Scientific Computing with MATLAB

1. Front Matter

   Pages i-ix

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2. What can’t be ignored

   • Alfio Quarteroni, Fausto Saleri

   Pages 1-35

3. Nonlinear equations

   • Alfio Quarteroni, Fausto Saleri

   Pages 37-55

4. Approximation of functions and data

   • Alfio Quarteroni, Fausto Saleri

   Pages 57-82

5. Numerical differentiation and integration

   • Alfio Quarteroni, Fausto Saleri

   Pages 83-102

6. Linear systems

   • Alfio Quarteroni, Fausto Saleri

   Pages 103-136

7. Eigenvalues and eigenvectors

   • Alfio Quarteroni, Fausto Saleri

   Pages 137-152

8. Ordinary differential equations

   • Alfio Quarteroni, Fausto Saleri

   Pages 153-186

9. Numerical methods for boundary-value problems

   • Alfio Quarteroni, Fausto Saleri

   Pages 187-206

10. Solutions of the exercises

    • Alfio Quarteroni, Fausto Saleri

    Pages 207-244

11. Back Matter

    Pages 245-257

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"It is important to prove, is more but it important to improve." This textbook is an introduction to Scientific Computing. We will illustrate several numerical methods for the computer solution of cer­ tain classes of mathematical problems that cannot be faced by paper and pencil. We will 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. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with real and complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will adopt the programming environment MATLAB ® 1 as a faithful companion. We will gradually discover its principal commands, statements and con­ structs. We will show how to execute all the algorithms that we intro­ duce throughout the book. This will enable us to furnish an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raised through exercises and examples, often stemming from specific ap­ plications.

• Approximation
• MATLAB
• Matlab programming
• mathematics
• numerical mathematics
• scientific computing

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 section of each chapter is a list of exercises, adapted to the level of the reader. … exercises are essential because the emphasis is clearly on the practical implementation … . after working through this book, the reader is brought to a relatively experienced lower step up the ladder of scientific computing.” (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)

• Ecole Polytechnique Fédérale de Lausanne 1015 Lausanne, Switzerland

  Alfio Quarteroni

• Politecnico de Milano, Milano, Italy

  Alfio Quarteroni, Fausto Saleri

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