Название: Introduction to Scientific Computing and Data Analysis, 2nd Edition
Автор: Mark H. Holmes
Издательство: Springer
Год: 2023
Страниц: 563
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

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. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. All of the codes used in the computational examples in the text are available from the author’s GitHub repository. This new edition includes material necessary for an upper division course in computational linear algebra.

The second theme is the importance in scientific computing of having a solid grasp of the theory underlying the methods being used. A computer has the unfortunate ability to produce answers even if the methods used to find the solution are completely wrong. Consequently, it is essential to have an understanding of how the method works, and how the error in the computation depends on the method being used. Needless to say, is also important to be able to code these methods, and in the process be able to adapt them to the particular problem being solved. There is considerable room for interpretation on what this means. To explain, in terms of computing languages, the current favorites are MATLAB and Python. Using the commands they provide, a text such as this one becomes more of a user’s manual, reducing the entire book down to a few commands.

The MATLAB codes used to produce almost every figure,and table with numerical output, in this text are available from the author’s website as well as from Springer-Link. In other words, the MATLAB codes for all of the methods considered, and the examples used, are available. These can be used as a learning tool. This also goes to the importance in computational-based research, and education, of providing open source to guarantee the correctness and reproducibility of the work.