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Applied Numerical Methods for Engineers Using MATLAB and C

ISBN: 9780534370145 | 0534370144
Edition: 1st
Format: Hardcover
Publisher: Cengage Learning
Pub. Date: 9/16/1999

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SummaryTable of Contents
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 MATLABŪ 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 MATLABŪ and C, detailed objectives, numerous worked-... MORE
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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 MATLAB533(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 C584(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 Matrices661(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 Problems669(34)
Index703


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