Solving Question 2: Separation of Variables

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SUMMARY

The discussion focuses on solving a specific problem from a mathematics assignment involving the separation of variables in a three-variable context. The user attempts to apply the method by letting u = T(t)R(r)K(theta) but struggles with the Bessel function solution and the constants arising from the separation process. The user expresses uncertainty about linking the constants and the derivation of omega. Ultimately, the user acknowledges a misunderstanding in their algebraic approach.

PREREQUISITES
  • Understanding of separation of variables in partial differential equations
  • Familiarity with Bessel functions and their applications
  • Knowledge of trigonometric functions and their properties
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the application of separation of variables in three-dimensional problems
  • Learn about Bessel functions and their role in solving differential equations
  • Review trigonometric identities and their implications in mathematical solutions
  • Practice algebraic techniques for linking constants in differential equations
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Students studying advanced mathematics, particularly those tackling partial differential equations and separation of variables, as well as educators seeking to clarify these concepts for their students.

FunkyDwarf
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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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