CALCULUS Understanding Its Concepts and Methods

Initial value problem

Given two numbers
*a*
and
*b*,
and a function
*f*(*x*,*y*)
of two variables, the initial value problem is
to find an interval
*I*
containing
*a*,
and a function
*g*(*x*)
defined on
*I*,
such that
*g*(*a*) = *b*
andfor
all
*x*
in
*I*.
It is called an initial value problem because we think of
*x*
as starting at
*a*,
so we are given the initial value
*b*
of the function
*g*
that we are trying to find.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.