Sadly, most of the “better” (read understandable) texts in NA date back to the late 1980s, when there was no internet (there were 50 websites in 1992 when Clinton took office). I teach computers to do math, so– disclaimer– I’m on the applied, not pure math side of NA. Yes, the applications today are way beyond what they were in 1987, and we finally have an NA text that covers not only the basics, but MANY cutting edge areas– like fractals– that weren’t even taken seriously back then. I am an undergraduate student in Applied Mathematics who just used this text in a course on Numerical Analysis in one of the last courses I’m taking before moving on to grad school for Computer Science. Oh, and yes, you do learn analysis here too, including the proofs and pure math sides if your track is math. Your email address will not be published. Next come two-point boundary value problems and the numerical solution of partial differential equations (PDEs). You are about to access "Numerical Methods". History note for a few emailers: Thanks for reminding me that 1987 is “recent” compared to many NA techniques that adapt Euler to algorithmic form– by “recent” I also mean that these authors use examples like web surfing and Google’s (secret sauce) analytics. Author : Anne Greenbaum & Timothy P. ChartieFile Size : 16.9 MBLast Checked : 12:24:06am 2020/11/27Status : AVAILABLE As a previous reviewer noted, this text really goes out of its way to motivate the reader with a bit of a firehose approach to introducing all the different ways in which this material can be applied to computing problems, from graphics processing to machining to airfoil simulation to web search. You won’t find any of these applications in most NA texts– the present work is a gem, and unique in being up to date on many NOW applications, including several beyond the traditional physics and engineering examples. Who uses computers to “guess” at difficult PDE solutions other than astrophysicists? It is also assumed that they have had a linear algebra course. Acknowledgments. Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. There isn’t much complexity analysis, and what little there is should not be challenging if you have any background in more general algorithmic analysis/discrete math. The mathematics is completely rigorous and I applaud the authors for doing such a marvelous job.”―Michele Benzi, Emory University“Filled with polished details and a plethora of examples and illustrations, this ambitious and substantial text touches every standard topic of numerical analysis. The harder part is the error analysis, and you really need to slow down, write it all down and figure out what’s happening before you move on. The authors have done a huge amount of work and produced a major textbook for this subject.”―Lloyd N. Trefethen, University of Oxford. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. We have attempted to draw on the popularity of mathematical modeling in a variety of new applications, such as movie animation and information retrieval, to demonstrate the importance of numerical methods, not just in engineering and scientific computing, but in many other areas as well. The next chapters contain more standard topics in numerical analysis— solution of a single nonlinear equation in one unknown, floating-point arithmetic, conditioning of problems and stability of algorithms, solution of linear systems and least squares problems, and polynomial and piecewise polynomial interpolation.Numerical Methods, Most of this material is standard, but we do include some recent results about the efficacy of polynomial interpolation when the interpolation points are Chebyshev points. If you’re a prof– don’t you want to orient your students via examples that are being used right now? Try Neurologists modeling cognition as Dynamic Systems! This includes a short section on solving systems of nonlinear equations, which should be an easy generalization of the material on solving a single nonlinear equation, assuming that the students have had multivariable calculus. There are two distinct sides to NA– pure, as a way of defining formal proofs with “results” as much as methods, and applied– solving problems, especially using algorithms, via close approximation, guessing, brute force, iteration, and other “cheats.” The problem with many of the classic NA texts is that “applied” usually means, you guessed it, physics and engineering. If you’re in a course being taught by a professor, the professor will grade and provide feedback and answer homework questions. (2012) Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms.Princeton University Press. We also thank Danny Kaplan of Macalester College for using an early version of the text in his classes there, and we thank Dan Goldman for information about the use of numerical methods in special effects. Downsides: This may or may not be a downside depending upon what you’re looking for, but this is very much a university textbook.

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