projects	p. 120
SolderBaat-A Circuit Board Assembly and Test System	p. 121
Task Scheduling	p. 123
Teamwork and Results	p. 126
Heuristics	p. 128
Write It Down	p. 129
Restate in Simpler Terms	p. 129
Draw a Picture	p. 129
Do You Know a Related Problem?	p. 129
Work Backwards/Forwards	p. 130
Work Top-Down/Bottom-Up	p. 131
Divide and Conquer	p. 131
Check for Unnecessary Constraints	p. 133
Discuss	p. 134
Try Solving a Scaled-Down Version of the Problem	p. 134
Try Solving a Simpler but Related Problem	p. 135
Use Models	p. 135
Guess and Check	p. 136
Use an Analogy	p. 137
Change Your Perspective	p. 139
Look at the Big Picture	p. 140
Do the Easy Parts First	p. 140
Plug in Numbers	p. 140
Keep Track of Progress	p. 141
Change the Representation	p. 141
Replan	p. 142
Pay Attention to Hunches	p. 142
Take a Break	p. 142
Problems	p. 143
Model-Based Design	p. 149
Laws of Nature and Theoretical Models	p. 151
Engineering Models	p. 151
Evolution of Theory	p. 154
Models of Motion	p. 156
Aristotle's Physics	p. 156
Galileo and the Scientific Method	p. 157
Rene Descartes and Conservation of Motion	p. 160
The Royal Society	p. 162
Huygens' Improvements to Descartes' Model	p. 163
Newton's Laws of Motion	p. 167
Leibniz and the "Living Force," Work and Energy	p. 169
Modeling the "Spring of Air"	p. 171
The Horror of the Vacuum	p. 171
Boyle's Law	p. 173
Hooke's Law	p. 175
The Birth of the Piston Engine	p. 178
Newcomen's Engine	p. 178
James Watt's Improvements to Newcomen's Design	p. 181
The Science of Thermodynamics	p. 183
Sadi Carnot and the Limits of Engine Efficiency	p. 183
James Joule: From Building a Better Brewery to a Theory of Heat and Energy	p. 185
Conservation of Mass	p. 188
Robert Boyle and The Sceptical Chymist	p. 188
Antoine Lavoisier	p. 189
Analysis Example: The Internal Combustion Engine	p. 190
Operation of a Four-Stroke Engine	p. 190
Efficiency of the Intake Stroke and Air/Fuel Ratio	p. 191
Efficiency of the Compression Stroke and the Compression Ratio	p. 192
Design Example: The Handpump	p. 195
Problem Definition and Plan of Attack	p. 195
Modeling Forces on the Piston	p. 199
Modeling the Handle Lever Arm	p. 202
Modeling Pump Efficiency	p. 205
Problems	p. 208
Data Analysis and Empirical Models	p. 214
Introduction	p. 214
Theory and Data	p. 215
Validating Boyle's Law	p. 215
Exponential Change, Log Plots, and Moore's Law	p. 218
Empirical Models	p. 222
Introduction	p. 222
Running an Experiment	p. 222
Interpolation and Fitting a Line to the Data	p. 223
Using Statistics to Quantify Uncertainty	p. 226
Sources of Uncertainty	p. 227
Mean and Standard Deviation: Systematic and Random Error	p. 228
Estimating Probability	p. 230
Frequency of Results and Histograms	p. 233
The Theory of the Bell Curve	p. 234
Trade Studies: Evaluating Tradeoffs Between Design Variables	p. 236
Methodology: Making and Using Maps	p. 238
Problem Definition and Plan of Attack	p. 240
Mapping the Design Space	p. 242
Finding Settings to Satisfy Distance Constraints	p. 245
Minimizing Energy while Launching at a Target	p. 248
Problems	p. 253
Modeling Interrelationships in Systems: Lightweight Structures	p. 261
Introduction	p. 261
The Statics Perspective	p. 263
Force as a Vector	p. 263
Addition of Forces	p. 265
Equilibrium of a Point or Particle	p. 269
Equilibrium of Pinned Joints and Bars	p. 270
Loads, Supports, and Reaction Forces	p. 273
Static Analysis of a Complete Truss	p. 275
The Materials Perspective	p. 279
Bars as Springs: Hooke's Law and Young's Modulus	p. 279
Strength of Materials	p. 285
Buckling	p. 289
Putting It All Together	p. 291
Statics Perspective	p. 291
Materials Perspective	p. 293
Statically Determinate and Indeterminate Trusses	p. 294
Example: A Trade Study of Strength versus Weight in a Truss	p. 296
Problem Definition and Plan of Attack	p. 296
Implementation of the Plan	p. 301
Finding an Acceptable Design	p. 306
Problems	p. 307
Modeling Interrelationships in Systems: Digital Electronic Circuits	p. 315
Introduction	p. 315
Computing Machines	p. 316
The Logical and Physical Views	p. 316
History and Background	p. 321
Digital Circuits from the Symbolic and Logical Perspective	p. 325
Boolean Logic	p. 326
Building Computing Machines Out of Switches	p. 330
Binary Representation of Numbers	p. 332
Adding Numbers with Switches	p. 335
Digital Circuits from the Electronics Perspective	p. 337
Electricity	p. 337
Electronic Devices	p. 343
Electrical Circuits	p. 347
Putting It All Together: Design of an Inverter	p. 353
Background	p. 353
Problem Definition and Plan of Attack	p. 354
Choosing Device Sizes	p. 356
Calculating Power Consumption	p. 358
Problems	p. 360
Modeling Change in Systems	p. 366
Introduction	p. 366
Predicting the Future: Accumulation of Change	p. 367
The State of a System	p. 367
Euler's Method: Predicting Change from One State to the Next	p. 370
Launching a Softball	p. 373
Problem Definition and Plan of Attack	p. 374
Modeling the Softball Trajectory Without Drag	p. 376
Modeling the Softball Trajectory with Drag	p. 379
Continuous Versus Discrete Models	p. 384
Running Out of Gas	p. 385
Background	p. 386
Problem Definition and Plan of Attack	p. 395
Flow Rates and Conservation of Mass	p. 396
Growth at a Constant Rate: Population and Per-Capita Oil Consumption	p. 398
Putting It All Together	p. 400
Will We Really Run Out of Oil by 2040?	p. 406
Problems	p. 407
Problem Solving with Matlab	p. 417
Getting Started with MATLAB	p. 419
Your First MATLAB Session	p. 419
Interpreting Simple Arithmetic Expressions	p. 419
Variables	p. 421
Scripts	p. 422
Examples	p. 424
Determining Velocities After a Collision	p. 424
Mass of CO[subscript 2] Produced by a Car	p. 425
Problems	p. 426
Vector Operations in MATLAB	p. 432
Introduction	p. 432
Basic Operations	p. 433
Defining and Accessing Vectors	p. 433
Element-Wise Arithmetic Operations on Vectors	p. 435
Example: Validating Boyle's Law	p. 436
Simple Two-Dimensional Plots and Graphs	p. 438
Plot Basics	p. 438
Adding Titles and Labels	p. 439
Changing Line Styles	p. 440
Multiple Plots on One Set of Axes	p. 440
Multiple Sets of Axes in One Figure	p. 441
Plotting Functions	p. 442
Specialized Plotting	p. 443
Example: Plotting the Results of Boyle's Experiment	p. 444
Example: Moore's Law and Log Plots	p. 446
Statistics	p. 448
The Basics: Minimum, Maximum, Averages, etc.	p. 449
Counting Values in a Range	p. 450
Bin Counts and Histograms	p. 453
Where to Learn More	p. 455
Problems	p. 455
Matrix Operations in MATLAB	p. 463
Basic Operations	p. 463
Defining and Accessing Matrices	p. 463
Element-Wise Arithmetic Operations on Matrices	p. 467
Parameter Sweeps Over Two Variables	p. 468
Creating Tables Using Code meshgrid	p. 468
Example: Force on the Piston of a Pump Versus Well Depth and Cylinder Radius	p. 469
Plotting 3-Dimensional Data	p. 471
Mesh and Surface Plots	p. 471
Contour Plots	p. 472
Side-View Cross-Section Plots	p. 473
Matrix Arithmetic	p. 474
Zero Matrix	p. 474
Equality of Matrices	p. 475
Matrix Addition	p. 475
Multiplication of a Matrix by a Scalar	p. 476
Matrix Subtraction	p. 477
Matrix Multiplication	p. 477
Solving Systems of Linear Equations	p. 480
Linear Equations in Matrix Form	p. 480
The Identity Matrix and the Inverse of a Matrix	p. 481
Solving Matrix Equations Using Inversion	p. 483
Solving Matrix Equations Using the Backslash Operator	p. 484
Example: Analysis of a Truss	p. 484
Example: Analysis of Electrical Circuits	p. 487
Problems	p. 492
Introduction to Algorithms and Programming In MATLAB	p. 498
Algorithms, Flow Charts, and Pseudocode	p. 498
What Is an Algorithm?	p. 498
Describing Simple Sequences of Operations	p. 499
Subroutines	p. 501
Conditional Branches	p. 502
Loops	p. 506
MATLAB Functions	p. 510
Mathematical Functions Versus MATLAB Functions	p. 510
Functions Calling Functions	p. 513
Watching a Function Call Through the MATLAB Debugger	p. 514
Conditional Selection Statements	p. 517
Review of Logic Expressions	p. 518
IF/ELSE Statements	p. 519
Stepping Through an IF Statement in the Debugger	p. 520
Loops or Repetition Statements	p. 522
WHILE Loops	p. 522
FOR Loops	p. 523
Watching a Loop in the Debugger	p. 523
Nested Loops	p. 524
Common Loop Bugs	p. 525
Examples of Functions, Conditionals, and Loops	p. 526
Subfunctions: The Cake Recipe	p. 526
Vector and Matrix Functions	p. 527
Accumulation of Change	p. 529
Review: Modeling Population Growth	p. 530
Modeling the Trajectory of a Softball with Drag	p. 532
Problems	p. 534
Problem Solving Process	p. 548
Bloom's Taxonomy: Levels of Understanding	p. 550
Engineering Societies and Professional Organizations	p. 551
Systems of Units	p. 554
The SI System	p. 554
Non-SI Units and Conversion Factors	p. 556
Bibliography	p. 558
Index	p. 565
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