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Computer Methods for Engineering with MATLAB® Applications 2nd edition [Kõva köide]

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(Rutgers University, New Brunswick, New Jersey, USA)
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Computer Methods for Engineering with MATLAB® Applications 2nd editionSuurem pilt
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Püsilink: https://www.kriso.ee/db/9781591690368.html
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Substantially revised and updated, Computer Methods for Engineering with MATLAB® Applications, Second Edition presents equations to describe engineering processes and systems. It includes computer methods for solving these equations and discusses the nature and validity of the numerical results for a variety of engineering problems. This edition now uses MATLAB in its discussions of computer solution.

New to the Second Edition











Recent advances in computational software and hardware A large number of MATLAB commands and programs for solving exercises and to encourage students to develop their own computer programs for specific problems Additional exercises and examples in all chapters New and updated references

The text follows a systematic approach for obtaining physically realistic, valid, and accurate results through numerical modeling. It employs examples from many engineering areas to explain the elements involved in the numerical solution and make the presentation relevant and interesting. It also incorporates a wealth of solved exercises to supplement the discussion and illustrate the ideas and methods presented. The book shows how a computational approach can provide physical insight and obtain inputs for the analysis and design of practical engineering systems.
Preface to the Second Edition xiii
Preface to the First Edition xvii
Author xxi
Chapter 1 Introduction 1(20)
1.1 Introductory Remarks
1(3)
1.2 Numerical Solution
4(2)
1.3 Importance of Analytical Results
6(3)
1.4 Physical Considerations
9(4)
1.5 Application of Computer Methods to Engineering Problems
13(2)
1.6 Outline and Scope of the Book
15(6)
1.6.1 Basic Features
15(1)
1.6.2 Computer Programs
16(1)
1.6.3 Examples and Problems
16(1)
1.6.4 A Preview
17(4)
Chapter 2 Basic Considerations in Computer Methods 21(38)
2.1 Introduction
21(2)
2.2 Computational Procedure
23(15)
2.2.1 Method Selection
23(2)
2.2.2 Programming Language
25(5)
2.2.3 Computer System
30(1)
2.2.4 Program Development
31(4)
2.2.4.1 Algorithm
31(3)
2.2.4.2 Available Programs
34(1)
2.2.4.3 Validation
35(1)
2.2.5 Serial versus Parallel Computing
35(3)
2.3 Numerical Errors and Accuracy
38(10)
2.3.1 Round-Off Error
40(2)
2.3.2 Truncation Error
42(3)
2.3.3 Accuracy of Numerical Results
45(1)
2.3.4 Numerical Stability
46(2)
2.4 Iterative Convergence
48(3)
2.4.1 Conditions for Convergence
49(1)
2.4.2 Rate of Convergence
50(1)
2.4.3 Termination of Iteration
50(1)
2.5 Numerical Parameters
51(3)
2.5.1 Step Size
52(1)
2.5.2 Convergence Criterion
52(1)
2.5.3 Other Arbitrarily Chosen Variables
53(1)
2.6 Summary
54(2)
Problems
56(3)
Chapter 3 A Review of MATLAB® Programming 59(26)
3.1 Introduction
59(1)
3.2 MATLAB® Environment
59(11)
3.2.1 Basic Commands
59(2)
3.2.2 Matrices
61(1)
3.2.3 Arrays and Vectorization
62(1)
3.2.4 Matrix Algebra
63(2)
3.2.5 Polynomials
65(1)
3.2.6 Root Solving
66(1)
3.2.7 Linear Algebraic Equations
67(1)
3.2.8 Curve Fitting
67(1)
3.2.9 Flow Control
68(2)
3.3 Ordinary Differential Equations
70(2)
3.4 Input/Output
72(4)
3.5 Script in-Files
76(2)
3.6 Function m-Files
78(3)
3.7 Plotting
81(1)
3.8 Summary
82(1)
Problems
83(2)
Chapter 4 Taylor Series and Numerical Differentiation 85(36)
4.1 Introduction
85(1)
4.2 Taylor Series
86(9)
4.2.1 Basic Features
86(1)
4.2.2 Finite Difference Calculus
87(8)
4.3 Direct Approximation of Derivatives
95(3)
4.4 Taylor-Series Approach and Accuracy
98(11)
4.4.1 Finite Difference Approximation of the First Derivative
98(1)
4.4.2 Second Derivative
99(2)
4.4.3 Higher-Order Derivatives
101(2)
4.4.4 Higher-Accuracy Approximations
103(6)
4.5 Polynomial Representation
109(3)
4.6 Partial Derivatives
112(5)
4.7 Summary
117(1)
Problems
118(3)
Chapter 5 Roots of Equations 121(50)
5.1 Introduction
121(2)
5.2 Search Method for Real Roots
123(7)
5.3 Bisection Method
130(3)
5.4 Regula Falsi and Secant Methods
133(5)
5.4.1 Regula Falsi Method
133(1)
5.4.2 Secant Method
134(4)
5.5 Newton–Raphson Method and Modified Newton's Method
138(9)
5.5.1 Newton–Raphson Method
138(3)
5.5.2 Modified Newton's Method
141(1)
5.5.3 Convergence
142(5)
5.6 Successive Substitution Method
147(3)
5.7 Other Methods
150(12)
5.7.1 Muller's Method
151(2)
5.7.2 Iterative Factorization of Polynomials
153(5)
5.7.3 Graeffe's Method
158(2)
5.7.4 Additional Methods
160(2)
5.8 Summary
162(1)
Problems
162(9)
Chapter 6 Numerical Solution of Simultaneous Algebraic Equations 171(76)
6.1 Introduction
171(3)
6.2 Gaussian Elimination
174(15)
6.2.1 Basic Approach
174(1)
6.2.2 Computational Procedure
175(3)
6.2.3 Solution Accuracy
178(2)
6.2.3.1 III-Conditioned Set
179(1)
6.2.3.2 Error Correction
179(1)
6.2.3.3 Pivoting
180(1)
6.2.4 Matrix Inversion and Determinant Evaluation
180(1)
6.2.5 Tri-diagonal Systems
181(8)
6.3 Gauss–Jordan Elimination
189(5)
6.3.1 Mathematical Procedure
189(1)
6.3.2 Computational Scheme
190(4)
6.4 Compact Methods
194(7)
6.4.1 Matrix Decomposition
194(2)
6.4.2 Matrix Decomposition in MATLAIP
196(1)
6.4.3 Crout's Method
197(4)
6.5 Numerical Solution of Linear Systems by Matrix Inversion
201(5)
6.5.1 Computational Procedure
202(2)
6.5.2 Additional Considerations
204(2)
6.6 Iterative Methods
206(8)
6.6.1 Basic Approach
206(1)
6.6.2 Jacobi and Gauss–Seidel Methods
207(1)
6.6.3 Convergence
208(1)
6.6.4 An Example
209(1)
6.6.5 Relaxation Methods
210(4)
6.7 Homogeneous Linear Equations
214(11)
6.7.1 The Eigenvalue Problem
215(5)
6.7.2 The Power Method
220(4)
6.7.2.1 Largest Eigenvalue
220(1)
6.7.2.2 Smallest Eigenvalue
221(1)
6.7.2.3 Intermediate Eigenvalues
222(2)
6.7.3 Other Methods
224(1)
6.8 Solution of Simultaneous Nonlinear Equations
225(9)
6.8.1 Newton–Raphson Method
226(1)
6.8.2 Modified Jacobi and Gauss–Seidel Methods
227(1)
6.8.3 Convergence
228(6)
6.9 Summary
234(1)
Problems
235(12)
Chapter 7 Numerical Curve Fitting and Interpolation 247(60)
7.1 Introduction
247(4)
7.1.1 Exact and Best Fit
247(2)
7.1.2 Interpolation and Extrapolation
249(1)
7.1.3 Basic Approach
249(2)
7.1.4 Use of MATLAB® Commands
251(1)
7.2 Exact Fit and Interpolation
251(7)
7.2.1 Exact Fit with an nth-Order Polynomial
252(3)
7.2.2 Uniformly Spaced Independent Variable
255(3)
7.3 Lagrange Interpolation
258(4)
7.4 Newton's Divided-Difference Interpolating Polynomial
262(10)
7.4.1 Genera] Formulas
263(3)
7.4.2 Uniformly Spaced Data
266(2)
7.4.3 Extrapolation
268(4)
7.5 Numerical Interpolation with Splines
272(6)
7.6 Method of Least Squares for a Best Fit
278(15)
7.6.1 Basic Considerations
278(3)
7.6.2 Linear Regression
281(2)
7.6.3 Best Fit with a Polynomial
283(2)
7.6.4 Nonpolynomial Forms
285(8)
7.6.4.1 Linearization
286(7)
7.7 Function of Two or More Independent Variables
293(6)
7.7.1 Exact Fit
294(2)
7.7.2 Best Fit
296(3)
7.8 Summary
299(1)
Problems
300(7)
Chapter 8 Numerical Integration 307(58)
8.1 Introduction
307(3)
8.1.1 Engineering Examples
309(1)
8.2 Rectangular and Trapezoidal Rules for Integration
310(12)
8.2.1 The Rectangular Rule
311(1)
8.2.2 The Trapezoidal Rule
312(1)
8.2.3 Truncation Error
313(9)
8.2.3.1 Rectangular Rule
115(200)
8.2.3.2 Trapezoidal Rule
315(1)
8.2.3.3 Total Error
316(2)
8.2.3.4 Accuracy
318(4)
8.3 Simpson's Rules for Numerical Integration
322(10)
8.3.1 Simpson's One-Third Rule
322(2)
8.3.2 Simpson's Three-Eighths Rule
324(2)
8.3.3 Truncation Errors
326(4)
8.3.4 Use of MATLAB° Integration Commands
330(2)
8.4 Higher-Accuracy Methods
332(8)
8.4.1 Richardson Extrapolation
332(2)
8.4.2 Romberg Integration
334(2)
8.4.3 Higher-Order Newton–Cotes Formulas
336(4)
8.5 Integration with Segments of Unequal Width
340(9)
8.5.1 Unequally Spaced Data
340(1)
8.5.2 Adaptive Quadrature
341(2)
8.5.3 Gauss Quadrature
343(6)
8.6 Numerical Integration of Improper Integrals..
349(7)
8.6.1 Integrals with Infinite Limits
350(1)
8.6.2 Singular Integrand
351(5)
8.6.3 Multiple Integrals
356(1)
8.7 Summary
356(1)
Problems
357(8)
Chapter 9 Numerical Solution of Ordinary Differential Equations 365(80)
9.1 Introduction
365(5)
9.1.1 Initial and Boundary Value Problems
366(1)
9.1.2 Reduction of Higher-Order Equations to First-Order Equations
366(3)
9.1.3 Solution Methods
369(1)
9.2 Euler's Method
370(10)
9.2.1 Computational Formula and Physical Interpretation of the Method
370(2)
9.2.2 Solution of a System of Equations
372(2)
9.2.3 Errors, Convergence, and Stability
374(6)
9.3 Improvements in Euler's Method
380(4)
9.3.1 Heun's Method
380(3)
9.3.2 Modified Euler's Method
383(1)
9.4 Runge–Kutta Methods
384(13)
9.4.1 Computational Formulas
386(3)
9.4.2 Truncation Error and Accuracy
389(2)
9.4.3 System of Equations
391(6)
9.5 Multistep Methods
397(4)
9.5.1 Adams Multistep Methods
397(4)
9.5.2 Additional Considerations
401(1)
9.6 Predictor–Corrector Methods
401(15)
9.6.1 Basic Features
402(1)
9.6.2 Adams Method
403(1)
9.6.3 Milne's Method
404(1)
9.6.4 Hamming's Method
405(1)
9.6.5 Accuracy and Stability of Predictor–Corrector Methods
406(4)
9.6.5.1 Truncation Errors
406(2)
9.6.5.2 Step Size
408(1)
9.6.5.3 Stability
409(1)
9.6.6 Simultaneous Equations
410(1)
9.6.7 Concluding Remarks on Predictor–Corrector Methods
410(6)
9.7 Boundary-Value Problems
416(14)
9.7.1 Shooting Methods
417(3)
9.7.1.1 Linear Equations
419(1)
9.7.2 Finite Difference Methods
420(3)
9.7.3 Eigenvalue Problems
423(7)
9.8 Summary
430(2)
Problems
432(13)
Chapter 10 Numerical Solution of Partial Differential Equations 445(64)
10.1 Introduction
445(4)
10.1.1 Classification
445(1)
10.1.2 Examples
446(2)
10.1.3 Basic Considerations
448(1)
10.2 Parabolic PDEs
449(18)
10.2.1 Numerical Solution with an Explicit Scheme
450(3)
10.2.2 Stability of Euler's (FTCS) Method
453(1)
10.2.3 Implicit Methods
454(2)
10.2.4 Other Methods and Considerations
456(2)
10.2.5 Multidimensional Problems
458(9)
10.3 Elliptic PDEs
467(22)
10.3.1 Finite Difference Approach
467(5)
10.3.2 Numerical Solution by Iterative and Direct Methods
472(4)
10.3.2.1 Point Relaxation
474(2)
10.3.2.2 Direct Methods
476(1)
10.3.3 Other Methods
476(1)
10.3.4 Other Geometries and Boundary Conditions
477(3)
10.3.5 Finite Element and Other Solution Methods
480(9)
10.4 Hyperbolic PDEs
489(11)
10.4.1 Basic Aspects
489(1)
10.4.2 Method of Characteristics
489(1)
10.4.3 Finite Difference Methods
490(10)
10.5 Summary
500(2)
Problems
502(7)
Appendix A: Some Common Commands in MATLAB® 509(4)
Appendix B: Computer Programs in MATLAB® 513(40)
Appendix C: Computer Programs in FORTRAN 553(38)
References 591(4)
Index 595
Yogesh Jaluria is a Board of Governors Professor in the Mechanical and Aerospace Engineering Department at Rutgers University. He has contributed to more than 450 technical articles and received numerous honors, including the Kern Award from AIChE, the Max Jakob Memorial Award from ASME and AIChE, and the Robert Henry Thurston Lecture Award, Freeman Scholar Award, Worcester Reed Warner Medal, and Heat Transfer Memorial Award, all from ASME.