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

2+2=5, How could 2+2 will be Equal to 5

How could 2+2 will be Equal to 5

Geometry, prove angle MJL is congruent to angle KNL

prove angle MJL is congruent to angle KNL

Linear equation, tens digit of a 2-digit number is twice its unit digit. If...

tens digit of a 2-digit number is twice its unit digit. If the sum of the digit is 12, find the number.

SOLID MENSURATION, The base of an isosceles triangle and the altitude drawn...

The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18cm and 15cm, respectively. Find the lengths of the sides of the triangle.

Function to convert a complex number in algebraic form, Go back to the com...

Go back to the complex numbers code in Figures 50 and 51 of your notes. Add code fragments to handle the following: 1. A function for adding two complex numbers given in algeb

Matrices, how to find inverse of matrix

how to find inverse of matrix

Calculate the linear equation, Calculate the linear equation: Example...

Calculate the linear equation: Example: Solve the equation 4x + 3 = 19 by transposing. Solution: Step 1. Transpose the 3 from the left-hand to the right-hand si

Relative measures of dispersion-illustration, Illustration 2 In a ...

Illustration 2 In a described farm located in the UK the average salary of the employees is £ 3500 along with a standard deviation of £150 The similar firm has a local

Show that 3cos-4cos3 = 0, If sin? =  1/2 , show that 3cos?-4cos 3 ? = 0. ...

If sin? =  1/2 , show that 3cos?-4cos 3 ? = 0. Ans:    Sin ? = ½ ⇒ ? = 30 o Substituting in place of ? =30 o . We get 0.

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