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Lecture 14

MATH 417 Lecture 14: Day 14
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Department
Mathematics
Course
MATH 417
Professor
All Professors
Semester
Spring

Description
Section 5 L Initial value problems for ODE an IVP of the form ve Example y t +1 y lo D (to) stems Review of basic theory Goal unders-and conditions that guarantee stabilty and well posedness of IVP tweaking the a bit will not change the results -Defn t, y) satisnes a Lipschutz Coman hon in the variable y the set D e R" if th is Loo ,t. Note Assume tal f y) is continuously differentiable in y, w Then D is convex, f is Lipschite on D Cowwex net convex assume that f is cont. Lipscute in y on D. Then the IVP is uniquely solvable for Section 5 L Initial value problems for ODE an IVP of the form ve Example y t +1 y lo D (to) stems Review of basic theory Goal unders-and conditions that guarantee stabilty and well posedness of IVP tweaking the a bit will not change the results -Defn t, y) satisnes a Lipschutz Coman hon in the variable y the set D e R" if th is Loo ,t. Note Assume tal f y) is continuously differentiable in y, w Then D is convex, f is Lipschite on D Cowwex net convex assume that f is cont. Lipscute in y on D. Then the IVP is uniquely solvable forContinuous Lipschite Sin y Sin MVT Some 5 (y Thus, f is C Lipschitz n y and the IVP y's siny-t y (a) ou has a unigue solution any a, ok a well-posed it 1) There is a unique y (t) and There are constants ani k 3t. any whenever St s continuous V a t b and E the perturbed IVP dt 2(a)
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