# hmk#2_s.pdf - ENM510 - Foundations of Engineering...

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ENM510-Foundations of Engineering Mathematics I(Homework#2)Fall Semester, 2020M. Carchidi———————————————————————————————————————Problem#1(12 points)We have seen in class that a general solution to the partial differential equation (PDE)T02wx,tx202wx,tt2for 0t, 0xLand the boundary conditions (BCs)w0,t0andwL,t0for 0t, iswx,tn1AncosntBnsinntnx(for arbitrary constantsAnandBn) withnxsinnx,nnLandnnT00.Using a similar set of steps that lead to this solution, determine a general solution to thePDET02wx,tx202wx,tt2for 0t, 0xLand the boundary conditions (BCs)wx,txx00andwL,t0for 0t.———————————————————————————————————————Problem#2(12 points)Using a similar set of steps as in Problem #1, determine a general solution to the PDET02wx,tx202wx,tt2for 0t, 0xLand the boundary conditions (BCs)w0,t0andwx,txxL0for 0t.———————————————————————————————————————
———————————————————————————————————————Problem#3(20 points)Using a similar set of steps as in Problem #1, determine a general solution to the PDE———————————————————————————————————————
Problem#4(12 points)Using a similar set of steps as in Problem #1, show that a general solution to the partialdifferential equation (PDE)Problem#5(12 points)
Using a similar set of steps as in Problem #4, determine a general solution to the PDE
Problem#6(12 points)Using a similar set of steps as in Problem #4, determine a general solution to the PDE2wx,tx21kwx,tt(for constantk)for 0t, 0xLand the boundary conditions (BCs)w0,t0andwx,txxL0for0t.———————————————————————————————————————2
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Partial differential equation, x, x L, t