An Introduction to Computational Science

Description

This textbook provides an introduction to the growing interdisciplinary field of computational science. It combines a foundational development of numerical methods with a variety of illustrative applications spread across numerous areas of science and engineering. The intended audience is the undergraduate who has completed introductory coursework in mathematics and computer science. Students gain computational acuity by authoring their own numerical routines and by practicing with numerical methods as they solve computational models. This education encourages students to learn the importance of answering: How expensive is a calculation, how trustworthy is a calculation, and how might we model a problem to apply a desired numerical method? The text is written in two parts. Part I provides a succinct, one-term inauguration into the primary routines on which a further study of computational science rests. The material is organized so that the transition to computational science from coursework in calculus, differential equations, and linear algebra is natural. Beyond the mathematical and computational content of Part I, students gain proficiency with elemental programming constructs and visualization, which are presented in MATLAB syntax. The focus of Part II is modeling, wherein students build computational models, compute solutions, and report their findings. The models purposely intersect numerous areas of science and engineering to demonstrate the pervasive role played by computational science. Front Matter ....Pages i-xvi Front Matter ....Pages 1-1 Solving Single Variable Equations (Allen Holder, Joseph Eichholz)....Pages 3-31 Solving Systems of Equations (Allen Holder, Joseph Eichholz)....Pages 33-65 Approximation (Allen Holder, Joseph Eichholz)....Pages 67-121 Optimization (Allen Holder, Joseph Eichholz)....Pages 123-189 Ordinary Differential Equations (Allen Holder, Joseph Eichholz)....Pages 191-235 Stochastic Methods and Simulation (Allen Holder, Joseph Eichholz)....Pages 237-268 Computing Considerations (Allen Holder, Joseph Eichholz)....Pages 269-303 Front Matter ....Pages 305-308 Modeling with Matrices (Allen Holder, Joseph Eichholz)....Pages 309-353 Modeling with Ordinary Differential Equations (Allen Holder, Joseph Eichholz)....Pages 355-376 Modeling with Delay Differential Equations (Allen Holder, Joseph Eichholz)....Pages 377-387 Partial Differential Equations (Allen Holder, Joseph Eichholz)....Pages 389-402 Modeling with Optimization and Simulation (Allen Holder, Joseph Eichholz)....Pages 403-430 Regression Modeling (Allen Holder, Joseph Eichholz)....Pages 431-445 Back Matter ....Pages 447-470