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
Approximation of Functions | 1 |
Direct Methods for Linear Systems | 109 |
Solution of Nonlinear Equations | 161 |
Iterative Methods for Linear Systems | 221 |
Eigenvalue Problems | 283 |
Numerical Integration | 313 |
Ordinary Differential Equations | 349 |
Difference Methods for PDEs | 395 |
Introduction to Finite Elements | 447 |
Divided Differences | 477 |
Chebyshev Polynomials | 483 |
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Common terms and phrases
A₁ algorithm analog apply associated basis functions bounded Chapter coefficients compute condition constant construct COROLLARY cubic defined denote derivatives diagonal entries difference differentiable discuss eigenvalues eigenvectors Equation error estimate example Figure Fourier function f Gauss Gauss-Seidel Gauss-Seidel method graph grid function implies induction initial guess x(0 inner product inner-product space integral interval iterative scheme Jacobi method Lemma linear system Lipschitz LU factorization matrix norm mesh size h multistep methods multistep scheme Newton-Cotes formulas Newton's method nodes nonsingular nonzero one-step method orthogonal permutation matrix pivoting polynomial interpolation positive definite problem PROOF prove QR decomposition quadrature row reduction satisfies secant method Section sequence solve spline stepsize subinterval successive substitution symmetric and positive theorem tion triangle inequality tridiagonal truncation error Un+1 upper triangular values vanishes vector space yields zero