Modern Numerical Methods in Engineering
Autor: Adalbert Kovacs | Radu-Emil Precup | Bela Palancz | Levente Kovacs
Editura: Politehnica Timisoara
Seria: Matematici moderne
Format: 17x24 cm
Nr. pagini: 484
Coperta: brosata
ISBN: 978-606-554-503-8
Anul aparitiei: 2012
DESPRE CARTE:
The book is addressed especially for Bsc and Msc students of technical universities, but it is also useful for all those specialists who are working or researching physical/technical/mathematical models of different processes.
Referent stiintific - Conf.dr. Romeo Negrea
CONTENTS:
PREFACE 5
FIRST PART
1. AN INTRODUCTION TO MATHEMATICA 14
1.1. Initial notions 14
1.2. Structured objects 22
1.3. Processing objects in Mathematica 28
1.4. Graphics in Mathematica 42
1.5. Programming elements under Mathematica 55
1.6. References 59
2. AN INTRODUCTION TO MATLAB 60
2.1. Initial notions 60
2.2. Commands with general effect 61
2.3. Commands used to control the variables 62
2.4. Predefined constants and variables in MATLAB 66
2.5. File-types in MATLAB 67
2.6. Programming elements in MATLAB 68
2.7. Loops (for, while) and conditional instructions 70
2.8. Graphics in MATLAB 74
2.9. Symbolic and numeric computations in MATLAB 79
2.10. References 86
3. AN INTRODUCTION TO MATHCAD 87
3.1. Mathcad basics 87
3.2. Mathematical expressions 89
3.3. Mathcad document editing 96
3.4. Range, index and array variables 97
3.5. Matrices and vectors 100
3.6. Mathcad 2D and 3D plots 105
3.7. Symbolic computations in Mathcad 107
3.8. Elements of Mathcad programming 110
3.9. References 112
4. NUMERICAL METHODS FOR SOLVING SYSTEMS OF LINEAR EQUATIONS 113
4.1. Direct methods 115
4.2. Iterative methods 125
4.3. Applications 131
4.4. References 139
5. NUMERICAL METHODS FOR SOLVING NONLINEAR EQUATIONS AND SYSTEMS OF NONLINEAR EQUATIONS 140
5.1. Methods for nonlinear equations 141
5.2. Methods for systems of nonlinear equations 151
5.3. Applications 161
5.4. References 172
6. POLYNOMIAL INTERPOLATION. FUNCTION APPROXIMATION 173
6.1. Lagrange and Hermite interpolations 173
6.2. Least squares approximation 179
6.3. Interpolation with spline cubic functions 181
6.4. Applications 189
6.5. References 206
7. NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATION 207
7.1. General aspects. Method of succesive approximations 207
7.2. The direct numerical method (unistep) 211
7.3. The indirect numerical method (multistep) 228
7.4. Applications 238
7.5. References 253
SECOND PART
8. GLOBAL METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS 256
8.1. Homotopy continuation analysis 257
8.2. Gauss-Jacobi combinatorial method 270
8.3. Parallel computation 276
8.4. References 281
9. FUNDAMENTAL PRINCIPLES OF THE FINITE ELEMENT METHOD (FEM) 283
9.1. Introduction to FEM 283
9.2. Topological properties in the FEM 286
9.3. Local and global systems of coordinates. Interpolation functions 291
9.4. Energetical and numerical methods in FEM. Galerkin`s Method 298
9.5. Mathematical simulation in engineering by FEM 307
9.6. References 399
10. AN INTRODUCTION TO BOUNDARY ELEMENT METHOD (BEM) 400
10.1. General aspects. Direct and indirect formulations of the boundary element method 400
10.2. One-Dimensional Problems Solved by BEM 405
10.3. Two-dimensional problems solved by BEM 439
10.4. Some Developments in Applicability of CVBEM (Complex Variable Boundary Elements Method) 464
10.5. References 482