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أخواني في الله أحضرت لكم كتاب Introduction to MATLAB with Numerical Preliminaries Alexander Stanoyevitch
![كتاب Introduction to MATLAB with Numerical Preliminaries M_s_a_21](https://i.servimg.com/u/f61/15/36/74/14/m_s_a_21.jpg) و المحتوى كما يلي :
Contents Preface Chapter 1: Chapter 2: Chapter 3 : Chapter 4: Chapter 5: M A T L A B Basics 1 What Is MATLAB? Starting and Ending a MATLAB Session A First MATLAB Tutorial Vectors and an Introduction to MATLAB Graphics A Tutorial Introduction to Recursion on MATLAB Basic Concepts of Numerical Analysis 23 with Taylor's T h e o r e m What Is Numerical Analysis? Taylor Polynomials Taylor's Theorem Introduction to M-Files 45 What Are M-files? Creating an M-file for a Mathematical Function P r o g r a m m i n g in M A T L A B 57 Some Basic Logic Logical Control Flow in MATLAB Writing Good Programs Floating Point Arithmetic and Error Analysis 85 Floating Point Numbers Floating Point Arithmetic: The Basics Floating Point Arithmetic: Further Examples and Details C h a p t e r 6: Rootfinding 107 6.1: A Brief Account of the History of Rootfinding 6.2: The Bisection Method 6.3: Newton's Method *6.4: The Secant Method *6.5: Error Analysis and Comparison of Rootfinding Methods C h a p t e r 7: M a t r i c e s a n d L i n e a r S y s t e m s 143 7.1: Matrix Operations and Manipulations with MATLAB *7.2: Introduction to Computer Graphics and Animation 7.3: Notations and Concepts of Linear Systems 7.4: Solving General Linear Systems with MATLAB 7.5: Gaussian Elimination, Pivoting, and LU Factorization *7.6: Vector and Matrix Norms, Error Analysis, and Eigendata 7.7: Iterative Methods A p p e n d i x A : M A T L A B ' s S y m b o l i c T o o l b o x 2 8 5 A p p e n d i x B: Solutions to All Exercises for the R e a d e r 2 9 3 R e f e r e n c e s 3 2 3 M A T L A B C o m m a n d I n d e x 3 2 7 I n d e x 3 2 9 General Index Abel, Niels Henrik, 108,109 Actual error, 24 Affine transformation, 163 Algebraic multiplicity, 243 Approximation, 24 Associated matrix norm, 226 Asymptotic error constant, 133 Augmented matrix, 195 Back substitution, 206 Banded matrix, 152 Base, 85, 94 Basis theorem, 193 Binary arithmetic, 85 Birthday problem, 70 Bisection method, 110 Bracket, 116 Cantor, Georg F.L.P., 169 Cantor square, 184 Cardano, Girolamo, 108 Central difference formula, 43 Characteristic polynomial, 241 Chopped arithmetic, 89 Clay Foundation, 68 Cofactor expansion, 76 Collatz, Lothar, 77 Collatz conjecture, 67, 68 Column, 143 Combinatorics: alternating power sums, 202 Combinatorics: power sums, 202 Component-wise operation, 9 Computed solution, 231 Computer graphics, 157 Condition number, 228-230 Convergence order, 132 Convergence theorem, 262,264,266 Counter, 60 Cramer, Gabriel, 203 Cramer's rule, 203 Cycling, 122 Determinant, 75, 222 Degree, 25 Diagonal matrix, 147 Diameter, 71 Dilation, 172 Dimension, 171 Direct method, 252 Divided difference, 131 Dot product, 22, 144 Double root, 130 Eigendata, 240 Eigenspace, 243 Eigenvalue, 240 Eigenvector, 240 Elementary matrix, 208 Elementary row operation (ERO), 207 Epicycloids, 13 Equivalent linear system, 195 Error bound via residual, 233 Error function, 42 Error term, 231 Essentially disjoint, 172 Euclidean length, 224 Exact answer, 24,231 Expected value, 83 False, 57 Fern leaf fractal, 185 First generation, 170 Fixed point iteration, 140 Floating point number, 85 Flop, 74 Flop counts (for Gaussian elimination), 226 Fontana, Niccolo 108 Forward substitution, 207 Forward difference formula, 43 Fractals (fractal sets), 169 Future value annuities, 72,73 Galois, Evariste, 109 Gauss, Carl Friedrich, 204 Gaussian elimination, 203-213 Gauss-Seidel iteration, 256 Generalized minimum residual method, 273 Geometric multiplicity, 243 Global variables, 46 Gosper island fractal, 185,186 Hilbert, David, 193 Hilbert matrix, 192 Homogeneous coordinates, 163,164 Hyper convergence of order a, 133 Identity matrix, 148 IEEE double precision standard, 86 Ill-conditioned, 102 Ill-posed, 187 Inline function, 51 Infinite loop, 16 Infinity matrix norm, 227 Infinity (vector) norm, 225 Input-output analysis, 200,201 329 330 General Index Internal demand matrix, 201 Inverse of a matrix, 148 Invertible (nonsingular), 148 Iterative, 109 Iterative method, 252 Iterative refinement, 249 Jacobi-Gauss Convergence Theorem, 262 Jacobi iteration, 253 Julia, Gaston, 169 Leading one, 195 Leontief, Wassily, 200 Linear convergence, 133 Linear transformation, 160 Local variables, 46 Logic, 57 Logical operators, 58 Lower triangular, 205 LU decomposition (or factorization), 213 Machin, John, 43 Machine epsilon, 86 Maclaurin, Colin, 39 Maclaurin series, 38 Mandelbrot, Benoit, 170 Mantissa, 87 Matrix, 143 Matrix arithmetic, 144 Max norm, 225 M-file, 45 - Function M-files, 45 - Script M-files, 45 Monte-Carlo method, 173 Mother loop, 62 Multiple root, 125 Multiplicity 1, 55 Nearly singular (poorly conditioned), 228 Nested loop, 61 Newton's method, 118,119 Nonsingular (invertible), 148 Numerical differentiation, 43 Order, 130 Output matrix, 201 Overflow, 88 Parallel, 239 Parametric equations, 11 Partial pivoting, 211 Path (MATLAB's), 45 Peano, Guiseppe, 169 Perfect number, 81 Pivot, 211 Polynomial, 25 Polynomial interpolation, 189,197-199 Poorly conditioned matrix, 150,228 Positive definite matrix, 265 Preconditioned conjugate gradient method, 273 Preconditioning, 273 Prime number, 81 Prompt, 2 Quadratic convergence, 139 Quadrature, 51 Quartic, 108 Quintic, 108 Random integer matrix generator, 152 Random walk, 82 Recursion formulas, 15 Reduced row echelon form, 195 Reflection, 162 Relative error bound (via residual), 233 Relaxation parameter, 258 Remainder (Taylor's), 35 Residual, 116 Residual matrix, 250 Residual vector, 232 Rhind Mathematical Papyrus, 107 Root, 110 Rotation, 161 Rounded arithmetic, 89 Row, 143 Scalar, 240 Scalar multiplication, 144 Scaling, 161 Secant method, 128,129 Self-similarity property, 169 Shearing, 181 Shift transformation, 162 Sierpinski, Waclaw, 170 Sierpinski carpet fractal, 184,185 Sierpinski gasket fractal, 170 Significant digits, 85 Similarity transformation, 172 Simple root, 125 Simulation, 79 SOR (successive over relaxation), 258 SOR convergence theorem, 264 Sparse matrix, 151,269-278 Special function, 289 Spectrum, 251 Statement, 57 Strictly diagonally-dominant (by columns), 221 Strictly dagonally-dominant (by rows), 264 Submatrix, 76 Symbolic computation, 285 Symmetric matrix, 243 Tartaglia, 108 Taylor, Brook, 34 Taylor polynomial, 25 Taylor series, 38 Taylor's theorem, 35 Technology matrix, 201 General Index Tessellation, 186 Thomas, Llewellyn H., 220 Thomas method, 220 Tolerance, 24 Traffic logistics, 199,200 Transpose, 7 Tridiagonal matrix, 150 Triple root, 126 True, 57 Truth value, 57 Underflow, 88 Unit roundoff, 86 Upper triangular matrix, 204 Vandermonde matrix, 197 Variable precision arithmetic, 285 Vector, 7 Vector norm, 225 von Koch, Niels F.H., 179 von Koch snowflake, 179 Weierstrass, Karl, 179 Well-conditioned, 102 Well-posed, 187 Zero divisors, 105 Zeroth generation, 170 #ماتلاب,#متلاب,#Matlab,
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