Course Hero Logo

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

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 1 - 4 out of 13 pages.

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
———————————————————————————————————————

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 13 pages?

Upload your study docs or become a

Course Hero member to access this document

Term
Fall
Professor
N/A
Tags
Partial differential equation, x, x L, t

Newly uploaded documents

Show More

Newly uploaded documents

Show More

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture