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

Formulas, A house painter uses the formula, c = $110.50 + $39.50h, where c ...

A house painter uses the formula, c = $110.50 + $39.50h, where c is the total cost and h is the number of hours he works, to determine how much he charges his customers. How much s

Volume of grains in the silo , The volume of grains in a silo at a particul...

The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the silo from first princ

Example of making connections of a child with maths, After a lot of effort,...

After a lot of effort, 8-year-old Hari worked out 2 x 88 = 176. When asked to say what 2 x 89 was, after a lot of hard work, he produced the answer 178. How would you help him to r

If pth term of ap is q and qth term is p. p.t its nth term, If the p th te...

If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans:    APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p

Determine the price paid for a land, A parcel of land, value $250,000 is so...

A parcel of land, value $250,000 is sold to an investor who signs a contract agreeing to pay a deposit of $25,000 followed by equal quarterly payments for as long as necessary, wit

Decimals, how do you turn a fraction into a decimals

how do you turn a fraction into a decimals

Lower than average, A local police precinct has seen a recent enhance in th...

A local police precinct has seen a recent enhance in the number of complaints filed regarding how officers are interacting with the public. Before addressing the issue, the command

Children learn maths from each other, Children Learn From Each Other :  Th...

Children Learn From Each Other :  The other day I had gone to a, nearby school to observe the teacher-children interaction. The children were working on a problem that the teacher

Marketing management, successful marketing research relies on accurate iden...

successful marketing research relies on accurate identification of the research objectives. Critically discuss when setting relevant research objectives, drawing on marketing theor

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