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Scientific Computing with MATLAB

Author: Alfio Quarteroni; Fausto Saleri
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003.
Series: Texts in computational science and engineering, 2.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. To make the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alfio Quarteroni; Fausto Saleri
ISBN: 9783642593390 3642593399
OCLC Number: 851759961
Description: 1 online resource (ix, 257 pages).
Contents: 1. What can't be ignored --
1.1 Real numbers --
1.2 Complex numbers --
1.3 Matrices --
1.4 Real functions --
1.5 To err is not only human --
1.6 A few more words about MATLAB --
1.7 What we haven't told you --
1.8 Exercises --
2. Nonlinear equations --
2.1 The bisection method --
2.2 The Newton method --
2.3 Fixed point iterations --
2.4 What we haven't told you --
2.5 Exercises --
3. Approximation of functions and data --
3.1 Interpolation --
3.2 Piecewise linear interpolation --
3.3 Approximation by spline functions --
3.4 The least squares method --
3.5 What we haven't told you --
3.6 Exercises --
4. Numerical differentiation and integration --
4.1 Approximation of function derivatives --
4.2 Numerical integration --
4.3 Simpson adaptive formula --
4.4 What we haven't told you --
4.5 Exercises --
5. Linear systems --
5.1 The LU factorization method --
5.2 The technique of pivoting --
5.3 How accurate is the LU factorization? --
5.4 How to solve a tridiagonal system --
5.5 Iterative methods --
5.5.1 How to construct an iterative method --
5.6 When should an iterative method be stopped? --
5.7 Richardson method --
5.8 What we haven't told you --
5.9 Exercises --
6. Eigenvalues and eigenvectors --
6.1 The power method --
6.2 Generalization of the power method --
6.3 How to compute the shift --
6.4 Computation of all the eigenvalues --
6.5 What we haven't told you --
6.6 Exercises --
7. Ordinary differential equations --
7.1 The Cauchy problem --
7.2 Euler methods --
7.3 The Crank-Nicolson method --
7.4 Zero-stability --
7.5 Stability on unbounded intervals --
7.6 High order methods --
7.7 The predictor-corrector methods --
7.8 Systems of differential equations --
7.9 What we haven't told you --
7.10 Exercises --
8. Numerical methods for boundary-value problems --
8.1 Approximation of boundary-value problems --
8.2 Finite differences in 2 dimensions --
8.3 What we haven't told you --
8.4 Exercises --
9. Solutions of the exercises --
9.1 Chapter 1 --
9.2 Chapter 2 --
9.3 Chapter 3 --
9.4 Chapter 4 --
9.5 Chapter 5 --
9.6 Chapter 6 --
9.7 Chapter 7 --
9.8 Chapter 8 --
Index of MATLAB Programs.
Series Title: Texts in computational science and engineering, 2.
Responsibility: by Alfio Quarteroni, Fausto Saleri.

Abstract:

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. To make the presentation concrete and appealing, the programming environment Matlab is adopted as a faithful companion. All the algorithms introduced throughout the book are shown, thus furnishing an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. The book also contains the solution to several problems raised through exercises and examples, often originating from specific applications. A specific section is devoted to subjects which were not addressed in the book and indicate the bibliographical references for a more comprehensive treatment of the material.

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From the reviews: "Can be used either as a complement to a basic or more advanced course in numerical analysis, or as a do-book for a short and practical introduction to the subject ... . closing Read more...

 
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