An Introduction to Numerical Methods: A MATLAB Approach, Second Edition
Numerical methods are a mainstay of researchers and professionals across the many mathematics, scientific, and engineering disciplines. The importance of these methods combined with the power and availability of today's computers virtually demand that students in these fields be well versed not only in the numerical techniques, but also in the use of a modern computational software package.
Updated to reflect the latest version of MATLAB, the second edition of An Introduction to Numerical Methods continues to fulfill both these needs. It introduces the theory and applications of the most commonly used techniques for solving numerical problems on a computer. It covers a wide range of useful algorithms, each presented with full details so that readers can visualize and interpret each step.
Highlights of the second edition:
Emphasis on understanding how the methods work, a simple, direct style, and thorough coverage make this book an outstanding initiation that allows students to see almost immediate results. It will boost their confidence in their ability to master the subject and give them valuable experience in the use of MATLAB.
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algorithm applied approximate the solution augmented matrix best ﬁts bisection method boundary-value problem coefficient composite trapezoidal rule COMPUTER PROBLEM SET Consider cubic spline d|sp data points decimal places deﬁned deﬁnition derivative diagonal differential equations disp eigenpairs eigenvalues eigenvectors end end estimate Euler’s method evaluate exact solution EXAMPLE EXERCISE SET false position method FIGURE ﬁnd ﬁnding ﬁrst ﬁxed point following MATLAB function function f Gauss-Seidel Gaussian elimination Gaussian quadrature given golden section search initial-value problem interpolating polynomial interval iterative method least squares linear system M-file M-function method of order method to ﬁnd natural cubic spline Newton’s method nonlinear number of iterations numerical method obtained plot polynomial of degree root round-off error Runge-Kutta method satisﬁes secant method Section shooting method Simpson’s rule solve the IVP solve the system subintervals system of equations Taylor series Theorem trapezoidal rule truncation error vector zero