Theorem of continuous functions, Mathematics

Assignment Help:

Consider the subsequent IVP.

y' = f(t,y) ,        y(t0) = y0

If f(t,y) and ∂f/∂y are continuous functions in several rectangle a < t < b, g < y  < d, containing the point  (to, yo) then there is a unique solution to the IVP in some interval to - h < t < to + h which is included in a < t < b.

That's it.  Unlike the first theorem, this one cannot really be used to find an interval of validity. Thus, we will know that a unique solution exists if the conditions of the theorem are met, but we will in fact need the solution in order to find out its interval of validity.  Remember as well that for non-linear differential equations it emerges that the value of y0 may influence the interval of validity.

Here is an illustration of the problems that can happen when the conditions of this theorem are not met.


Related Discussions:- Theorem of continuous functions

Covariance, Covariance The variance is a measure of the variabil...

Covariance The variance is a measure of the variability or dispersion in a variable or data set. A measure of the variability of one variable (or data set) in relatio

Describe multiplication and division equations, Describe Multiplication and...

Describe Multiplication and Division Equations? Multiplication Equations :  To solve multiplication equations, divide both sides of the equation by the number being multiplie

Calculus, sin(xy)+x=5y Find the derivative.

sin(xy)+x=5y Find the derivative.

MAT201, #There is a balance of $1,234 and this person receive a refund chec...

#There is a balance of $1,234 and this person receive a refund check in the amount of $25 with her paycheck that was deposited into her account for $1500 which made her balance $27

Hierarchical multiple regression, A group of children who lived near a lead...

A group of children who lived near a lead smelter in El Paso, Texas, were identified and their blood levels of lead were measured. An exposed group of 46 children were identified w

Fundamental theorem of calculus, Fundamental Theorem of Calculus, Part I ...

Fundamental Theorem of Calculus, Part I As noted through the title above it is only the first part to the Fundamental Theorem of Calculus. The first part of this theorem us

Statistics, find the number of ways 17 employees can b chosen from 327

find the number of ways 17 employees can b chosen from 327

What are the properties of normal distribution, What are the properties of ...

What are the properties of Normal distribution? The normal curve is symmetrical when p=q or p≈q The normal curve is a single peaked curve The normal curve is asymptotic t

Determine the direction cosines and direction angles, Determine or find out...

Determine or find out the direction cosines and direction angles for a = (2, 1, -4) Solution We will require the magnitude of the vector. ||a|| = √ (4+1+16) = √ (21)

Trigonometry.., if b+c=3a then the value of cotB/2.cotC/2 is equal to

if b+c=3a then the value of cotB/2.cotC/2 is equal to

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd