Unformatted text preview: [5 marks] (c) Use the appropriate series expansion about the point x = 0 to determine two independent solutions to (1). You only need to determine the f rst three non-zero terms in each case. [35 marks] 2. Apply the method of separation of variables to determine the solution to the one dimensional heat equation with the following homogeneous Neumann boundary conditions: ∂ u ∂ t = ∂ 2 u ∂ x 2 , < x < π , t > BC : ∂ u ∂ x (0 ,t ) = 0 = ∂ u ∂ x ( π ,t ) IC : u ( x, 0) = 1 [30 marks] 1...
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- Fall '08
- Math, order differential equation, Neumann boundary condition, irregular singular points