Initial conditions and boundary conditions, Mathematics

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.

Posted Date: 9/13/2012 7:46:26 AM | Location : United States







Related Discussions:- Initial conditions and boundary conditions, Assignment Help, Ask Question on Initial conditions and boundary conditions, Get Answer, Expert's Help, Initial conditions and boundary conditions Discussions

Write discussion on Initial conditions and boundary conditions
Your posts are moderated
Related Questions

At an office, the manager earns 40% more than a first year employees. The employee earns what fraction of the manager earnings?

Applications of derivatives : At last, let's not forget about our applications of derivatives. Example    Assume that the amount of air in a balloon at any time t is specified

00000000110 write in scientific notation

Marci filled her car's gas tank on Monday, and the odometer read 32,461.3 miles. On Friday while the car's odometer read 32,659.7 miles and she filled the car's tank again. It will

when i couulate the formula f 64 divided by 65 how do i do this


what is slope


a. Cassie has seven skirts, five blouses, and ten pairs of shoes. How many possible outfits can she wear? b. Cassie decides that four of her skirts should not be worn to school.