2.4-2.5 - Sections 2.4-2.5 Existence and uniqueness Theorem 2.4.1 is a simplified version of Theorem 2.4.2 Major difference being existence and

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Sections 2.4-2.5 Existence and uniqueness Theorem 2.4.1 is a simplifed version oF Theorem 2.4.2. Major di±erence being: existence and uniqueness is sort oF global For Theorem 2.4.1, but only guaranteed locally on a fxed interval ( t 0 h,t 0 + h )( h unspecifed) For Theorem 2.4.2. This is why nonlinear equations tend to be harder to analyze than linear equations in general. And linear equations will be our major concern For the remaining oF this semester. You can glance through page 69, it’s not that important. Pay attention to the remark Following Theorem 2.4.2, which states that existence is guaranteed locally on the basis oF the continuity oF f alone. Also pay attention to item 3 oF the summary on page 75. ²ollow these steps to approach an initial value problem dy dt = f ( t,y ) ,y ( t 0 )= y 0 . Step 1: Determine the interval oF continuity For f and ∂f ∂y . (Recall the defnition!) Step 2: Check where the given point ( t 0 ,y 0 ) lies. Dependent on the di±erent scenarios, you will draw di±erent conclusions.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/13/2012 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.

Page1 / 2

2.4-2.5 - Sections 2.4-2.5 Existence and uniqueness Theorem 2.4.1 is a simplified version of Theorem 2.4.2 Major difference being existence and

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online