Numerical AnalysisBeside providing a foundation in modern numerical-approximation techniques, Burden and Faires' well-respected Numerical Analysis, Sixth Edition, explains how, why, and when the techniques can be expected to work. The authors use real-life problems from areas such as engineering, computer science, biology, and physics to show students how numerical methods are applied. more than 2,000 exercises are included, ranging from elementary applications of methods and algorithms to more rigorous generalizations and extensions of theory. Where appropriate, the text demonstrates how computer algebra systems can be of value in solving these problems. As with earlier editions, this text is designed to give students the preparation they need to pass the Actuaries' examination in Numerical Methods. To that end, the edition includes many more exercises of the type often found on the exam. |
Contents
Mathematical Preliminaries | 1 |
Numerical Solutions to PartialDifferential | 12 |
Solutions of Equations in One Variable | 47 |
Copyright | |
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Common terms and phrases
a₁ actual solution y(t Algorithm applied approximate the solution b₁ Bisection method coefficients Composite Simpson's rule compute constant convergence cubic spline defined derivative determine differential equation eigenvalues eigenvector endpoints entries Euler's method evaluations EXAMPLE EXERCISE SET f(xo Figure fixed-point formula function ƒ Gaussian elimination given gives initial approximation initial-value problem integral interpolating polynomial interval k₁ Lagrange polynomial least squares linear system matrix method of order Müller's method multistep method Newton's method nodes norm number of iterations obtained OUTPUT p₁ polynomial of degree quadratic quadrature relative error Repeat Exercise root rounding arithmetic roundoff error Runge-Kutta method Secant method Section sequence Simpson's rule solve Step 1 Set subroutine Suppose Table Taylor polynomial technique Theorem Trapezoidal rule truncation error vector w₁ Wi+1 x₁ y₁ zero