by Tobin A. Driscoll and Richard J. Braun
2017 / xxx + 559 pages / Hardcover / ISBN 978-1-611975-07-9 List Price $104.00 / SIAM Member Price $72.80 / Order Code: OT154
Keywords: numerical analysis, scientific computing, MATLAB
“If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of the correspondence between quantitative information and mathematical manipulation.”
-from the Preface
Fundamentals of Numerical Computation is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking.
Professors Driscoll and Braun have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book.
The authors describe their goals and intentions for the book in specific terms. “Our guiding point of view is that the student users of the book are far more likely to apply and remix fundamental computational algorithms than to reinvent them. We want to prepare them for more advanced courses in numerical analysis, but we place a higher priority on conveying foundational skills in scientific computation. Accordingly, we emphasize knowing how to cast a problem into a form that can be coded and solved, tradeoffs between different methods for a problem, and assessing the correctness and convergence of the results. We do not, however, make much of an issue of optimizing the speed of implementations, except when orders of magnitude are in play, nor do we discuss parallelism.
“Above all, we emphasize linear algebra. Linear algebra is the lingua franca of scientific computing—a fact in no small measure established and affirmed by MATLAB over more than three decades. Matrices and vectors enter our presentation in Chapter 2 and are rarely far from view in the rest of the text. They usually simplify, or at least shorten, the presentation of analysis or algorithms. We found that concise linear-algebraic expressions often turn into tidy (though not necessarily optimal) implementations. We try to gently but gradually wean students from the habits of componentwise expressions and nested loops, so that they are prepared for higher-order thinking. By the time differential PDE are solved in the last chapters of the book, the use of discretization to replace operators by matrices and functions by vectors should seem routine and maybe even obvious.”
Fundamentals of Numerical Computation is intended for advanced undergraduates in math, applied math, engineering, or science disciplines, as well as for researchers and professionals looking for an introduction to a subject they missed or overlooked in their education.
About the Authors
Tobin A. Driscoll is a Professor of mathematics in the Department of Mathematical Sciences at the University of Delaware. His research is in numerical methods for and applications of scientific computing, and he has contributed to open-source MATLAB software, including the Chebfun project. He is the author of over 50 refereed articles and three other books, including Learning MATLAB.
Richard J. Braun is a Professor of mathematics in the Department of Mathematical Sciences at the University of Delaware. His research interests include mathematical modeling to create models to subsequently solve numerically. The problems most often include free boundaries, partial differential equations, and mathematical models for the tear film and ocular surface. He is the author of over 70 scientific articles in a wide range of journals in mathematics and applications and is on editorial boards of five scientific journals.
View this book