Scientific Computing with MATLAB and Octave

1. Front Matter

   Pages I-XVI

   PDF

2. What can’t be ignored

   • Alfio Quarteroni, Fausto Saleri

   Pages 1-38

3. Nonlinear equations

   • Alfio Quarteroni, Fausto Saleri

   Pages 39-69

4. Approximation of functions and data

   • Alfio Quarteroni, Fausto Saleri

   Pages 71-99

5. Numerical differentiation and integration

   • Alfio Quarteroni, Fausto Saleri

   Pages 101-122

6. Linear systems

   • Alfio Quarteroni, Fausto Saleri

   Pages 123-166

7. Eigenvalues and eigenvectors

   • Alfio Quarteroni, Fausto Saleri

   Pages 167-185

8. Ordinary differential equations

   • Alfio Quarteroni, Fausto Saleri

   Pages 187-236

9. Numerical methods for (initial-)boundary-value problems

   • Alfio Quarteroni, Fausto Saleri

   Pages 237-265

10. Solutions of the exercises

    • Alfio Quarteroni, Fausto Saleri

    Pages 267-305

11. Back Matter

    Pages 307-324

    PDF

Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- 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 di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with realand complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate 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 s- ci?c applications.

• MATLAB
• computer
• computer-aided design (CAD)
• learning
• modeling
• numerical methods
• programming
• scientific computing

From the reviews:

" ... Scientific Computing with MATLAB is written in a clear and concise style, figures, tables and formula boxes complement the explanations... The whole book is an invitation, if not a request, of the authors to the reader to play with MATLAB, apply its powerful menagerie of functions to solve the given (or own) problems - in brief, supervised learning by doing .... is a stimulating introductory textbook about numerical methods that successfully combines mathematical theory with programming experience..." Anselm A.C. Horn, Journal of Molecular Modeling 2004

"... An excellent addition to academic libraries and university bookstores, this book will be useful for self-study and as a complement to other MATLAB-based books. Highly recommended. Upper-division undergraduates through professionals." S.T. Karris, Choice 2003

From the reviews of the second edition:

"The authors present … details about the MATLAB and Octave environments, with information about how the two products can be acquired. … readers will find a useful set of about 60 references to books and articles about numerical methods and algorithms. … If you work on a daily basis with things like Fourier transformations … and Chebyshev interpolations, then you’ll find this book invaluable. If, like me, you are required to support people who work with those things, you’ll need this book … ." (G. K. Jenkins, ACM Computing Reviews, Vol. 49 (12), December, 2008)

• Ecole Polytechnique Fédérale de Lausanne, CMCS-Modeling and Scientific Computing, Lausanne, Switzerland

  Alfio Quarteroni

• MOX-Politecnico di Milano, Milano, Italy

  Alfio Quarteroni, Fausto Saleri

Policies and ethics