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NUMERICAL ANALYSIS WITH APPLICATIONS IN MECHANICS AND ENGINEERING
A much-needed guide on how to use numerical methods to solve practical engineering problems
Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results.
Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes:
How to deal with errors in numerical analysis
Approaches for solving problems in linear and nonlinear systems
Methods of interpolation and approximation of functions
Formulas and calculations for numerical differentiation and integration
Integration of ordinary and partial differential equations
Optimization methods and solutions for programming problems
Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.
Autorentext
PETRE TEODORESCU, PHD, is a Professor in the Faculty of Mathematics and Computer Science at the University of Bucharest in Romania and the author of 250 papers and twenty-eight books.
NICOLAE-DORU STNESCU, PHD, is a Professor in the Faculty of Mechanics and Technology at the University of Piteti in Romania and the author of 200 papers and ten books. NICOLAE PANDREA, PHD, is a Professor in the Faculty of Mechanics and Technology at the University of Piteti in Romania and the author of 250 papers and six books.
Zusammenfassung
NUMERICAL ANALYSIS WITH APPLICATIONS IN MECHANICS AND ENGINEERING A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes:
Inhalt
Preface xi 1 Errors in Numerical Analysis 1
1.1 Enter Data Errors, 1
1.2 Approximation Errors, 2
1.3 Round-Off Errors, 3
1.4 Propagation of Errors, 3
1.4.1 Addition, 3
1.4.2 Multiplication, 5
1.4.3 Inversion of a Number, 7
1.4.4 Division of Two Numbers, 7
1.4.5 Raising to a Negative Entire Power, 7
1.4.6 Taking the Root of pth Order, 7
1.4.7 Subtraction, 8
1.4.8 Computation of Functions, 8
1.5 Applications, 8
Further Reading, 14
2 Solution of Equations 17
2.1 The Bipartition (Bisection) Method, 17
2.2 The Chord (Secant) Method, 20
2.3 The Tangent Method (Newton), 26
2.4 The Contraction Method, 37
2.5 The NewtonKantorovich Method, 42
2.6 Numerical Examples, 46
2.7 Applications, 49
Further Reading, 52
3 Solution of Algebraic Equations 55
3.1 Determination of Limits of the Roots of Polynomials, 55
3.2 Separation of Roots, 60
3.3 Lagrange's Method, 69
3.4 The LobachevskiGraeffe Method, 72
3.4.1 The Case of Distinct Real Roots, 72
3.4.2 The Case of a Pair of Complex Conjugate Roots, 74
3.4.3 The Case of Two Pairs of Complex Conjugate Roots, 75
3.5 The Bernoulli Method, 76
3.6 The BiergeVi`ete Method, 79
3.7 Lin Methods, 79
3.8 Numerical Examples, 82
3.9 Applications, 94
Further Reading, 109
4 Linear Algebra 111
4.1 Calculation of Determinants, 111
4.1.1 Use of Definition, 111
4.1.2 Use of Equivalent Matrices, 112
4.2 Calculation of the Rank, 113
4.3 Norm of a Matrix, 114
4.4 Inversion of Matrices, 123
4.4.1 Direct Inversion, 123
4.4.2 The GaussJordan Method, 124
4.4.3 The Determination of the Inverse Matrix by its Partition, 125
4.4.4 Schur's Method of Inversion of Matrices, 127
4.4.5 The Iterative Method (Schulz), 128
4.4.6 Inversion by Means of the Characteristic Polynomial, 131
4.4.7 The FrameFadeev Method, 131
4.5 Solution of Linear Algebraic Systems of Equations, 132
4.5.1 Cramer's Rule, 132
4.5.2 Gauss's Method, 133
4.5.3 The GaussJordan Method, 134
4.5.4 The LU Factorization, 135
4.5.5 The Schur Method of Solving Systems of Linear Equations, 137
4.5.6 The Iteration Method (Jacobi), 142
4.5.7 The GaussSeidel Method, 147
4.5.8 The Relaxation Method, 149
4.5.9 The Monte Carlo Method, 150
4.5.10 Infinite Systems of Linear Equations, 152
4.6 Determination of Eigenvalues and Eigenvectors, 153
4.6.1 Introduction, 153
4.6.2 Krylov's Method, 155
4.6.3 Danilevski's Method, 157
4.6.4 The Direct Power Method, 160
4.6.5 The Inverse Power Method, 165
4.6.6 The Displacement Method, 166
4.6.7 Leverrier's Method, 166
4.6.8 The LR (LeftRight) Method, 166
4.6.9 The Rotation Method, 168
4.7 QR Decomposition, 169
4.8 The Singular Value Decomposition (SVD), 172
4.9 Use of the Least Squares Method in Solving the Linear Overdetermined Systems, 174
4.10 The Pseudo-Inverse of a Matrix, 177
4.11 Solving of the Underdetermined Linear Systems, 178
4.12 Numerical Examples, 178
4.13 Applications, 211
Further Reading, 269
5 Solution of Systems of Nonlinear Equations 273
5.1 The Iteration Method (Jacobi), 273
5.2 Newton's Method, 275
5.3 The Modified Newton's Method, 276
5.4 The NewtonRaphson Method, 277
5.5 The Gradient Method, 277
5.6 The Method of Entire Series, 280
5.7 Numerical Example, 281
5.8 Applications, 287 Further Reading, 304</p&g...