Titlebook: Lectures on Numerical Mathematics; Heinz Rutishauser,Martin Gutknecht Book 1990 Birkh?user Boston 1990 Approximation.Interpolation.calculu

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LAP

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Interpolation,Interpolation is the art of reading between the lines of a mathematical table. It can be used to express nonelementary functions approximately in terms of the four basic arithmetic operations, thus making them accessible to computer evaluation.

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Boundary Value Problems For Ordinary Differential Equations,For a differential equation of order ., or a system of differential equations whose orders add up to ., one needs . in order to single out one solution from among a family of ∞.. if these . conditions refer to a single point x., one speaks of an ., since — apart from singular cases — one has enough information to integrate away from x..

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Linear Equations and Inequalities,countless problems in applied mathematics ultimately — if only approximately — can be reduced to linear equations. Not surprisingly, therefore, interest in this problem has grown enormously in the computer age; what previously was viewed as tedious work has since become a legitimate and actively pursued area of mathematical research.(.)

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Approximation,ximate a given function .(.) on a (relatively large) interval. by . polynomial. Such an approximation polynomial, naturally, must be of a higher degree than in the case where .(.) is approximated by polynomial pieces.

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Initial Value Problems for Ordinary Differential Equations,lytical methods. Even when this is possible, it may not necessarily be useful. For example, the second-order differential equation with two initial conditions, . has the . solution . but when this formula is evaluated, say at the point x =.01, one obtains with 8-digit computation . which is no longer very accurate.

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Parabolic and Hyperbolic Partial Differential Equations,nd (x=0) the temperature is prescribed as a function .(.) of time. Let the thermal conductivity of the rod be .(.), the initial temperature be given as .(x), and let there be interior heat generation .(.) (cf. Fig. 11.1).