Numerical Methods for Engineers and Scientists, Second Edition,

Front Cover
CRC Press, May 31, 2001 - Mathematics - 840 pages
4 Reviews
Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."
 

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Contents

Introduction
1
02 Organization of the Book
2
04 Programs
3
06 Significant Digits Precision Accuracy Errors and Number Representation
4
07 Software Packages and Libraries
6
08 The Taylor Series and the Taylor Polynomial
7
Basic Tools of Numerical Analysis
11
I2 Eigenproblems
13
78 Extrapolation Methods
378
79 Multipoint Methods
381
710 Summary of Methods and Results
391
711 Nonlinear Implicit Finite Difference Equations
393
712 HigherOrder Ordinary Differential Equations
397
713 Systems of FirstOrder Ordinary Differential Equations
398
714 Stiff Ordinary Differential Equations
401
715 Programs
408

I3 Roots of Nonlinear Equations
14
I5 Numerical Differentiation and Difference Formulas
15
I6 Numerical Integration
16
Systems of Linear Algebraic Equations
17
11 Introduction
18
12 Properties of Matrices and Determinants
21
13 Direct Elimination Methods
30
14 LU Factorization
45
15 Tridiagonal Systems of Equations
49
16 Pitfalls of Elimination Methods
52
17 Iterative Methods
59
18 Programs
67
19 Summary
76
Exercise Problems
77
Eigenproblems
81
22 Mathematical Characteristics of Eigenproblems
85
23 The Power Method
89
24 The Direct Method
101
25 The QR Method
104
26 Eigenvectors
110
27 Other Methods
111
28 Programs
112
29 Summary
118
Exercise Problems
119
Nonlinear Equations
127
32 General Features of Root Finding
130
33 Closed Domain Bracketing Methods
135
34 Open Domain Methods
140
35 Polynomials
155
36 Pitfalls of Root Finding Methods and Other Methods of Root Finding
167
37 Systems of Nonlinear Equations
169
38 Programs
173
39 Summary
179
Exercise Problems
181
Polynomial Approximation and Interpolation
187
41 Introduction
188
42 Properties of Polynomials
190
43 Direct Fit Polynomials
197
44 Lagrange Polynomials
198
45 Divided Difference Tables and Divided Difference Polynomials
204
46 Difference Tables and Difference Polynomials
208
47 Inverse Interpolation
217
48 Multivariate Approximation
218
49 Cubic Splines
221
410 Least Squares Approximation
225
411 Programs
235
412 Summary
242
Exercise Problems
243
Numerical Differentiation and Difference Formulas
251
52 Unequally Spaced Data
254
53 Equally Spaced Data
257
54 Taylor Series Approach
264
55 Difference Formulas
270
57 Programs
273
58 Summary
279
Numerical Integration
285
62 Direct Fit Polynomials
288
63 NewtonCotes Formulas
290
64 Extrapolation and Romberg Integration
297
65 Adaptive Integration
299
66 Gaussian Quadrature
302
67 Multiple Integrals
306
68 Programs
311
69 Summary
315
Exercise Problems
316
Ordinary Differential Equations
323
II3 Classification of Ordinary Differential Equations
325
II4 Classification of Physical Problems
326
II5 InitialValue Ordinary Differential Equations
327
II6 BoundaryValue Ordinary Differential Equations
330
II7 Summary
332
OneDimensional InitialValue Ordinary Differential Equations
335
71 Introduction
336
72 General Features of InitialValue ODEs
340
73 The Taylor Series Method
343
74 The Finite Difference Method
346
75 The FirstOrder Euler Methods
352
76 Consistency Order Stability and Convergence
359
77 SinglePoint Methods
364
716 Summary
414
Exercise Problems
416
OneDimensional BoundaryValue Ordinary Differential Equations
435
81 Introduction
436
82 General Features of BoundaryValue ODEs
439
83 The Shooting InitalValue Method
441
84 The Equilibrium BoundaryValue Method
450
85 Derivative and Other Boundary Conditions
458
86 HigherOrder Equilibrium Methods
466
87 The Equilibrium Method for Nonlinear BoundaryValue Problems
471
88 The Equilibrium Method on Nonuniform Grids
477
89 Eigenproblems
480
810 Programs
483
811 Summary
488
Exercise Problems
490
Partial Differential Equations
501
III2 General Features of Partial Differential Equations
502
III3 Classification of Partial Differential Equations
504
III4 Classification of Physical Problems
511
III5 Elliptic Partial Differential Equations
516
III6 Parabolic Partial Differential Equations
519
III7 Hyperbolic Partial Differential Equations
520
III8 The ConvectionDiffusion Equation
523
III9 Initial Values and Boundary Conditions
524
III10 WellPosed Problems
525
III11 Summary
526
Elliptic Partial Differential Equations
527
92 General Features of Elliptic PDEs
531
93 The Finite Difference Method
532
94 Finite Difference Solution of the Laplace Equation
536
95 Consistency Order and Convergence
543
96 Iterative Methods of Solution
546
97 Derivative Boundary Conditions
550
98 Finite Difference Solution of the Poisson Equation
552
99 HigherOrder Methods
557
910 Nonrectangular Domains
562
911 Nonlinear Equations and ThreeDimensional Problems
570
912 The Control Volume Method
571
913 Programs
575
914 Summary
580
Exercise Problems
582
Parabolic Partial Differential Equations
587
102 General Features of Parabolic PDEs
591
103 The Finite Difference Method
593
104 The ForwardTime CenteredSpace FTCS Method
599
105 Consistency Order Stability and Convergence
605
106 The Richardson and DuFortFrankel Methods
611
107 Implicit Methods
613
108 Derivative Boundary Conditions
623
109 Nonlinear Equations and Multidimensional Problems
625
1010 The ConvectionDiffusion Equation
629
1011 Asymptotic Stead State Solution to Propagation Problems
637
1012 Programs
639
1013 Summary
645
Exercise Problems
646
Hyperbolic Partial Differential Equations
651
112 General Features of Hyperbolic PDEs
655
113 The Finite Difference Method
657
114 The ForwardTime CenteredSpace FTCS Method and the Lax Method
659
115 LaxWendroff Type Methods
665
116 Upwind Methods
673
117 The BackwardTime CenteredSpace BTCS Method
677
118 Nonlinear Equations and Multidimensional Problems
682
119 The Wave Equation
683
1110 Programs
691
1111 Summary
701
Exercise Problems
702
The Finite Element Method
711
122 The RayleighRitz Collocation and Galerkin Methods
713
123 The Finite Element Method for Boundary Value Problems
724
124 The Finite Element Method for the Leplace Poisson Equation
739
125 The Finite Element Method for the Diffusion Equation
752
126 Programs
759
127 Summary
769
Exercise Problems
770
References
775
Answers to Selected Problems
779
Index
795
Copyright

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About the author (2001)

Joe D. Hoffman is Professor of Mechanical Engineering and Director of the Maurice J. Zucrow Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana.

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