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1-D EQUATIONS

• Heat Equation
• Step 0: Introduce a change of variable such that the new unknown has new homogeneous boundary conditions
• Step 1: Determine the appropriate orthogonal basis of eigen functions
• Step 2: Write the unknown as a linear combination of the eigenfucntion and substitute into the DEqn
• Step 3: Expand the rhs in terms of orthogonal basis and equate coefficients to find an equation for Cn(t)
• Step 4: Expand the initial condition in terms of eigen function to obtain an IC for Cn(t)
• Step 5: Solve for Cn(t)
• Step 6: Write the solution
• Wave Equation
• Step 0
• Step 1
• Step 2
• Step 3
• Step 4
• Step 5
• Step 6

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