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

Function, f(x)=x^2-5x+6, determine inverse of f(x)!

f(x)=x^2-5x+6, determine inverse of f(x)!

How to subtract fractions with the same denominators, Q. How to Subtract fr...

Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul

Math, how to compare fractions

how to compare fractions

Linear probability model, Pepsi:               A dummy variable where 1 den...

Pepsi:               A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise Price_P:           The price of a 2-liter bottle of Pepsi at the time

The rank correlation coefficient (r), The Rank Correlation Coefficient (R) ...

The Rank Correlation Coefficient (R) Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among tw

Domain and range, Taxable income Tax rate 0 - $18,200 0% $18,201- $37,000 1...

Taxable income Tax rate 0 - $18,200 0% $18,201- $37,000 19% $37,001 - $80,000 32.5% $80,001- $180,000 37% $180,001 and over 45% if this is graphed as a step fuction graph whats t

Play and learn maths, PLAY AND LEARN :  Children can learn many basic math...

PLAY AND LEARN :  Children can learn many basic mathematical concepts through games. They enjoy Mathematical concepts can be playing within familiar contexts. Their games also gen

Matrices, what are eigen values

what are eigen values

Function, definition and examples and types

definition and examples and types

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