دانلود کتاب تحلیل عددی و محاسبات علمی

The fundamental law of computer science: As machines become more powerful, the e_ciency of algorithms grows more important, not less. Nick Trefethen Surely [one imagines], we compute only when everything else fails, when math- ematical theory cannot deliver an answer in a comprehensive, pristine form and thus we are compelled to throw a problem onto a number-crunching computer and produce boring numbers by boring calculations. This, I believe, is nonsense. Arieh Iserles This book represents the numerical analysis course I regularly teach at Rose- Hulman Institute of Technology, which is taken as an elective course by juniors and seniors majoring in computational science, computer science, mathematics, physics, and a variety of engineering disciplines. The students will have had three terms of calculus as well as di_erential equations with matrix algebra, but may not have had any real programming experience. The key features of my approach have been an immediate immersion in numerical methods, delaying a discussion of computer arithmetic and round-o_ error until students have gained some experience using numerical algorithms; a presentation of numerical linear algebra that more closely mirrors how it is actually implemented and used in modern practice; and an emphasis on analysis while still bringing out the practical hardware and software issues involved in modern scienti_c computing. In addition, optional MATLAB R subsections allow for students to teach themselves basic programming while experimenting with the methods of the section. I want students to come away with a strong understanding of the mathematical underpinning of modern scienti_c computing{and also be prepared to apply that knowledge in a practical way, whether they are doing the coding themselves or, more likely, using what they’ve learned to get better performance out of the software packages that are common in their field.