{"product_id":"9780387965161","title":"Power Series from a Computational Point of View","description":"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.","brand":"Kennan T. Smith","offers":[{"title":"Default Title","offer_id":45770291675454,"sku":"9780387965161","price":3012.78,"currency_code":"ZAR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9780387965161_251b5c9b-8dcb-45e9-914b-6549ebcb8602.jpg?v=1707250628","url":"https:\/\/exclusivebooks.co.za\/products\/9780387965161","provider":"Exclusive Books Online","version":"1.0","type":"link"}