Introduction to Scientific Computing and Data Analysis

by Mark H. Holmes

Overview

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. The codes used for most of the computational examples in the text are available on GitHub. This new edition includes material necessary for an upper division course in computational linear algebra.

Product Details

ISBN-13:	9783319302546
Publisher:	Springer International Publishing
Publication date:	05/31/2016
Series:	Texts in Computational Science and Engineering , #13
Edition description:	1st ed. 2016
Pages:	497
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Mark Holmes is a Professor at Rensselaer Polytechnic Institute. His current research interests include mechanoreception and sleep-wake cycles. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.

Table of Contents

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.- Taylor's Theorem.- Vector and Matrix Summary.- Answers.- References.- Index.

Editorial Reviews

The material is accompanied by many examples, exercises, as well as diagrams and tables of resulting data which are produced by MATLAB for which the programs are available on the author's website. The book is intended for beginners in scientific computing with basic knowledge in calculus, matrix algebra, and differential equations. … a good reading for the more advanced scientific engineer or lecturer in this field who may find numerous suggestions for working or teaching.” (Gudula Rünger, zbMATH 1368.65002, 2017)

From the Publisher