Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (2nd Edition)

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9780139491573: Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (2nd Edition)

Unique in content and approach, this book covers all the topics that are usually covered in an introduction to scientific computing--but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the connection between continuous mathematics and computing. MATLAB 5 is used throughout to encourage experimentation, and each chapter focuses on a different important theorem--allowing readers to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a “hard” problem that involves ill-conditioning, high dimension, etc.; 2)at least one theorem with both a rigorous proof and a “proof by MATLAB” experiment to bolster intuition; 3)at least one recursive algorithm; and 4)at least one connection to a real-world application. The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing. Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem. For engineers and mathematicians.

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From the Publisher:

This book presents a unique approach for one semester numerical methods and numerical analysis courses. Well organized but flexible, the text is brief and clear enough for introductory numerical analysis students to "get their feet wet," yet comprehensive enough in its treatment of problems and applications for higher-level students to develop a deeper grasp of numerical tools.

About the Author:

Charles F. Van Loan has been at Cornell University since 1975, where he is a Professor of Computer Science and the Joseph C. Ford Professor of Engineering. He is a SIAM Fellow and the author of Matrix Computations (with G. H. Golub; Johns Hopkins, 1996), Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (Prentice Hall, 1999), Computational Frameworks for the Fast Fourier Transform (SIAM, 1992), Handbook for Matrix Computations (with T. F. Coleman; SIAM, 1988), and Introduction to Computational Science and Mathematics (James and Bartlett, 1996).

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Charles F. Van Loan
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