AMATH350 Study Guide - Final Guide: Partial Derivative
3 May 2016
School
Department
Course
Professor
Document Summary
For a real number x and a positive value , the set of numbers x satisfying x0 < x < x0 + is called an open interval centered at x0. The general rst-order ode is y = f (x, y), y(x0) = y0. Suppose that f (x, y) is a continuous function de ned in some region. R = {(x, y) : x0 < x < x0 + , y0 < y < y0 + } y = x y + 1, y(1) = 2. containing the point (x0, y0). 1 (possibly smaller than ) so that a solution y = f (x) to (*) is de ned for x0 1 < x < x0 + 1. Suppose that both f (x, y) and f. Y (x, y) are continuous functions de ned on a re- gion r as in theorem 1. In this case, both the function f (x, y) = x y +1 and its partial derivative f.
