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Numerical Analysis, 2nd edition

 
지은이 : Scheid
출판사 : McGraw-Hill
ISBN : 0070552215
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 



If you want top grades and thorough understanding of numerical analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how you뭨e doing.) Famous for their clarity, wealth of illustrations and examples뾞nd lack of dreary minutiae뾖chaum뭩 Outlines have sold more than 30 million copies worldwide. This guide will show you why!

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide


What Is Numerical Analysis? The Collocation Polynomial.


Finite Differences.


Factorial Polynomials.


Summation.


The Newton Formula.


Operators and Collocation Polynomials.


Unequally-Spaced Arguments.


Splines.


Osculating Polynomials.


The Taylor Polynomial.


Interpolation.


Numerical Differentiation.


Numerical Integration.


Gaussian Integration.


Singular Integrals.


Sums and Series.


Difference Equations.


Differential Equations.


Differential Problems of Higher Order.


Least-Squares Polynomial Approximation.


Min-Max Polynomial Approximation.


Approximation By Rational Functions.


Trigonometric Approximation.


Nonlinear Algebra.


Linear Systems.


Linear Programming.


Overdetermined Systems.


Boundary Value Problems.


Monte Carlo Methods.


"
Looking for a supplementary text for my Numerical Analysis course, I had my students pick up this text- I have found that other Outlines give a lot of excellent worked examples and provide good summaries- Not this text. If you are a beginning student, go get yourself a real text (I would highly recommend Burden and Faires, or the new text by Tim Sauer). This text offers little to no insight into the algorithms or the analysis, and spends way too much space on one dimensional interpolation problems. If you're simply looking for summaries of algorithms and practical advice on implementation, a much better text is the "Numerical Recipes" books. In summary, I'm not sure who the audience is for this book- There are many, much better, options out there. "

"I've had this outline for years. My only complaint about Schaum's is that sometimes their answers are not in enough detail and their indexes are skimpy. Outlines live and die based on their detailed solutions to solved problems and their index. This particular outline is excellent. All the basic numerical methods are presented with the standard format: theory, solved problems, problems with answers. What could be added, either here, or in future text (separate) would be an optimization methods section: differential search, Hooke & Jeeves min./max. search and the Golden Mean search. The later, especially, is easy to program into Excel so it would useful to show the pitfalls in these methods. All in all, this is a text you want in your engineering collection for those problems that require detailed analysis.

"

"
Scheid gives us a broad range of methods in numerical analysis. The 846 problems can certainly keep you busy. Plus, the book is also useful as a concise summary of the most common and useful methods in the field. Students of maths, physical sciences and engineering should already be familiar with several of the methods. Like performing numerical integration or differentiation, because these mathematical steps are the fundamental calculus operations, and those fields all use these. So too is finding roots of equations, and for this, there is a chapter on Newton's method. Which tends to assume that you have an analytic form for the function and for its derivative, where you want the roots of the function.

The book also supports statistics. Unsurprisingly, since statistics is inherently about numerical evaluations. So we have least squares methods of curve fitting, and Monte Carlo methods, where the latter can also be used for numerical integration.

Ironically, while the Monte Carlo is described, the book is somewhat weak on methods for generating random numbers. And how to measure the "randomness" of such algorithms. For this, I suggest you turn to "The Art of Computer Programming" by Donald Knuth. He has an excellent length discussion on the subject.

Curve fitting is also discussed in a chapter on splines. You may already be acquainted with these, in the context of graphics packages which can fit B splines to data points. "
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