Scientific Computing - An Introduction using Maple and MATLAB
Springer Science & Business, Apr 23, 2014 - Mathematics - 905 pages
Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.
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algebraic algorithm approximation Chapter choose coefficients column compute condition number consider constraints convergence defined derivative diagonal differential equation digits eigenvalues eigenvectors elements end end example f(xk factor Figure fixed point fixed point iteration formula function f function values Gaussian elimination Givens rotations integral interpolation polynomial interval iterative methods Jacobi Lanczos least squares problem Lemma linear multistep methods linear system machine number Maple Matlab Matlab function minimize multiple Newton Newton’s method nodes nonlinear norm numerical method obtain OOOO orthogonal matrix orthogonal polynomials parameter pivoting plot polynomial of degree positive definite precision arithmetic PROOF QR decomposition quadratic quadrature rule recurrence residual result right hand side Rn×n Runge-Kutta Runge-Kutta methods Section sequence singular values solution solve step symmetric Theorem transform triangular tridiagonal matrix variables vector zero