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

Construction , construct of tangents a circle from an external point when ...

construct of tangents a circle from an external point when its centre is not known

Calculus with matrices, Calculus with Matrices There actually isn't a ...

Calculus with Matrices There actually isn't a whole lot to it other than to just ensure that we can deal along with calculus with matrices. Firstly, to this point we've onl

Direction cosines - vector, Direction Cosines This application of the ...

Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.

How much can they deduct from childcare expenses, A family may deduct 24% o...

A family may deduct 24% of their childcare expenses from their income tax owed. If a family had $1,345 in childcare expenses, how much can they deduct? Find out 24% of $1,345 b

Summation notation, SUMMATION NOTATION Under this section we require to...

SUMMATION NOTATION Under this section we require to do a brief review of summation notation or sigma notation.  We will start out with two integers, n and m, along with n a

Find the least and greatest number of coins, Marc goes to the store with ex...

Marc goes to the store with exactly $1 in change. He has at least one of each coin less than a half-dollar coin, but he does not have a half-dollar coin. a. What is the least nu

Rectilinear figures, Q1- different types of rectilinear figures? Q2- interi...

Q1- different types of rectilinear figures? Q2- interior and exterior angles of the polygon? Q3-relation between interior and exterior angles of polygons? Q4- properties of any fiv

Video games, Should video game companies continue to alter their products t...

Should video game companies continue to alter their products to include other functions, such as e-mail

Real and distinct roots, Now we start solving constant linear, coefficient ...

Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon

Curve tracing, Trace the curve (x/a)^3/2+(y/b)^2/3=1

Trace the curve (x/a)^3/2+(y/b)^2/3=1

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