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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Mathematical Preliminaries and Error Analysis
Solutions of Equations in One Variable
Interpolation and Polynomial Approximation
Numerical Differentiation and Integration
InitialValue Problems for Ordinary Differential Equations
Direct Methods for Solving Linear Systems
Iterative Techniques in Matrix Algebra
actual error actual solution y(t Algorithm applied approximate f approximate the solution Bisection method boundary-value problem Composite Simpson’s rule compute constant convergence cosx cubic spline deﬁned deﬁnite derivative determine diagonal eachi eigenvalues eigenvector endpoints entries error bound Euler’s method evaluations Example Exercise Set factorization Figure Find ﬁrst formula function f Gaussian elimination given gives implies initial approximation initial-value problems integral interpolating polynomial interval Lagrange polynomial least squares linear system Maple matrix maximum number method of order Newton’s method nodes norm number of iterations obtained OUTPUT partial differential equation polynomial of degree positive definite procedure quadrature Repeat Exercise requires round-off error rounding arithmetic Runge–Kutta method Secant method Section sequence Show sinx Step subroutine Suppose symmetric symmetric matrix Taylor polynomial technique Theorem Trapezoidal rule tridiagonal truncation error unique solution vector wi+1 zero