id: 06300894
dt: b
an: 2015e.00920
au: Lyche, Tom; Merrien, Jean-Louis
ti: Exercises in computational mathematics with MATLAB.
so: Problem Books in Mathematics. Berlin: Springer (ISBN 978-3-662-43510-6/hbk;
978-3-662-43511-3/ebook). xii, 372~p. (2014).
py: 2014
pu: Berlin: Springer
la: EN
cc: N15 U45
ut: basic topics in numerical analysis; problem book; theoretical problems;
solutions; programming problems; MATLAB codes; exercise; textbook;
matrices; linear systems; eigenvalues; eigenvectors; norms;
conditioning; iterative methods; polynomial interpolation; Bézier
curves; Bernstein polynomials; interpolation; linear least squares
methods
ci:
li: doi:10.1007/978-3-662-43511-3
ab: This is an interesting new kind of book in the area of numerical analysis.
The authors propose to study the standard topics of numerical analysis
by solving exercises. Consequently, the text consists mainly of
theoretical and programming exercises, 137 all together, and their
solution, consuming approximately 160 pages. Most chapters begin with a
short review of the corresponding topic. The reader is supposed to be
principially familiar with the material, e.g. from a textbook or a
lecture, but the idea is that he will study the topics more profoundly
by solving exercises. The book is subdivided into the following 13
chapters: Chapter 1. An introduction to MATLAB commands (8 pp.);
Chapter 2. Matrices and linear Systems (16 pp.); Chapter 3. Matrices,
eigenvalues and eigenvectors (18 pp.); Chapter 4. Matrices, norms and
conditioning (21 pp.); Chapter 5. Iterative methods (36 pp.); Chapter
6. Polynomial interpolation (28 pp.); Chapter 7. Bézier curves and
Bernstein polynomials (22 pp.); Chapter 8. Piecewise polynomials,
interpolation and applications (24 pp.); Chapter 9. Approximation of
integrals (44 pp.); Chapter 10. Linear least squares methods (29 pp.);
Chapter 11. Continuous and discrete approximations (32 pp.); Chapter
12. Ordinary differential equations, one step methods (41 pp.); Chapter
13. Finite differences for differential and partial differential
equations (43 pp.). A nice detail is that in most chapters a biography
of scientists who have made important contributions to the field is
included. It is widely accepted that solving exercises is essential to
achieve a deeper understanding of a mathematical topic. Under this
point of view the present book can be seen as an adequate vehicle to
really get into the field of numerical analysis. Of course, a good
portion of self-discipline is required. But the book can also serve as
a rich source of exercises for university courses.
rv: Rolf Dieter Grigorieff (Berlin)