Exercises in Computational Mathematics with MATLAB [electronic resource] / by Tom Lyche, Jean-Louis Merrien.
Contributor(s): Merrien, Jean-Louis [author.] | SpringerLink (Online service)Material type: TextSeries: Problem Books in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014Description: XII, 372 p. 136 illus., 90 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783662435113Subject(s): Mathematics | Computer-aided engineering | Matrix theory | Algebra | Approximation theory | Applied mathematics | Engineering mathematics | Computer mathematics | Mathematics | Computational Mathematics and Numerical Analysis | Linear and Multilinear Algebras, Matrix Theory | Appl.Mathematics/Computational Methods of Engineering | Approximations and Expansions | Applications of Mathematics | Computer-Aided Engineering (CAD, CAE) and DesignAdditional physical formats: Printed edition:: No titleDDC classification: 518 LOC classification: QA71-90Online resources: Click here to access online
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1 An Introduction to MATLAB commands -- 2 Matrices and Linear Systems -- 3 Matrices, Eigenvalues and Eigenvectors -- 4 Matrices, Norms and Conditioning -- 5 Iterative Methods -- 6 Polynomial Interpolation -- 7 Bézier Curves and Bernstein Polynomials -- 8 Piecewise Polynomials, Interpolation and Applications -- 9 Approximation of Integrals -- 10 Linear Least Squares Methods -- 11 Continuous and Discrete Approximations -- 12 Ordinary Differential Equations, One Step Methods -- 13 Finite Differences for differential and partial differential equations -- References -- Index of Names -- Subject Index -- MATLAB Index.
Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.