Download PDF Scientific Computing with MATLAB and Octave Second Edition by Alfio Quarteroni

Sinopsis

In this book we will systematically use elementary mathematical concepts which the reader should know already, yet he or she might not recall them immediately. We will therefore use this chapter to refresh them, as well as to introduce new concepts which pertain to the field of Numerical Analysis. We will begin to explore their meaning and usefulness with the help of MATLAB (MATrix LABoratory), an integrated environment for programming and visualization in scientific computing. We shall also use GNU Octave (in short, Octave) which is mostly compatible with MATLAB. In Sections 1.6 and 1.7 we will give a quick introduction to MATLAB and Octave, which is sufficient for the use that we are going to make in this book. We also make some notes about differences between MATLAB and Octave which are relevant for this book. However, we refer the interested readers to the manual [HH05] for a description of the MATLAB language and to the manual [Eat02] for a description of Octave. Octave is a reimplementation of part of MATLAB which includes a large part of the numerical facilities of MATLAB and is freely distributed under the GNU General Public License. Through the book, we shall often make use of the expression “MATLAB command”: in this case, MATLAB should be understood as the language which is the common subset of both programs MATLAB and Octave. We have striven to ensure a seamless usage of our codes and programs under both MATLAB and Octave. In the few cases where this does not apply, we will write a short explanation notice at the end of each corresponding section. In the present Chapter we have condensed notions which are typical of courses in Calculus, Linear Algebra and Geometry, yet rephrasing them in a way that is suitable for use in scientific computing.

While the set R of real numbers is known to everyone, the way in which computers treat them is perhaps less well known. On one hand, since machines have limited resources, only a subset F of finite dimension of R can be represented. The numbers in this subset are called floatingpoint numbers. On the other hand, as we shall see in Section 1.1.2, F is characterized by properties that are different from those of R. The reason is that any real number x is in principle truncated by the machine, giving rise to a new number (called the floating-point number), denoted by fl(x), which does not necessarily coincide with the original number x.

Content

1. What can’t be ignored
2. Nonlinear equations
3. Approximation of functions and data
4. Numerical differentiation and integration
5. Linearsystems
6. Eigenvalues and eigenvectors
7. Ordinary differential equations
8. Numerical methods for (initial-) boundary-value problems
9. Solutions of the exercises

Click here to download