An Engineers Guide to MATLAB

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**List of Examples xiv**

**Preface to Third Edition xx**

**1 Introduction 1**

**Edward B. Magrab**

**1.1 Introduction 1**

**1.1.1 Organization of the Book and Its Goals 2**

**1.1.2 Some Suggestions on How to Use MATLAB 2**

**1.1.3 Book Notation Conventions 3**

**1.2 The MATLAB Environment 3**

**1.2.1 Introduction 3**

**1.2.2 Preliminaries-Command Window Management 5**

**1.2.3 Executing Expressions from the MATLAB Command
Window-Basic MATLAB Syntax 8**

**1.2.4 Clarification and Exceptions to MATLAB'S Syntax
11**

**1.2.5 MATLAB Functions 14**

**1.2.6 Creating Scripts and Executing Them from the MATLAB
Editor 19**

**1.3 Online Help 29**

**1.4 The Symbolic Toolbox 33**

**1.5 Summary of Functions Introduced in Chapter 1 41**

**Exercises 42**

**2 Vectors and Matrices 51**

**Edward B. Magrab**

**2.1 Introduction 51**

**2.2 Definitions of Matrices and Vectors 52**

**2.3 Creation of Vectors 53**

**2.4 Creation of Matrices 64**

**2.5 Dot Operations 83**

**2.6 Mathematical Operations with Matrices 92**

**2.6.1 Addition and Subtraction 92**

**2.6.2 Multiplication 92**

**2.6.3 Determinants 101**

**2.6.4 Matrix Inverse 104**

**2.6.5 Solution of a System of Equations 107**

**2.7 Summary of Functions Introduced in Chapter 2 112**

**Exercises 113**

**3 Data Input/Output 127**

**Edward B. Magrab**

**3.1 Strings and Annotated Output 127**

**3.1.1 Creating Strings 127**

**3.1.2 Converting Numerical Values to Strings and Displaying
Them 130**

**3.2 Entering Data with input 135**

**3.2.1 Entering a Scalar with input 135**

**3.2.2 Entering a String with input 136**

**3.2.3 Entering a Vector with input 137**

**3.2.4 Entering a Matrix with input 137**

**3.3 Input/Output Data Files 137**

**3.4 Cell Arrays 141**

**3.5 Input Microsoft Excel Files 143**

**3.6 Summary of Functions Introduced in Chapter 3 144**

**Exercises 145**

**4 Program Flow Control 148**

**Edward B. Magrab**

**4.1 Introduction-The Logical Operator 148**

**4.2 Control of Program Flow 151**

**4.2.1 Branching-If Statement 151**

**4.2.2 Branching-Switch Statement 154**

**4.2.3 For Loop 155**

**4.2.4 While Loop 162**

**4.2.5 Early Termination of Either a for or a while Loop
166**

**4.3 Summary of Functions Introduced in Chapter 4 166**

**Exercises 167**

**5 Function Creation and Selected MATLAB Functions 172**

**Edward B. Magrab**

**5.1 Introduction 173**

**5.1.1 Why Use Functions 173**

**5.1.2 Naming Functions 174**

**5.1.3 Length of Functions 174**

**5.1.4 Debugging Functions 174**

**5.2 User-Defined Functions 175**

**5.2.1 Introduction 175**

**5.2.2 Function File 175**

**5.2.3 Subfunctions 181**

**5.2.4 Anonymous Functions 183**

**5.2.5 inline 184**

**5.2.6 Comparison of the Usage of Subfunctions, Anonymous
Functions, and inline 185**

**5.3 User-Defined Functions, Function Handles, and feval
186**

**5.4 MATLAB Functions that Operate on Arrays of Data
187**

**5.4.1 Introduction 187**

**5.4.2 Fitting Data with Polynomials-polyfit/polyval
188**

**5.4.3 Fitting Data with spline 190**

**5.4.4 Interpolation of Data-interp1 192**

**5.4.5 Numerical Integration-trapz 193**

**5.4.6 Area of a Polygon-polyarea 195**

**5.4.7 Digital Signal Processing-fft and ifft 196**

**5.5 MATLAB Functions that Require User-Defined Functions
201**

**5.5.1 Zeros of Functions-fzero and roots/poly 202**

**5.5.2 Numerical Integration-quadl and dblquad 207**

**5.5.3 Numerical Solutions of Ordinary Differential
Equations-ode45 212**

**5.5.4 Numerical Solutions of Ordinary Differential
Equations-bvp4c 217**

**5.5.5 Numerical Solutions of Delay Differential
Equations-dde23 231**

**5.5.6 Numerical Solutions of One-Dimensional
Parabolic-Elliptic Partial Differential Equations-pdepe 233**

**5.5.7 Local Minimum of a Function-fminbnd 235**

**5.5.8 Numerical Solutions of Nonlinear Equations-fsolve
238**

**5.6 Symbolic Solutions and Converting Symbolic Expressions
into Functions 240**

**5.7 Summary of Functions Introduced in Chapter 5 246**

**Exercises 247**

**6 2D Graphics 265**

**Edward B. Magrab**

**6.1 Introduction: Graphics Management 266**

**6.2 Basic 2D Plotting Commands 269**

**6.2.1 Introduction 269**

**6.2.2 Changing a Graph's Overall Appearance 281**

**6.2.3 Special Purpose Graphs 281**

**6.2.4 Reading, Displaying, and Manipulating Digital Images
288**

**6.3 Graph Annotation and Enhancement 290**

**6.3.1 Introduction 290**

**6.3.2 Axes and Curve Labels, Figure Titles, Legends, and Text
Placement 290**

**6.3.3 Filling Regions 294**

**6.3.4 Greek Letters, Mathematical Symbols, Subscripts, and
Superscripts 297**

**6.3.5 Altering the Attributes of Axes, Curves,Text, and
Legends 300**

**6.3.6 Positioning One Figure Inside Another Figure
304**

**6.3.7 Interactive Plotting Tools 306**

**6.3.8 Animation 307**

**6.4 Examples 310**

**6.5 Summary of Functions Introduced in Chapter 6 319**

**Exercises 320**

**7 3D Graphics 338**

**Edward B. Magrab**

**7.1 Lines in 3D 338**

**7.2 Surfaces 341**

**7.3 Summary of Functions Introduced in Chapter 7 369**

**Exercises 370**

**8 Engineering Statistics 377**

**Edward B. Magrab**

**8.1 Descriptive Statistical Quantities 377**

**8.2 Probability Distributions 383**

**8.2.1 Discrete Distributions 383**

**8.2.2 Continuous Distributions 387**

**8.3 Confidence Intervals 397**

**8.4 Hypothesis Testing 401**

**8.5 Linear Regression 404**

**8.5.1 Simple Linear Regression 404**

**8.5.2 Multiple Linear Regression 408**

**8.6 Design of Experiments 415**

**8.6.1 Single-Factor Experiments: Analysis of Variance
415**

**8.6.2 Multiple-Factor Factorial Experiments 419**

**8.7 Summary of Functions Introduced in Chapter 8 435**

**Exercises 436**

**9 Dynamics and Vibrations 445**

**Balakumar Balachandran**

**9.1 Dynamics of Particles and Rigid Bodies 446**

**9.1.1 Planar Pendulum 446**

**9.1.2 Orbital Motions 447**

**9.1.3 Principal Moments of Inertia 450**

**9.1.4 Stability of a Rigid Body 451**

**9.2 Single-Degree-of-Freedom Vibratory Systems 454**

**9.2.1 Introduction 454**

**9.2.2 Linear Systems: Free Oscillations 456**

**9.2.3 Linear Systems: Forced Oscillations 462**

**9.2.4 Nonlinear Systems: Free Oscillations 469**

**9.2.5 Nonlinear Systems: Forced Oscillations 478**

**9.3 Systems with Multiple Degrees of Freedom 481**

**9.3.1 Two-Degree-of-Freedom Systems: Free and Forced
Oscillations 481**

**9.3.2 Natural Frequencies and Mode Shapes 495**

**9.4 Free and Forced Vibrations of Euler-Bernoulli and
Timoshenko Beams 499**

**9.4.1 Natural Frequencies and Mode Shapes of Euler-Bernoulli
and Timoshenko Beams 499**

**9.4.2 Forced Oscillations of Euler-Bernoulli Beams
509**

**9.5 Summary of Functions Introduced in Chapter 9 Exercises
513**

**Exercises 514**

**10 Control Systems 524**

**Gregory C. Walsh**

**10.1 Introduction to Control System Design 525**

**10.1.1 Tools for Controller Design 527**

**10.1.2 Naming and File Conventions 528**

**10.2 Representation of Systems in MATLAB 528**

**10.2.1 State-Space Models 530**

**10.2.2 Transfer-Function Representation 535**

**10.2.3 Discrete-Time Models 538**

**10.2.4 Block Diagrams and SIMULINK 542**

**10.2.5 Conversion Between Representations 546**

**10.3 Response of Systems 547**

**10.3.1 Estimating Response from Systems 548**

**10.3.2 Estimating Response from Poles and Zeros 551**

**10.3.3 Estimating Systems from Response 558**

**10.4 Design Tools 560**

**10.4.1 Design Criteria 561**

**10.4.2 Design Tools 564**

**10.5 Design Examples 573**

**10.5.1 Notch Control of a Flexible Pointer 574**

**10.5.2 PID Control of a Magnetic Suspension System
582**

**10.5.3 Lead Control of an Inverted Pendulum 589**

**10.5.4 Control of a Magnetically Suspended Flywheel
596**

**10.6 Summary of Functions Introduced in Chapter 10
605**

**Exercises 606**

**11 Fluid Mechanics 614**

**James H. Duncan**

**11.1 Hydrostatics 614**

**11.1.1 Pressure Distribution in the Standard Atmosphere
615**

**11.1.2 Force on a Planar Gate 616**

**11.2 Internal Viscous Flow 621**

**11.2.1 Laminar Flow in a Horizontal Pipe with Circular Cross
Section 621**

**11.2.2 Downward Turbulent Flow in a Vertical Pipe 622**

**11.2.3 Three Connected Reservoirs 624**

**11.3 External Flow 626**

**11.3.1 Boundary Layer on an Infinite Plate Started Suddenly
from Rest 626**

**11.3.2 Blasius Boundary Layer 628**

**11.3.3 Potential Flow 631**

**11.3.4 Joukowski Airfoils 636**

**11.4 Open Channel Flow 641**

**11.5 Biological Flows 646**

**Exercises 648**

**12 Heat Transfer 659**

**Keith E. Herold**

**12.1 Conduction Heat Transfer 660**

**12.1.1 Transient Heat Conduction in a Semi-Infinite Slab with
Surface Convection 660**

**12.1.2 Transient Heat Conduction in an Infinite Solid
Cylinder with Convection 662**

**12.1.3 Transient One-Dimensional Conduction with a Heat
Source 664**

**12.2 Convection Heat Transfer 668**

**12.2.1 Internal Flow Convection: Pipe Flow 668**

**12.2.2 Thermal Boundary Layer on a Flat Plate: Similarity
Solution 672**

**12.2.3 Natural Convection Similarity Solution 677**

**12.3 Radiation Heat Transfer 682**

**12.3.1 Radiation View Factor: Differential Area to Arbitrary
Rectangle in Parallel Planes 682**

**12.3.2 View Factor Between Two Rectangles in Parallel Planes
685**

**12.3.3 Enclosure Radiation with Diffuse Gray Walls
687**

**12.3.4 Transient Radiation Heating of a Plate in a Furnace
690**

**Exercises 692**

**13 Optimization 702**

**Shapour Azarm**

**13.1 Definition, Formulation, and Graphical Solution
703**

**13.1.1 Introduction 703**

**13.1.2 Graphical Solution 703**

**13.2 Linear Programming 706**

**13.3 Binary Integer Programming 709**

**13.4 Nonlinear Programming: Unconstrained and Curve Fitting
710**

**13.4.1 Unconstrained Optimization 710**

**13.4.2 Curve Fitting: One Independent Variable 713**

**13.4.3 Curve Fitting: Several Independent Variables
715**

**13.5 Nonlinear Programming: Constrained Single Objective
719**

**13.5.1 Constrained Single-Variable Method 719**

**13.5.2 Constrained Multivariable Method 721**

**13.5.3 Quadratic Programming 730**

**13.5.4 Semi-Infinitely Constrained Method 732**

**13.6 Multiobjective Optimization 736**

**13.7 Genetic Algorithm-Based Optimization 742**

**13.8 Summary of Functions Introduced in Chapter 13
751**

**Exercises 752**

**14 Biological Systems: Transport of Heat, Mass, and Electric
Charge 769**

**Keith E. Herold**

**14.1 Heat Transfer in Biological Systems 770**

**14.1.1 Heat Transfer in Perfused Tissue 770**

**14.1.2 Thermal Conductivity Determination 773**

**14.2 Mass Transfer in Biological Systems 775**

**14.2.1 Bicarbonate Buffer System 775**

**14.2.2 Carbon Dioxide Transport in Blood 778**

**14.2.3 Oxygen Transport in Blood 779**

**14.2.4 Perfusion Bioreactor 782**

**14.2.5 Supply of Oxygen to a Spherical Tumor 786**

**14.2.6 Krogh Cylinder Model of Tissue Oxygenation 789**

**14.3 Charge Transport in Biological Systems 796**

**14.3.1 Hodgkin-Huxley Neuron Model 796**

**14.3.2 Hodgkin-Huxley Gating Parameters 797**

**14.3.3 Hodgkin-Huxley Model with Step Function Input
802**

**14.3.4 Action Potential 804**

**Exercises 807**

**Index**

**Dr. Magrab** is Emeritus Professor of Mechanical
Engineering at the University of Maryland, College Park, Maryland.
His research interests include the integration of design and
manufacturing, vibrations and acoustics, and the theoretical and
experimental analysis of structural systems. Prior to joining the
University of Maryland he held supervisory positions in the Center
for Manufacturing Engineering, at the National Institute of
Standards and Technology (NIST), which included being the head of
the Robot Metrology Group and manager of the vertical machining
workstation in the Automated Manufacturing Research Facility. He
went to NIST after being a professor for almost a decade in the
Department of Mechanics at the Catholic University of America in
Washington DC. Dr. Magrab is a Life Fellow in the American Society
of Mechanical Engineers and a registered professional engineer in
Maryland. He has authored seven textbooks and published numerous
journal articles. He holds one patent.

"The best features of this text are certainly the examples. The
combination of the worked examples from the first seven chapters
with the detailed material from the applications chapters makes for
an applied MATLAB text that is truly unmatched in scope or detail.
Together with the easily navigated List of Examples, I challenge a
mechanical engineer working in any field to read the text without
finding an application that becomes part of their default toolbox,
let alone one that simply interests them." - Adam Ufford, Texas
Tech

"I think that this book provides one of the most comprehensive
guides to MATLAB for engineering students. One of the major
strengths of the book is the wealth of worked-out examples and
exercises at the end of every single chapter." - Luca Lucchese,
Oregon State University

"I think that the book is well written and is accessible to both
beginners and experienced users alike. The large number of
worked-out examples and the clarity of their presentation are
certainly among the best features of the book." - Luca Lucchese,
Oregon State University

"The exercises are very good and very relevant. They complement the
examples well, making the combination very nice, and a step above
other texts in this area." - David Chopp, Northwestern
University

"The authors do a great job in presenting the material in a
readable and understandable fashion. They have good examples and
good problems. They also do a great job of logically introducing
MATLAB functionality and sequentially building on previous
concepts. Very good material!" - William Arrasmith, Florida
Institute of Technology

"The authors do a great job of integrating nuances of Matlab into
their examples. It is also nice to have so many examples supported
with the basic theory. It is also good that the authors are
attempting a multi-disciplinary (Aeronautical, Mechanical,
Electrical, and Civil Engineering) approach." - William Arrasmith,
Florida Institute of Technology

"In this book, you can find numerous programs and examples in a
wide range of engineering such as Machine Design, Vibrations,
Control Systems, Dynamics, Fluid Mechanics, Heat Transfer,
Statistics and Optimization. Those examples are very useful and
easy to follow. Good examples in all kinds of engineering fields
are one of the reasons that I am in favor of the books among all
kinds of MATLAB textbooks." - Jenny Zhou, Lamar University

"I think this is a very good text book and reference for a
mechanical engineering student. It is well written, easy to
comprehend. The examples in the book are extremely useful to solve
a wide range of engineering problems." - Jenny Zhou, Lamar
University

"To program MATLAB well, one must understand vectorization and
user-defined functions. This book stands out in giving
well-written, understandable examples." - Brad Burchett,
Rose-Hulman Institute of Technology

"The quality of the worked examples is truly unique to this
textbook. The examples in Chapters 1-7 are stimulating in their
content, but simple enough so that the complexity of the
application does not intimidate or take away from the educational
content. This is often a hard balance to find, but this text
succeeds." - Adam Ufford, Texas Tech

"The quality of the problems surpasses that of any other text. The
problems reinforce and test all of the necessary content, but
provide a stimulating opportunity to "go beyond" the typical canned
responses and apply skills to "real-world" problems." - Adam
Ufford, Texas Tech

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