Solving Question 2: Separation of Variables

In summary, the conversation is about a homework question involving separation of variables with three variables. The person is unsure how to apply this concept and has attempted to use a solution form of u = T(t)R(r)K(theta) but has not been successful. They mention a constant lambda and are unsure how to link it with the constant omega in the solution. They also mention having difficulty with algebra.
  • #1
FunkyDwarf
489
0

Homework Statement


Not sure if you guys can get this link
http://www.maths.uwa.edu.au/devsite/Units/math3341-s1-2008-crawley/assignments-solutions/Sheet%204
should be able to.
Question is question two.

Homework Equations


Not many besides the general separation of solutions sort of thing but I am a bit unsure how to apply that with three variables.

The Attempt at a Solution


In previous examples we had some symmetry that meant we could knock out say the theta dependence on something but I am not sure here. I tried letting u = T(t)R(r)K(theta) and just fiddling a bit but came up trumps as i tried to fit the R function to a solution of the bessel function which we expect from what's given. I get the T(t) function as a sin + cos solution with argument lambda*c where -lambda squared is the constant i assign to the two sets of functions in separation of variables. Thats sort of right i guess, not sure where the plus or minus comes from but then again i don't know how they get omega. I think I am on the right track looking for the solution form of u i gave I am just not sure how to follow through nor how to link the two constants that arise from applying separation of variables twice.

Hope that made sense :S
Cheers
-G

EDIT: Nevermind, I am retarded and can't read my own notes/do algebra properly. Mods can delete if you want.
 
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Related to Solving Question 2: Separation of Variables

1. What is separation of variables?

Separation of variables is a method used to solve differential equations. It involves separating the dependent variables in the equation and solving for each variable separately.

2. When is separation of variables used?

Separation of variables is commonly used in physics and engineering to solve problems involving systems with multiple variables. It is also used in mathematical methods such as Fourier series and Laplace transforms.

3. How does separation of variables work?

The method of separation of variables involves isolating the dependent variables in an equation, usually through algebraic manipulation, and then solving for each variable separately. This is done by considering each variable as a function of a single independent variable, and then finding the general solution for each variable.

4. What are the advantages of using separation of variables?

One advantage of separation of variables is that it can simplify the process of solving complex differential equations. By separating the variables, the equation can be broken down into smaller, more manageable parts. It is also a useful method for solving equations that cannot be solved using other techniques.

5. Are there any limitations to using separation of variables?

While separation of variables is a powerful tool, it can only be used on certain types of differential equations. It is most effective for equations that are linear and homogeneous, and may not work for equations with non-constant coefficients or nonlinear terms. In addition, it may not always provide the most accurate solution, as it relies on making certain assumptions about the equation.

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