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

Estimation of difference among two means-illustration, A comparison of the ...

A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and

Level curves or contour curves - three dimensional space, Level Curves or C...

Level Curves or Contour Curves Another topic that we should look at is that of level curves or also known as contour curves. The level curves of the function z = f (x, y) are t

Shortcomng methods for teaching hto in maths, 1.What are the strengths and ...

1.What are the strengths and shortcomings of the methods of teaching H T 0 in Examples 1 and 2? 2. a) Think of another activity for getting children to practise H T 0, especia

Piecewise, x=±4, if -2 = y =0 x=±2, if -2 = y = 0

x=±4, if -2 = y =0 x=±2, if -2 = y = 0

Error analysis: describle and correct the error in plotting, to plot (5,-4)...

to plot (5,-4), start at (0,0) and move 5 units left and 4 units down

Concrete operational stage, Concrete Operational Stage :  Piaget describes...

Concrete Operational Stage :  Piaget describes a five-year-old boy playing with a collection of pebbles. First, he laid them in a line and counted along the line from left to righ

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