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E-raamat: Numerical Analysis for Engineers: Methods and Applications, Second Edition

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(University of Maryland, College Park, USA), (University of Maryland, College Park, USA)
  • Formaat: 451 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 18-Sep-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482250367
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Numerical Analysis for Engineers: Methods and Applications, Second EditionSuurem pilt
  • Formaat: 451 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 18-Sep-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482250367
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Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations, and potentials.

Each chapter contains many computational examples, as well as a section on applications that contain additional engineering examples. Each chapter also includes a set of exercise problems.

The problems are designed to meet the needs of instructors in assigning homework and to help students with practicing the fundamental concepts. Although the book was developed with emphasis on engineering and technological problems, the numerical methods can also be used to solve problems in other fields of science.
Preface xv
Acknowledgments xvii
Authors xix
Chapter 1 Introduction 1(12)
1.1 Numerical Analysis in Engineering
1(3)
1.1.1 Decision Making in Engineering
2(1)
1.1.2 Expected Educational Outcomes
3(1)
1.2 Analytical versus Numerical Analysis
4(1)
1.3 Taylor Series Expansion
5(3)
1.4 Applications
8(2)
1.4.1 Taylor Series Expansion of the Square Root
8(1)
1.4.2 Example Series
9(1)
Problems
10(3)
Chapter 2 Matrices 13(38)
2.1 Introduction
13(4)
2.1.1 Definition of a Matrix
13(1)
2.1.2 Formation of a Matrix
13(2)
2.1.3 Types of Matrices
15(2)
2.2 Matrix Operations
17(9)
2.2.1 Matrix Equality
17(1)
2.2.2 Matrix Addition and Subtraction
17(1)
2.2.3 Matrix Multiplication: An Introductory Example
18(2)
2.2.4 Matrix Multiplication: General Rules
20(1)
2.2.5 Matrix Multiplication by a Scalar
21(1)
2.2.6 Matrix Inversion
22(1)
2.2.7 Matrix Singularity
23(1)
2.2.8 Additional Topics in Matrix Algebra
24(2)
2.3 Vectors
26(3)
2.3.1 Definitions
26(1)
2.3.2 Vector Operations
27(1)
2.3.3 Orthogonal and Normalized Vectors
27(2)
2.4 Determinants
29(4)
2.5 Rank of a Matrix
33(2)
2.6 Applications
35(7)
2.6.1 Reactions of a Beam Due to Loads
35(4)
2.6.2 Correlation Analysis of Water-Quality Data
39(1)
2.6.3 Regression Analysis for Predicting Bus Ridership
40(2)
Problems
42(9)
Chapter 3 Introduction to Numerical Methods 51(24)
3.1 Introduction
51(3)
3.1.1 Characteristics of Numerical Methods
51(3)
3.2 Accuracy, Precision, and Bias
54(2)
3.3 Significant Figures
56(3)
3.4 Analysis of Numerical Errors
59(5)
3.4.1 Error Types
59(2)
3.4.2 Measurement and Truncation Errors
61(1)
3.4.3 Error Analysis in Numerical Solutions
62(2)
3.5 Advantages and Disadvantages of Numerical Methods
64(1)
3.6 Applications
65(6)
3.6.1 Pipe Design
65(3)
3.6.2 Bending Moment for a Beam
68(3)
Problems
71(4)
Chapter 4 Roots of Equations 75(38)
4.1 Introduction
75(1)
4.2 Eigenvalue Analysis
76(2)
4.3 Direct-Search Method
78(5)
4.4 Bisection Method
83(4)
4.4.1 Error Analysis and Convergence Criterion
84(3)
4.5 Newton—Raphson Iteration
87(5)
4.5.1 Nonconvergence
89(3)
4.6 Secant Method
92(2)
4.7 Polynomial Reduction
94(2)
4.8 Synthetic Division
96(4)
4.8.1 Programming Considerations
97(3)
4.9 Multiple Roots
100(1)
4.10 Systems of Nonlinear Equations
101(4)
4.11 Applications
105(2)
4.11.1 Pipe Flow Evaluation
105(1)
4.11.2 Gas Law
106(1)
Problems
107(6)
Chapter 5 Simultaneous Linear Equations 113(56)
5.1 Introduction
113(6)
5.1.1 General Form fora System of Equations
116(1)
5.1.2 Solution of Two Equations
116(1)
5.1.3 Classification of Systems of Equations Based on Graphical Interpretation
117(2)
5.2 Gaussian Elimination
119(10)
5.2.1 Permissible Operations
119(1)
5.2.2 Matrix Representation of the System of Equations
120(1)
5.2.3 Gaussian Elimination Procedure
121(8)
5.3 Gauss—Jordan Elimination
129(2)
5.4 Additional Considerations for Elimination Procedures
131(2)
5.4.1 Accumulated Roundoff Errors
131(1)
5.4.2 Zero Pivot Element
132(1)
5.4.3 Considerations in Programming
132(1)
5.5 LU Decomposition
133(7)
5.5.1 General Case
133(5)
5.5.2 Banded Matrices
138(1)
5.5.3 Symmetric Matrices
138(2)
5.6 Iterative Equation-Solving Methods
140(10)
5.6.1 Jacobi Iteration
141(2)
5.6.2 Gauss—Seidel Iteration
143(2)
5.6.3 Convergence Considerations of the Iterative Methods
145(4)
5.6.4 Considerations in Programming
149(1)
5.7 Use of Determinants
150(4)
5.7.1 Considerations in Programming
154(1)
5.8 Matrix Inversion
154(3)
5.9 Applications
157(4)
5.9.1 Flexibility and Stiffness Analyses of a Beam
157(2)
5.9.2 Concrete Mix Design
159(2)
Problems
161(8)
Chapter 6 Numerical Interpolation 169(40)
6.1 Introduction
169(1)
6.2 Method of Undetermined Coefficients
169(4)
6.3 Gregory—Newton Interpolation Method
173(3)
6.4 Finite-Difference Interpolation
176(5)
6.4.1 Finite-Difference Table
179(2)
6.5 Newton's Method
181(4)
6.6 Lagrange Polynomials
185(2)
6.7 Interpolation Using Splines
187(6)
6.7.1 Linear Splines
188(1)
6.7.2 Quadratic Splines
189(3)
6.7.3 Cubic Splines and Other Higher Order Splines
192(1)
6.8 Guidelines for Choice of Interpolation Method
193(1)
6.9 Multidimensional Interpolation
194(3)
6.9.1 Linear Interpolation in Two Dimensions
195(2)
6.10 Applications
197(3)
6.10.1 Probability of Wind Loading
197(1)
6.10.2 Shear Stress of Oil between Two Parallel Plates
198(2)
Problems
200(9)
Chapter 7 Differentiation and Integration 209(36)
7.1 Numerical Differentiation
209(10)
7.1.1 Finite-Difference Differentiation
209(4)
7.1.2 Differentiation Using a Finite-Difference Table
213(2)
7.1.3 Differentiating an Interpolating Polynomial
215(1)
7.1.4 Differentiation Using Taylor Series Expansion
216(3)
7.2 Numerical Integration
219(13)
7.2.1 Interpolation Formula Approach
220(2)
7.2.2 Trapezoidal Rule
222(5)
7.2.3 Simpson's Rule
227(2)
7.2.4 Romberg Integration
229(3)
7.3 Applications
232(5)
7.3.1 Estimating Areas
232(1)
7.3.2 Pipe Flow Rate
233(2)
7.3.3 Volume of Gabion Retaining Wall
235(1)
7.3.4 Sediment Loads in Rivers
235(1)
7.3.5 Probability Computations Using the Standard Normal Probability Distribution
236(1)
Problems
237(8)
Chapter 8 Differential Equations 245(54)
8.1 Introduction
245(2)
8.1.1 Definitions
245(1)
8.1.2 Origin of Differential Equations
246(1)
8.2 Taylor Series Expansion
247(3)
8.2.1 Fundamental Case
247(3)
8.2.2 General Case
250(1)
8.3 Euler's Method
250(3)
8.3.1 Errors with Euler's Method
251(2)
8.4 Modified Euler's Method
253(2)
8.5 Runge—Kutta Methods
255(5)
8.5.1 Second-Order Runge—Kutta Methods
255(2)
8.5.2 Third-Order Runge—Kutta Methods
257(1)
8.5.3 Fourth-Order Runge—Kutta Methods
257(3)
8.6 Predictor—Corrector Methods
260(5)
8.6.1 Euler—Trapezoidal Method
260(3)
8.6.2 Milne—Simpson Method
263(2)
8.7 Least-Squares Method
265(4)
8.8 Galerkin Method
269(1)
8.9 Higher Order Differential Equations
270(4)
8.10 Boundary-Value Problems
274(2)
8.10.1 Shooting Method
275(1)
8.10.2 Finite-Difference Methods
275(1)
8.11 Integral Equations
276(1)
8.12 Applications
276(18)
8.12.1 Motion of a Falling Body
276(1)
8.12.2 Electrical Circuit
277(2)
8.12.3 One-Dimensional Heat Flow
279(2)
8.12.4 Estimating Biochemical Oxygen Demand
281(2)
8.12.5 Accumulation of Eroded Soil in a Sediment Trap
283(1)
8.12.6 Growth Rate of Bacteria
284(1)
8.12.7 Bending Moment and Shear Force for a Beam
285(2)
8.12.8 Dynamic Response of a Structure
287(2)
8.12.9 Deflection of a Beam
289(5)
Problems
294(5)
Chapter 9 Data Description and Treatment 299(32)
9.1 Introduction
299(1)
9.2 Classification of Data
299(2)
9.2.1 Nominal Scale
300(1)
9.2.2 Ordinal Scale
300(1)
9.2.3 Interval Scale
300(1)
9.2.4 Ratio Scale
301(1)
9.2.5 Dimensionality of Data
301(1)
9.3 Graphical Description of Data
301(9)
9.3.1 Area Charts
302(1)
9.3.2 Pie Charts
303(1)
9.3.3 Bar Charts
303(2)
9.3.4 Column Charts
305(1)
9.3.5 Scatter Diagrams
305(1)
9.3.6 Line Graphs
306(2)
9.3.7 Combination Charts
308(2)
9.3.8 Three-Dimensional Charts
310(1)
9.4 Histograms and Frequency Diagrams
310(4)
9.5 Descriptive Measures
314(6)
9.5.1 Central Tendency Measures
315(1)
9.5.2 Dispersion Measures
316(2)
9.5.3 Percentiles
318(1)
9.5.4 Box-and-Whisker Plots
319(1)
9.6 Applications
320(4)
9.6.1 Two Random Samples
320(3)
9.6.2 Stage and Discharge of a River
323(1)
Problems
324(7)
Chapter 10 Curve Fitting and Regression Analysis 331(64)
10.1 Introduction
331(1)
10.2 Correlation Analysis
331(7)
10.2.1 Graphical Analysis
332(2)
10.2.2 Bivariate Correlation
334(1)
10.2.3 Separation of Variation
335(1)
10.2.4 Correlation: Fraction of Explained Variation
336(1)
10.2.5 Computational Form for Correlation Coefficient
337(1)
10.3 Introduction to Regression
338(4)
10.3.1 Elements of Statistical Optimization
339(1)
10.3.2 Zero-Intercept Model
339(2)
10.3.3 Regression Definitions
341(1)
10.4 Principle of Least Squares
342(2)
10.4.1 Definitions
342(1)
10.4.2 Solution Procedure
342(2)
10.5 Reliability of the Regression Equation
344(6)
10.5.1 Correlation Coefficient
345(1)
10.5.2 Standard Error of Estimate
345(2)
10.5.3 Standardized Partial Regression Coefficients
347(1)
10.5.4 Assumptions Underlying the Regression Model
348(2)
10.6 Correlation versus Regression
350(1)
10.7 Applications of Bivariate Regression Analysis
351(7)
10.7.1 Estimating Trip Rate
351(1)
10.7.2 Breakwater Cost
351(2)
10.7.3 Stress—Strain Analysis
353(1)
10.7.4 Project Cost versus Time
354(2)
10.7.5 Effect of Extreme Event
356(1)
10.7.6 Variable Transformation
357(1)
10.8 Multiple Regression Analysis
358(12)
10.8.1 Correlation Matrix
359(2)
10.8.2 Calibration of the Multiple Linear Model
361(2)
10.8.3 Standardized Model
363(1)
10.8.4 Intercorrelation
364(1)
10.8.5 Criteria for Evaluating a Multiple Regression Model
365(2)
10.8.6 Analysis of Residuals
367(1)
10.8.7 Computational Example
367(3)
10.9 Regression Analysis of Nonlinear Models
370(5)
10.9.1 Common Nonlinear Alternatives
370(1)
10.9.2 Calibration of Polynomial Models
371(1)
10.9.3 Fitting a Power Model
372(1)
10.9.4 Goodness of Fit
373(1)
10.9.5 Additional Model Forms
374(1)
10.10 Applications
375(11)
10.10.1 One-Predictor Polynomial of Sediment Yield versus Slope
375(1)
10.10.2 One-Predictor Polynomial of Evaporation versus Temperature
375(1)
10.10.3 Single-Predictor Power Model
376(2)
10.10.4 Multivariate Power Model
378(2)
10.10.5 Estimating Breakwater Costs
380(1)
10.10.6 Trip Generation Model
381(1)
10.10.7 Estimation of the Reaeration Coefficient
382(2)
10.10.8 Estimating Slope Stability
384(2)
Problems
386(9)
Chapter 11 Numerical Optimization 395(28)
11.1 Introduction
395(1)
11.2 The Response Surface Analysis
396(1)
11.3 Numerical Least Squares
397(2)
11.4 Steepest Descent Method
399(4)
11.4.1 The Distance D
400(1)
11.4.2 The Tolerance for Convergence
400(1)
11.4.3 Advantages and Disadvantages
401(2)
11.5 Illustrating Applications
403(11)
11.6 Applications
414(5)
11.6.1 Composite Regression of Snowmelt Runoff Data
414(3)
11.6.2 A Multicomponent Time Series Model
417(2)
11.7 Concluding Remarks
419(1)
Problems
420(3)
Index 423
Bilal Ayyub, PhD, is a professor of civil and environmental engineering at the University of Maryland, College Park, and the director of the Center for Technology and Systems Management at the A. James Clark School of Engineering. Dr. Ayyub is a fellow of the American Society of Civil Engineers, the American Society of Mechanical Engineers, the Society of Naval Architects and Marine Engineers, and the Society for Risk Analysis, and is also a senior member of the Institute of Electrical and Electronics Engineers (IEEE). He has completed many research and development projects for many governmental and private entities. Dr. Ayyub has received numerous awards and is the author or coauthor of more than 600 publications in journals, conference proceedings, and reports including 8 textbooks and 14 edited books.

Richard H. McCuen, PhD, is the Ben Dyer Professor of civil and environmental engineering at the University of Maryland, College Park. Dr. McCuen earned degrees from Carnegie Mellon University and the Georgia Institute of Technology. Topics in statistical hydrology and stormwater management are his primary research interests. He received numerous awards and is the author of 26 books and over 250 professional papers.
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