Numerical Analysis for Applied ScienceWritten for graduate students in applied mathematics, engineering and science courses, the purpose of this book is to present topics in "Numerical Analysis" and "Numerical Methods." It will combine the material of both these areas as well as special topics in modern applications. Included at the end of each chapter are a variety of theoretical and computational exercises. |
Contents
0 Some Useful Tools | 1 |
1 Approximation of Functions | 27 |
2 Direct Methods for Linear Systems | 109 |
3 Solution of Nonlinear Equations | 161 |
4 Iterative Methods for Linear Systems | 221 |
5 Eigenvalue Problems | 283 |
6 Numerical Integration | 313 |
7 Ordinary Differential Equations | 349 |
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Common terms and phrases
algorithm analog analysis apply approximation associated assume basis boundary bounded Chapter coefficients column compute condition consider consistent constant construct continuous convergence corresponding defined DEFINITION denote derivatives determine diagonal difference differential direction discuss dominant eigenvalues element entries Equation error establish estimate exact example exists fact factorization Figure find first function function f given gives graph grid idea identity illustrates implies independent inequality initial guess integral interpolation interval involving iteration Lemma linear system matrix method multiplicity nodes nonzero norm numerical observation operations orthogonal piecewise polynomial positive definite possible practical problem PROOF properties prove quadrature reasoning reduces requires rule scheme sequence solution solve space stability step substitution successive Suppose symmetric theorem tion transformations triangular typically unknown upper values vanishes vector yields zero