Holmes M.H. Introduction to Scientific Computing and Data Analysis

2nd ed. — Springer, 2023. — 562 p. — (Texts in Computational Science and Engineering, 13). — ISBN 9783031224294, 3031224299.This textbook provides an introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression-based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science.
One of the principal reasons for this NEW edition is to include material necessary for an upper division course in computational linear algebra. So, least squares is covered more extensively, along with new material covering Householder QR, sparse matrix methods, preconditioning, and Markov chains. The computational implications of the Gershgorin, Perron-Frobenius, and Eckart-Young theorems have also been expanded. It is assumed in the development that a previous course in linear algebra has been taken, but as a refresher some of the more pertinent facts from such a course are given in an appendix. Other significant changes include a reorganization and expansion of the exercises. Also, the material on cubic splines, particularly related to data analysis, has been expanded (e.g., Section 6.4), and the presentation of Gaussian quadrature has been modified. There is also a new section providing an introduction to data-based modeling and dynamic modes.
As with the first edition, the material is developed and presented, independent of the language used for computing. So, there are no computer codes in the text. Rather, the procedures are written in a generic format, such as Newton’s method on page 41. There are, however, a few exercises where example MatLAB commands are given indicating how the problem can be done (e.g., the commands on page 198 for inputting, and displaying, a grayscale image). All of the codes used in the computational examples in the text are available from the author’s GitHub repository.Preface.
Preface to Second Edition.
Introduction to Scientific Computing.
Solving A Nonlinear Equation.
Matrix Equations.
Eigenvalue Problems.
Interpolation.
Numerical Integration.
Initial Value Problems.
Optimization: Regression.
Optimization: Descent Methods.
Data Analysis.
References.
Index.True PDF