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

Find out the total number people and the total number car, A national park ...

A national park remains track of how many people per car enter the park. Today, 57 cars had 4 people, 61 cars had 2 people, 9 cars had 1 person, and 5 cars had 5 people. What is th

Progressions, The sum of the series 1+1/2+1/4+......is

The sum of the series 1+1/2+1/4+......is

Application of statistics-human resource management, Human resource managem...

Human resource management Statistics may be utilized in efficient employ of human resources for example we may provide questionnaires to workers to find out where the manageme

Give introduction to pythagorean theorem, Give Introduction to Pythagorean ...

Give Introduction to Pythagorean Theorem ? The Pythagorean Theorem says that for any right triangle: a 2 + b 2 = c 2 , where c is the hypotenuse, and a and b are the legs. T

Linear equation, The sum of the digit number is 7. If the digits are revers...

The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number

Show line graphs and histograms, Q. Show Line graphs and Histograms? A...

Q. Show Line graphs and Histograms? Ans. Line graphs are closely related to histograms. Look at the graph below. It shows the line graph of the example above but also in

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