Applied Numerical Methods for Engineers Using MATLAB and C

by Schilling, Robert J.; Harris, Sandra L

• ISBN13: 9780534370145
• ISBN10: 0534370144
• Edition: CD
• Format: Hardcover
• Copyright: 1999-09-16
• Publisher: CL Engineering
• More Book Details
• Purchase Benefits

Summary

This book provides a comprehensive discussion of numerical computing techniques with an emphasis on practical applications in the fields of civil, chemical, electrical, and mechanical engineering. It features two software libraries that implement the algorithms developed in the text - a MATLAB? toolbox, and an ANSI C library. This book is intended for undergraduate students. Each chapter includes detailed case study examples from the four engineering fields with complete solutions provided in MATLAB? and C, detailed objectives, numerous worked-out examples and illustrations, and summaries comparing the numerical techniques. Chapter problems are divided into separate analysis and computation sections. Documentation for the software is provided in text appendixes that also include a helpful review of vectors and matrices. The Instructor's Manual includes a disk with software documentation and complete solutions to both problems and examples in the book.

Table of Contents

Numerical Computation	1	(36)
Motivation and Objectives	1	(2)
A Simple Calculation	1	(1)
Chapter Objectives	2	(1)
Mathematical Background	3	(1)
Number Representation	3	(5)
Binary, Decimal, and Hexadecimal	3	(3)
Integers	6	(1)
Floats	7	(1)
Machine Precision	8	(2)
Round-Off Error	10	(4)
Chopping and Rounding	10	(1)
Error Propagation	11	(3)
Truncation Error	14	(1)
Random Number Generation	15	(7)
Uniform Distribution	15	(4)
Gaussian Distribution	19	(3)
Numerical Software	22	(4)
A Numerical Library: NLIB	23	(1)
NLIB Example Browser	24	(1)
Pseudo-Prototypes	25	(1)
Applications	26	(6)
Throwing Darts to Estimate π: Matlab	26	(3)
Monte Carlo Integration: C	29	(3)
Summary	32	(5)
Problems	34	(1)
Analysis	34	(1)
Computation	35	(2)
Linear Algebraic Systems	37	(59)
Motivation and Objectives	37	(4)
Robotic Arm	38	(1)
Converter Circuit	38	(1)
DC Motor	39	(1)
Chapter Objectives	40	(1)
Gauss-Jordan Elimination	41	(9)
Gaussian Elimination	50	(4)
LU Decomposition	54	(10)
LU Factorization	55	(4)
Forward and Back Substitution	59	(3)
Tridiagonal Systems	62	(2)
Ill-Conditioned Systems	64	(6)
Vector and Matrix Norms	64	(2)
Condition Number	66	(2)
Approximate Condition Number	68	(1)
Iterative Improvement	69	(1)
Iterative Methods	70	(9)
Jacobi's Method	71	(2)
Gauss-Seidel Method	73	(1)
Relaxation Methods	74	(3)
Convergence	77	(2)
Applications	79	(10)
Chemical Absorption Process: MATLAB	79	(3)
Planar Truss: C	82	(2)
DC Bridge Circuit: MATLAB	84	(2)
Mass-Spring-Damper System: C	86	(3)
Summary	89	(7)
Problems	91	(1)
Analysis	91	(2)
Computation	93	(3)
Eigenvalues and Eigenvectors	96	(49)
Motivation and Objectives	97	(5)
Seismograph	97	(2)
Convergence of Iterative Methods	99	(2)
Chapter Objectives	101	(1)
The Characteristic Polynomial	102	(3)
Power Methods	105	(6)
Direct Power Method	105	(4)
Inverse Power Method	109	(2)
Jacobi's Method	111	(2)
Householder Transformation	113	(3)
QR Method	116	(4)
Deflation	118	(1)
Shifting	119	(1)
Danilevsky's Method	120	(4)
Polynomial Roots	124	(2)
Applications	126	(14)
Transient Analysis of an Absorption Process: C	126	(4)
Population Growth Model: MATLAB	130	(3)
Telescope Position Control: C	133	(3)
Rotating Masses and Torsional Springs: MATLAB	136	(4)
Summary	140	(5)
Problems	141	(1)
Analysis	142	(1)
Computation	143	(2)
Curve Fitting	145	(48)
Motivation and Objectives	146	(3)
Gravitational Acceleration	146	(1)
Circadian Rhythms	147	(1)
Chapter Objectives	148	(1)
Interpolating	149	(7)
Piecewise-Linear Interpolation	150	(1)
Polynomial Interpolation	151	(2)
Lagrange Interpolation Polynomials	153	(2)
Polynomials	155	(1)
Newton's Difference Formula	156	(2)
Cubic Splines	158	(7)
Least Squares	165	(9)
Straight Line Fit	166	(2)
Polynomial Fit	168	(1)
Orthogonal Polynomials	168	(6)
Two-Dimensional Interpolation	174	(3)
Applications	177	(11)
Pressure-Temperature Curves: MATLAB	177	(3)
Water Resource Management: C	180	(2)
Voltage Regulator Circuit: MATLAB	182	(3)
Nonlinear Friction Model: C	185	(3)
Summary	188	(5)
Problems	189	(1)
Analysis	190	(1)
Computation	191	(2)
Root Finding	193	(57)
Motivation and Objectives	194	(5)
Tunnel Diode Circuit	194	(2)
Leaky Tank	196	(1)
Bacterial Chemostat	197	(1)
Chapter Objectives	198	(1)
Bracketing Methods	199	(6)
Bisection Method	199	(3)
False Position Method	202	(3)
Contraction Mapping Method	205	(5)
Root Finding	207	(2)
Aitken Extrapolation	209	(1)
Secant Method	210	(2)
Muller's Method	212	(4)
Newton's Method	216	(3)
Polynomial Roots	219	(9)
Quadratic Formula	219	(2)
Synthetic Division	221	(3)
Laguerre's Method	224	(4)
Nonlinear Systems of Equations	228	(4)
Applications	232	(12)
Propane Cylinder: C	232	(4)
Bacterial Chemostat: MATLAB	236	(2)
Industrial High-Temperature Oven: C	238	(3)
Suspension Cable: MATLAB	241	(3)
Summary	244	(6)
Problems	246	(1)
Analysis	246	(1)
Computation	247	(3)
Optimization	250	(57)
Motivation and Objectives	251	(4)
Nonlinear Regression	251	(1)
Electrical Load Design	252	(1)
Container Design	253	(1)
Chapter Objectives	254	(1)
Local and Global Minima	255	(2)
Line Searches	257	(8)
Golden Section	257	(5)
Derivative Bisection	262	(1)
Inverse Parabolic Interpolation	263	(2)
Steepest Descent Method	265	(3)
Congugate-Gradient Method	268	(2)
Quasi-Newton Methods	270	(4)
Penalty Functions	274	(4)
Simulated Annealing	278	(8)
Annealing Schedules	280	(1)
Constrained Optimization	281	(5)
Applications	286	(14)
Heat Exchanger: MATLAB	286	(5)
Transportation Planning: C	291	(4)
Maximum Power Extraction: MATLAB	295	(3)
Container Design: C	298	(2)
Summary	300	(7)
Problems	302	(1)
Analysis	302	(2)
Computation	304	(3)
Differentiation and Integration	307	(54)
Motivation and Objectives	308	(4)
Magnetic Levitation	308	(1)
Mechanical Work	309	(1)
Water Management	310	(1)
Chapter Objectives	311	(1)
Numerical Differentiation	312	(7)
First Derivative	312	(3)
Second Derivative	315	(2)
Richardson Extrapolation	317	(2)
Noise-Corrupted Data	319	(2)
Newton-Cotes Integration Formulas	321	(7)
Trapezoid Rule	323	(1)
Simpson's Rules	324	(1)
Midpoint Rule	325	(3)
Romberg Integration	328	(3)
Gauss Quadrature	331	(6)
Legendre Polynomials	332	(2)
Chebyshev Polynomials	334	(1)
Laguerre Polynomials	335	(1)
Hermite Polynomials	336	(1)
Improper Integrals	337	(3)
Multiple Integrals	340	(5)
Parameterization Method	340	(2)
Monte Carlo Integration	342	(3)
Applications	345	(9)
Change in Enthalpy: C	345	(2)
Dam Design: MATLAB	347	(3)
RC Network: C	350	(3)
Link of Robotic Arm: MATLAB	353	(1)
Summary	354	(7)
Problems	357	(1)
Analysis	357	(1)
Computation	358	(3)
Ordinary Differential Equations	361	(61)
Motivation and Objectives	362	(4)
Satellite Attitude Control	363	(1)
Pendulum	364	(1)
Predator-Prey Ecological System	364	(1)
Chapter Objectives	365	(1)
Euler's Method	366	(2)
Runge-Kutta Methods	368	(4)
Step Size Control	372	(6)
Interval Halving	373	(1)
Runge-Kutta-Fehlberg Method	374	(1)
Step Size Adjustment	375	(3)
MultiStep Methods	378	(4)
Adams-Bashforth Predictor	378	(1)
Adams-Moulton Corrector	379	(3)
Bulirsch-Stoer Extrapolation Methods	382	(5)
Modified Midpoint Method	382	(1)
Richardson Extrapolation	383	(4)
Stiff Differential Equations	387	(8)
Implicit Methods	389	(2)
Semi-Implicit Extrapolation Method	391	(3)
Differential-Algebraic Systems	394	(1)
Boundary Value Problems	395	(6)
Shooting Method	396	(2)
Finite Difference Method	398	(3)
Applications	401	(12)
Chemical Reactor: MATLAB	401	(3)
Cantilever Beam: C	404	(2)
Phase-Locked Loop: MATLAB	406	(4)
Turbulent Flow and Chaos: C	410	(3)
Summary	413	(9)
Problems	415	(1)
Analysis	415	(1)
Computation	416	(6)
Partial Differential Equations	422	(53)
Motivation and Objectives	423	(5)
Laplace's Equation	423	(1)
Heat Equation	424	(1)
Wave Equation	425	(1)
Equation Classification	426	(1)
Chapter Objectives	427	(1)
Elliptic Equations	428	(9)
Central Difference Method	428	(3)
Boundary Conditions	431	(1)
Iterative Solution Methods	432	(5)
One-Dimensional Parabolic Equations	437	(7)
Explicit Forward Euler Method	437	(3)
Implicit Backward Euler Method	440	(2)
Crank-Nicolson Method	442	(2)
Two-Dimensional Parabolic Equations	444	(4)
One-Dimensional Hyperbolic Equations	448	(7)
d'Alembert's Solution	449	(3)
Explicit Central Difference Method	452	(3)
Two-Dimensional Hyperbolic Equations	455	(4)
Applications	459	(9)
Heated Rod: C	460	(2)
Plate Deflection: MATLAB	462	(2)
Electrostatic Field: C	464	(2)
Twisted Bar: MATLAB	466	(2)
Summary	468	(7)
Problems	469	(1)
Analysis	469	(3)
Computation	472	(3)
Digital Signal Processing	475	(58)
Motivation and Objectives	476	(2)
Harmonic Distortion	476	(1)
Radar	477	(1)
Chapter Objectives	477	(1)
Fourier Transform	478	(2)
Fast Fourier Transform (FFT)	480	(7)
Correlation	487	(3)
Convolution	490	(5)
Pulse Response	491	(2)
Stability	493	(2)
Digital Filters	495	(7)
Frequency Response	495	(2)
FIR Filter Design	497	(5)
Two-Dimensional FFT	502	(4)
System Identification	506	(8)
Least-Squares Method	507	(4)
Adaptive LMS Method	511	(3)
Applications	514	(10)
Heat Exchanger Frequency Response: MATLAB	514	(2)
Flagpole Motion: C	516	(3)
Band Pass Filter: MATLAB	519	(3)
Helicopter Noise: C	522	(2)
Summary	524	(9)
Problems	526	(1)
Analysis	526	(1)
Computation	527	(3)
References and Further Reading	530	(3)
APPENDIX 1 NLIB Using MATLAB	533	(51)
A Numerical Toolbox: NLIB	534	(2)
Toolbox Installation	534	(1)
NLIB Example Browser	535	(1)
Main-Program Support	536	(8)
Tabular Display	536	(2)
Graphical Display	538	(4)
Utility Functions	542	(2)
Linear Algebraic Systems	544	(4)
Eigenvalues and Eigenvectors	548	(4)
Curve Fitting	552	(3)
Root Finding	555	(3)
Optimization	558	(5)
Differentiation and Integration	563	(4)
Ordinary Differential Equations	567	(4)
Partial Differential Equations	571	(7)
Digital Signal Processing	578	(6)
APPENDIX 2 NLIB Using C	584	(77)
A Numerical Library: NLIB	585	(3)
NLIB Installation	585	(1)
Library Usage	585	(2)
NLIB Example Browser	587	(1)
NLIB Data Types	588	(3)
Scalars	588	(1)
Vectors	588	(1)
Matrices	589	(1)
Precision	590	(1)
NLIB Core	591	(14)
Vector and Matrix Allocation	591	(3)
Vector and Matrix Input/Output	594	(4)
Matrix Algebra	598	(2)
Complex Arithmetic	600	(2)
Random Number Generation	602	(2)
Utility Functions	604	(1)
Tabular Display	605	(3)
Screen	605	(1)
Keyboard	606	(1)
Printer	607	(1)
Graphical Display	608	(6)
Curves	609	(3)
Surfaces	612	(2)
Linear Algebraic Systems	614	(5)
Eigenvalues and Eigenvectors	619	(4)
Curve Fitting	623	(3)
Root Finding	626	(5)
Optimization	631	(6)
Differentiation and Integration	637	(4)
Ordinary Differential Equations	641	(5)
Partial Differential Equations	646	(7)
Digital Signal Processing	653	(8)
APPENDIX 3 Vectors and Matrices	661	(8)
Vector and Matrix Notation	661	(2)
Basic Operations	663	(2)
Matrix Inverse	665	(1)
Eigenvalues and Eigenvectors	666	(2)
Vector Norms	668	(1)
APPENDIX 4 Answers to Selected Problems	669	(34)
Index	703