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Viac informácií o knihe Power Series from a Computational Point of View

• Parametre knihy
• Anotácia kniha
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Anotácia knihy

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: Cauchy's Integral Theorem, Cauchy's 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, o's, and N's.

Parametre knihy

Zaradenie knihy Knihy po anglicky Mathematics & science Mathematics Calculus & mathematical analysis

• Celý názov: Power Series from a Computational Point of View
• Autor: Kennan T. Smith
• Jazyk: Angličtina
• Väzba: Brožovaná
• Počet strán: 132
• EAN: 9780387965161
• ISBN: 0387965165
• ID: 06793868
• Nakladateľ: Springer, Berlin
• Hmotnosť: 229 g
• Rozmery: 235 × 155 × 7 mm
• Dátum vydania: 16. November 2012

Obľúbené z iného súdka

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