9780073101569

Numerical Methods for Engineers

by ;
  • ISBN13:

    9780073101569

  • ISBN10:

    0073101567

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2005-06-14
  • Publisher: McGraw-Hill Science/Engineering/Math
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Summary

The fifth edition of "Numerical Methods for Engineers" continues its tradition of excellence. Instructors love this text because it is a comprehensive text that is easy to teach from. Students love it because it is written for them--with great pedagogy and clear explanations and examples throughout. The text features a broad array of applications, including all engineering disciplines. The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. Users will find use of software packages, specifically MATLAB and Excel with VBA. This includes material on developing MATLAB m-files and VBA macros. Approximately 80% of the problems are new or revised for this edition. The expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical engineering.

Table of Contents

Preface xiii
Guided Tour xvi
About the Authors xviii
PART ONE MODELING, COMPUTERS, AND ERROR ANALYSIS
3(102)
Motivation
3(2)
Mathematical Background
5(3)
Orientation
8(3)
Mathematical Modeling and Engineering Problem Solving
11(14)
A Simple Mathematical Model
11(7)
Conservation Laws and Engineering
18(7)
Problems
21(4)
Programming and Software
25(25)
Packages and Programming
25(1)
Structured Programming
26(9)
Modular Programming
35(2)
Excel
37(4)
Matlab
41(4)
Other Languages and Libraries
45(5)
Problems
46(4)
Approximations and Round-Off Errors
50(23)
Significant Figures
51(2)
Accuracy and Precision
53(1)
Error Definitions
54(3)
Round-Off Errors
57(16)
Problems
72(1)
Truncation Errors and the Taylor Series
73(32)
The Taylor Series
73(16)
Error Propagation
89(4)
Total Numerical Error
93(2)
Blunders, Formulation Errors, and Data Uncertainty
95(4)
Problems
97(2)
Epilogue: Part One
99(1)
Trade-Offs
99(3)
Important Relationships and Formulas
102(1)
Advanced Methods and Additional References
102(3)
PART TWO ROOTS OF EQUATIONS
105(112)
Motivation
105(2)
Mathematical Background
107(1)
Orientation
108(4)
Bracketing Methods
112(21)
Graphical Methods
112(4)
The Bisection Method
116(8)
The False-Position Method
124(6)
Incremental Searches and Determining Initial Guesses
130(3)
Problems
131(2)
Open Methods
133(27)
Simple Fixed-Point Iteration
134(5)
The Newton-Raphson Method
139(6)
The Secant Method
145(5)
Multiple Roots
150(3)
Systems of Nonlinear Equations
153(7)
Problems
157(3)
Roots of Polynomials
160(27)
Polynomials in Engineering and Science
160(3)
Computing with Polynomials
163(3)
Conventional Methods
166(1)
Muller's Method
167(4)
Bairstow's Method
171(5)
Other Methods
176(1)
Root Location with Libraries and Packages
176(11)
Problems
185(2)
Case Studies: Roots of Equations
187(30)
Ideal and Nonideal Gas Laws (Chemical/Bio Engineering)
187(3)
Open-Channel Flow (Civil/Environmental Engineering)
190(4)
Design of an Electric Circuit (Electrical Engineering)
194(2)
Vibration Analysis (Mechanical/Aerospace Engineering)
196(16)
Problems
203(9)
Epilogue: Part Two
212(1)
Trade-Offs
212(1)
Important Relationships and Formulas
213(1)
Advanced Methods and Additional References
213(4)
PART THREE LINEAR ALGEBRAIC EQUATIONS
217(114)
Motivation
217(2)
Mathematical Background
219(8)
Orientation
227(4)
Gauss Elimination
231(33)
Solving Small Numbers of Equations
231(7)
Naive Gauss Elimination
238(6)
Pitfalls of Elimination Methods
244(6)
Techniques for Improving Solutions
250(7)
Complex Systems
257(1)
Nonlinear Systems of Equations
257(2)
Gauss-Jordan
259(2)
Summary
261(3)
Problems
261(3)
LU Decomposition and Matrix Inversion
264(1)
LU Decomposition
264(9)
The Matrix Inverse
273(4)
Error Analysis and System Condition
277
Problems
283
Special Matrices and Gauss-Seidel
265(40)
Special Matrices
285(4)
Gauss-Seidel
289(7)
Linear Algebraic Equations with Libraries and Packages
296(9)
Problems
303(2)
Case Studies: Linear Algebraic Equations
305(26)
Steady-State Analysis of a System of Reactors (Chemical/Bio Engineering)
305(3)
Analysis of a Statically Determinate Truss (Civil/Environmental Engineering)
308(4)
Currents and Voltages in Resistor Circuits (Electrical Engineering)
312(2)
Spring-Mass Systems (Mechanical/Aerospace Engineering)
314(13)
Problems
317(10)
Epilogue: Part Three
327(1)
Trade-Offs
327(1)
Important Relationships and Formulas
328(1)
Advanced Methods and Additional References
328(3)
PART FOUR OPTIMIZATION
331(94)
Motivation
331(5)
Mathematical Background
336(1)
Orientation
337(4)
One-Dimensional Unconstrained Optimization
341(14)
Golden-Section Search
342(7)
Quadratic Interpolation
349(2)
Newton's Method
351(4)
Problems
353(2)
Multidimensional Unconstrained Optimization
355(20)
Direct Methods
356(4)
Gradient Methods
360(15)
Problems
373(2)
Constrained Optimization
375(25)
Linear Programming
375(11)
Nonlinear Constrained Optimization
386(1)
Optimization with Packages
387(13)
Problems
398(2)
Case Studies: Optimization
400(25)
Least-Cost Design of a Tank (Chemical/Bio Engineering)
400(5)
Least-Cost Treatment of Wastewater (Civil/Environmental Engineering)
405(4)
Maximum Power Transfer for a Circuit (Electrical Engineering)
409(4)
Mountain Bike Design (Mechanical/Aerospace Engineering)
413(9)
Problems
415(7)
Epilogue: Part Four
422(1)
Trade-Offs
422(1)
Additional References
423(2)
PART FIVE CURVE FITTING
425(144)
Motivation
425(2)
Mathematical Background
427(9)
Orientation
436(4)
Least-Squares Regression
440(34)
Linear Regression
440(16)
Polynomial Regression
456(4)
Multiple Linear Regression
460(3)
General Linear Least Squares
463(5)
Nonlinear Regression
468(6)
Problems
471(3)
Interpolation
474(33)
Newton's Divided-Difference Interpolating Polynomials
475(11)
Lagrange Interpolating Polynomials
486(5)
Coefficients of an Interpolating Polynomial
491(1)
Inverse Interpolation
491(1)
Additional Comments
492(3)
Spline Interpolation
495(12)
Problems
505(2)
Fourier Approximation
507(37)
Curve Fitting with Sinusoidal Functions
508(6)
Continuous Fourier Series
514(3)
Frequency and Time Domains
517(4)
Fourier Integral and Transform
521(2)
Discrete Fourier Transform (DFT)
523(2)
Fast Fourier Transform (FFT)
525(7)
The Power Spectrum
532(1)
Curve Fitting with Libraries and Packages
533(11)
Problems
542(2)
Case Studies: Curve Fitting
544(25)
Linear Regression and Population Models (Chemical/Bio Engineering)
544(4)
Use of Splines to Estimate Heat Transfer (Civil/Environmental Engineering)
548(2)
Fourier Analysis (Electrical Engineering)
550(1)
Analysis of Experimental Data (Mechanical/Aerospace Engineering)
551(12)
Problems
553(10)
Epilogue: Part Five
563(1)
Trade-Offs
563(1)
Important Relationships and Formulas
564(2)
Advanced Methods and Additional References
566(3)
PART SIX NUMERICAL DIFFERENTIATION AND INTEGRATION
569(102)
Motivation
569(9)
Mathematical Background
578(3)
Orientation
581(3)
Newton-Cotes Integration Formulas
584(29)
The Trapezoidal Rule
586(10)
Simpson's Rules
596(9)
Integration with Unequal Segments
605(3)
Open Integration Formulas
608(1)
Multiple Integrals
608(5)
Problems
610(3)
Integration of Equations
613(19)
Newton-Cotes Algorithms for Equations
613(2)
Romberg Integration
615(5)
Gauss Quadrature
620(7)
Improper Integrals
627(5)
Problems
631(1)
Numerical Differentiation
632(14)
High-Accuracy Differentiation Formulas
632(3)
Richardson Extrapolation
635(2)
Derivatives of Unequally Spaced Data
637(1)
Derivatives and Integrals for Data with Errors
638(1)
Numerical Integration/Differentiation with Libraries and Packages
639(7)
Problems
643(3)
Case Studies: Numerical Integration and Differentiation
646(25)
Integration to Determine the Total Quantity of Heat (Chemical/Bio Engineering)
646(2)
Effective Force on the Mast of a Racing Sailboat (Civil/Environmental Engineering)
648(2)
Root-Mean-Square Current by Numerical Integration (Electrical Engineering)
650(3)
Numerical Integration to Compute Work (Mechanical/Aerospace Engineering)
653(14)
Problems
657(10)
Epilogue: Part Six
667(1)
Trade-Offs
667(1)
Important Relationships and Formulas
668(1)
Advanced Methods and Additional References
668(3)
PART SEVEN ORDINARY DIFFERENTIAL EQUATIONS
671(142)
Motivation
671(4)
Mathematical Background
675(2)
Orientation
677(4)
Runge-Kutta Methods
681(45)
Euler's Method
682(11)
Improvements of Euler's Method
693(8)
Runge-Kutta Methods
701(10)
Systems of Equations
711(5)
Adaptive Runge-Kutta Methods
716(10)
Problems
724(2)
Stiffness and Multistep Methods
726(26)
Stiffness
726(4)
Multistep Methods
730(22)
Problems
750(2)
Boundary-Value and Eigenvalue Problems
752(29)
General Methods for Boundary-Value Problems
753(6)
Eigenvalue Problems
759(12)
ODEs and Eigenvalues with Libraries and Packages
771(10)
Problems
779(2)
Case Studies: Ordinary Differential Equations
781(32)
Using ODEs to Analyze the Transient Response of a Reactor (Chemical/Bio Engineering)
781(7)
Predator-Prey Models and Chaos (Civil/Environmental Engineering)
788(4)
Simulating Transient Current for an Electric Circuit (Electrical Engineering)
792(5)
The Swinging Pendulum (Mechanical/Aerospace Engineering)
797(11)
Problems
801(7)
Epilogue: Part Seven
808(1)
Trade-Offs
808(1)
Important Relationships and Formulas
809(1)
Advanced Methods and Additional References
809(4)
PART EIGHT PARTIAL DIFFERENTIAL EQUATIONS
813(88)
Motivation
813(3)
Orientation
816(4)
Finite Difference: Elliptic Equations
820(20)
The Laplace Equation
820(2)
Solution Techniques
822(6)
Boundary Conditions
828(6)
The Control-Volume Approach
834(3)
Software to Solve Elliptic Equations
837(3)
Problems
838(2)
Finite Difference: Parabolic Equations
840(17)
The Heat Conduction Equation
840(1)
Explicit Methods
841(4)
A Simple Implicit Method
845(4)
The Crank-Nicolson Method
849(3)
Parabolic Equations in Two Spatial Dimensions
852(5)
Problems
855(2)
Finite-Element Method
857(27)
The General Approach
858(4)
Finite-Element Application in One Dimension
862(9)
Two-Dimensional Problems
871(4)
Solving PDEs with Libraries and Packages
875(9)
Problems
881(3)
Case Studies: Partial Differential Equations
884(17)
One-Dimensional Mass Balance of a Reactor (Chemical/Bio Engineering)
884(4)
Deflections of a Plate (Civil/Environmental Engineering)
888(2)
Two-Dimensional Electrostatic Field Problems (Electrical Engineering)
890(3)
Finite-Element Solution of a Series of Springs (Mechanical/Aerospace Engineering)
893(6)
Problems
897(2)
Epilogue: Part Eight
899(1)
Trade-Offs
899(1)
Important Relationships and Formulas
899(1)
Advanced Methods and Additional References
900(1)
Appendix A: The Fourier Series 901(2)
Appendix B: Getting Started with Matlab 903(8)
Bibliography 911(4)
Index 915

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