Heister T., Rebholz L.G. Scientific Computing: For Scientists and Engineers

2nd Edition. — De Gruyter, 2023. — 184 p. — ISBN 978-3-11-099961-7.Научные вычисления: для ученых и инженеров
Scientific Computing for Scientists and Engineers is designed to teach undergraduate students relevant numerical methods and required fundamentals in scientific computing.Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations?Simple programming examples. This is an introductory programming course, and students need to learn the basics before all the bells and whistles. Hence whenever possible, we give code that is as simple as possible, without overcomplicating the main ideas and without excessive commenting. Also, we assume that students have at least seen and used MatLAB in some minimal capacity. Algorithms given in the text are written in the language of MatLAB and Octave. Currently at Clemson, all students have free access to MatLAB. Octave is a free version of MatLAB, which has almost all of the same functionality. Newer versions of MatLAB have more bells and whistles, but for the purposes of this book, either MatLAB or Octave can be used. We have created a website for the codes used in this book, where all MatLAB/Octave codes from the text can be downloaded. We have also posted Python versions of the codes.Scientific Computing for Scientists and Engineers covers:
An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems;
Scientific computing fundamentals like floating point representation of numbers and convergence;
Analysis of accuracy and efficiency;
Simple programming examples in MatLAB to illustrate the algorithms and to solve real life problems;
Exercises to reinforce all topics.Preface
1 Introduction
2 Computer representation of numbers and roundoff error
3 Solving linear systems of equations
4 Finite difference methods
5 Solving nonlinear equations
6 Accuracy in solving linear systems
7 Eigenvalues and eigenvectors
8 Fitting curves to data
9 Numerical integration
10 Initial value ODEs
A Getting started with Octave and MatLAB