Linearize poisson-boltzmann equation

  • Thread starter Thread starter barcafan
  • Start date Start date
  • Tags Tags
    Linearize
barcafan
Messages
4
Reaction score
0

Homework Statement


Need to linearize the poisson-boltzmann equation to be used later in the problem. I simply have never linearized an equation and searching google didn't really help me understand.

Homework Equations


http://img215.imageshack.us/img215/2149/eqnq.jpg

The Attempt at a Solution


Just need an idea of how to go about this in order to complete the question.
 
Last edited by a moderator:
Physics news on Phys.org
To "linearize" means take an expansion to its linear term. I am still stuck on this. Any help would be great.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Isomorphisms preserve linear independence
Replies
2
Views
2K
Calc: Find a definite integral for the mass
Replies
10
Views
4K
Calculating Variance of Y using Poisson and Binomial Distributions
Replies
2
Views
1K
Linear Differential equation problem
Replies
3
Views
1K
Linear Differential Equations and Linear Operator Problem
Replies
4
Views
2K
How would you explain to a dummy how a diff. eq. is linear?
Replies
6
Views
2K
Solving a Second Order Non-Linear PDE with Undetermined Coefficients
Replies
2
Views
1K
Solving a system of linear equations
Replies
28
Views
3K
Show: Elementary row operations don't affect solution sets
Replies
12
Views
7K
[LinAlg] Show that T:C[a,b] -> R is a linear transformation
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top