This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.
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2d Solutions of Equations in One Variable
5 Interpolation and Polynomial Approximation
Numerical Differentiation and Integration
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actual solution Algorithm Algorithm 6.7 applied approximate the solution boundary conditions boundary-value problem calculations coefficients column compare the results compute considered constant convergence cubic spline defined denotes derivatives determine diagonal differential equation eigenvalues eigenvector entries error bound Euler's method evaluations exact solution EXAMPLE Exercise Set formula function Gauss-Seidel method Gaussian elimination given gives hmax implies initial approximation initial-value problem INPUT integral interpolating polynomial interval involving Lagrange polynomial least-squares linear system maximum number method of order multistep method Newton-Cotes formulas Newton's method nodes nonsingular norm number of iterations partial-differential equation polynomial of degree positive definite proof quadratic quadrature real numbers Repeat Exercise root round-off error Runge-Kutta method satisfies Secant method Section sequence Show Simpson's rule solve Step 1 Set Suppose Table Taylor polynomial technique trapezoidal rule tridiagonal truncation error unique solution vector zero