Initial conditions and boundary conditions, Mathematics

Assignment Help:

Initial Conditions and Boundary Conditions

In many problems on integration, an initial condition (y = y0 when x = 0) or a boundary condition (y = y0 when x = x0 ) is given which uniquely determines the constant of integration. As a result of the unique determination of 'c', a specific curve can be singled out from a family of curves.

Example 

For the boundary condition, y = 15 when x = 2, the integral y =  ∫4dx is evaluated as follows:

y =  ∫4dx = 4x + c

Substituting, y = 15, when x = 2

15 = 4(2) + c or c  = 7

y = 4x + 7

Note that even though 'c' is specified, ∫4dx remains an indefinite integral because xn is unspecified. Thus, the integral 4x + 7 can assume an infinite number of possible values.


Related Discussions:- Initial conditions and boundary conditions

Eometry constructions, construct an isosceles triangle ABC when:base BC is ...

construct an isosceles triangle ABC when:base BC is 6.2 and altitude a.a

How many total inches of wood does he have, Eduardo is merging two 6-inch p...

Eduardo is merging two 6-inch pieces of wood with a piece in which measures 4 inches. How many total inches of wood does he have? This problem translates to the expression 6 ×

Triangle Treat, Triangle Treat is the page name. I don''t know the answer f...

Triangle Treat is the page name. I don''t know the answer for it, can someone give it to me?

Mensuration, How do mensuration relate to the real life issues

How do mensuration relate to the real life issues

Alternating series test - sequences and series, Alternating Series Test - S...

Alternating Series Test - Sequences and Series The final two tests that we looked at for series convergence has needed that all the terms in the series be positive.  Actually t

Probability, a die was rooled 500 times and number of times 4 came up was n...

a die was rooled 500 times and number of times 4 came up was noted if the imperical probability calculated from this information 7_10

Matrices, suppose you a business owner and selling cloth. the following rep...

suppose you a business owner and selling cloth. the following represents the number of items sold and the cost for each item. use matrix operation to determine the total revenue ov

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