Numerical Computing with MATLAB: Revised Reprint
SIAM, 01.01.2008 - 336 Seiten
Numerical Computing with MATLAB is a lively textbook for an introductory course in numerical methods, MATLAB, and technical computing. The emphasis is on the informed use of mathematical software; in particular, the presentation helps readers learn enough about the mathematical functions in MATLAB to use them correctly, appreciate their limitations, and modify them appropriately. The book makes extensive use of computer graphics, including interactive graphical expositions of numerical algorithms. It provides more than 70 M-files, which can be downloaded from the text Web site www.mathworks.com/moler. Many of the more than 200 exercises involve modifying and extending these programs. The topics covered include an introduction to MATLAB; linear equations; interpolation; zeros and roots; least squares; quadrature; ordinary differential equations; Fourier analysis; random numbers; eigenvalues and singular values; and partial differential equations. Motivating applications include modern problems from cryptography, touch-tone dialing, Google page-ranking, atmospheric science, and image processing, as well as classical problems from physics and engineering.
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algorithm approximation backslash operator behavior coefﬁcients column components condition number deﬁned deﬁnition diagonal difﬁculty digits discretization error eigenfunctions eigenvalues eigenvectors elements evaluated example factor FFTs of length Fibonacci Figure ﬁle ﬁnal ﬁnd ﬁrst ﬁt ﬁve ﬁxed ﬂoating-point arithmetic ﬂoating-point numbers Gaussian elimination golden ratio graph heat equation Hermite interpolation inﬁnite initial condition initial value integral interpolation interval inverse involves iteration least squares linear equations linear system M-ﬁle magic squares MATLAB MATLAB function matrix multiple Newton’s method nonlinear nonzero norm ode2 ode4 ordinary differential equation output PageRank parameters pchip pchiptx pivoting plot points Poisson problem polynomial problem produces pseudoinverse quadrature quadtx random number randtx reﬂection result roundoff error satisﬁes sequence singular values slopes solve sparse sparse matrix speciﬁed spline statement step Symbolic Toolbox tfinal tolerance trapezoid rule triangular variable vector zero