Numerical Methods for Engineers

by Chapra, Steven C.; Canale, Raymond P.

• ISBN13: 9780073101569
• ISBN10: 0073101567
• Edition: 5th
• Format: Hardcover
• Copyright: 2005-06-14
• Publisher: McGraw-Hill Science/Engineering/Math

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