Scientific Computing with MATLABSpringer Science & Business Media, 2003 - 257 pages This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how tonbsp;compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for thenbsp;solution of differential equations. To make the presentation concrete and appealing, the programming environmentnbsp;Matlab is adopted as a faithful companion. All the algorithms introduced throughout the booknbsp;are shown, thus furnishing an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. The book also contains the solution to several problemsnbsp;raised through exercises and examples, oftennbsp;originating from specific applications. A specific section is devotednbsp;to subjectsnbsp;which were not addressed in the book andnbsp;indicatenbsp;the bibliographical references for a more comprehensive treatment of the material. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp; |
Contents
I | 1 |
III | 2 |
IV | 4 |
V | 6 |
VI | 8 |
VII | 13 |
VIII | 14 |
IX | 16 |
XLIX | 122 |
L | 123 |
LI | 128 |
LII | 130 |
LIII | 134 |
LV | 137 |
LVI | 140 |
LVII | 142 |
X | 17 |
XI | 19 |
XII | 21 |
XIII | 24 |
XIV | 26 |
XV | 29 |
XVI | 30 |
XVII | 34 |
XIX | 37 |
XX | 38 |
XXI | 42 |
XXII | 47 |
XXIII | 50 |
XXIV | 51 |
XXV | 53 |
XXVI | 57 |
XXVII | 59 |
XXVIII | 60 |
XXIX | 66 |
XXX | 67 |
XXXI | 72 |
XXXII | 74 |
XXXIII | 80 |
XXXIV | 81 |
XXXV | 83 |
XXXVI | 84 |
XXXVII | 87 |
XXXIX | 89 |
XL | 92 |
XLI | 95 |
XLII | 99 |
XLIII | 100 |
XLIV | 103 |
XLV | 106 |
XLVI | 113 |
XLVII | 115 |
XLVIII | 120 |
LVIII | 144 |
LIX | 146 |
LX | 148 |
LXI | 149 |
LXII | 150 |
LXIII | 153 |
LXIV | 155 |
LXV | 156 |
LXVI | 158 |
LXVII | 162 |
LXVIII | 163 |
LXIX | 165 |
LXX | 168 |
LXXI | 174 |
LXXII | 176 |
LXXIII | 179 |
LXXIV | 182 |
LXXV | 184 |
LXXVI | 187 |
LXXVII | 190 |
LXXIX | 192 |
LXXX | 195 |
LXXXI | 202 |
LXXXII | 204 |
LXXXIII | 205 |
LXXXIV | 207 |
LXXXVI | 209 |
LXXXVII | 215 |
LXXXVIII | 219 |
LXXXIX | 223 |
XC | 228 |
XCI | 232 |
XCII | 241 |
245 | |
249 | |
251 | |
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Common terms and phrases
a₁ absolute stability algorithm approximation backward Euler method bisection method called Cauchy problem coefficients column vector complex number components composite compute the zeros condition number corresponding Crank-Nicolson method dashed line denote derivative differential equations dimension eigenvalues eigenvector equal exact solution Example Exercise f(xi Figure finite difference fixed point iterations following instructions forward Euler method function f Gauss factorization Gauss-Seidel method graph grid Heun method i-th initial vector input instance interpolating polynomial iterative method Jacobi method linear system MATLAB MATLAB command MATLAB program method converges midpoint Newton's method niter nmax null number of iterations numerical solution obtain parameters perturbation error polynomial of degree positive definite power method quadrature formula real numbers residual respect to h Runge-Kutta method Simpson formula Softcover solve suitable symmetric and positive tolerance triangular tridiagonal trigonometric interpolant Un+1 values variable verify y(tn
References to this book
MATLAB 7: Eine Einführung Christoph W. Überhuber,Stefan Katzenbeisser,Dirk Praetorius No preview available - 2004 |