Power Series from a Computational Point of View (Universitext), Smith, K.T. Kindle

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Power Series from a Computational Point of View (Universitext)


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Author: Smith, K.T.
ISBN: 9780387965161
At the end of the typical one quarter course on power series the students lack the means to decide 2 whether 1/(1+x ) has an expansion around any point ~ 0, or the tangent has an expansion anywhere and the means to evaluate and predict errors. In using power series for computation the main problems are: 1) To predict a priori the number N of terms needed to do the computation with a specified accuracy; and 2) To find the coefficients aO, ?.? ,a ? N These are the problems addressed in the book. Typical computations envisioned are: -6 calculate with error ~ 10 the integrals If/2 J (If/2-x)tan x dx o or the solution to the differential equation 2 y"+(sin x)Y+x y = 0, y(O) = 0, y(O) 1, on the interval 0 ~ x ~ 1. This computational point of view may seem narrow, but, in fact, such computations require the understa- ing and use of many of the important theorems of ele­ mentary analytic function theory: Cauchys Integral Theorem, Cauchys Inequalities, Unique Continuation, Analytic Continuation and the Monodromy Theorem, etc. The computations provide an effective motivation for learning the theorems and a sound basis for understa- ing them. To other scientists the rationale for the vi computational point of view might be the need for ef- cient accurate calculation; to mathematicians it is the motivation for learning theorems and the practice with inequalities, ~s, os, and Ns.

Title: Power Series from a Computational Point of ...

Publisher: Springer-Verlag

Publication Date: 1987

Binding: Hardcover

Book Condition:UsedGood



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Super share
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REP Added dude!
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I got 5 on this great share.
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very thanks, looks good, reps added.
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+5 Rep added and thanks for the post.
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Anyway, have you guys scanned it with virustotal?
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