WorkSheet.Week7 - conserved. What about the zero...

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MATH 2930 Summer 2009 Worksheet For Discussion on 24th July Topics covered: Heat And Wave Equations Ashivni Shekhawat 1. Derive the general form of the solution for the following heat equation for zero temperature and zero flux boundary conditions u t ( x,t ) = ku xx ( x,t ) (1) 2. Specialize the solution found in the previous question for u ( x, 0) = sin( x ) for both kinds of boundary conditions. 3. If the thermal energy per unit volume for a substance is proportional to its temperature then prove that the net thermal energy stored in a rod with zero flux boundary conditions remains
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Unformatted text preview: conserved. What about the zero temperature case? 4. Verify the dAlembert solution to the standard wave equation with zero initial velocity. 5. Consider a standard wave equation with a = 1, zero initial velocity and the following initial displacement u ( x, 0) = < x < L/ 4 x-L/ 4 L/ 4 < x < L/ 2 3 L/ 4-x L/ 2 < x < 3 L/ 4 3 L/ 4 < x < L (2) Draw sketches of the wave at representative times in the future based on your understanding of dAlemberts solution. 1...
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).

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