Week 14

Tutorial 14: Laplace’s Equations

Question PDF

TUTORIAL 14 PDE Laplace Eqn.pdf

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Class Recording

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Solve the Laplace's equation for a rectangular plate

subject to the given boundary conditions

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Solution

Using and as a separation constant leads to

and

Then

for so that

Imposing

gives

so that

where

Solve the Laplace's equation for a rectangular plate

subject to the given boundary conditions

👉

Solution

Using and as a separation constant leads to

and

Then

for and

for so that

Imposing

gives

and

for so that

Solve the Laplace's equation for a rectangular plate

subject to the given boundary conditions

👉

Solution

Using and as a separation constant leads to

and

Then

for so that

Imposing

gives

for so that

👉

Note that the question changed for Question 4

Solve the Laplace's equation for a rectangular plate

subject to the given boundary conditions Answer:

👉

Solution

This boundary-value problem has the form of Problem 2 in this section, with and . Thus, the solution has the form

The boundary condition implies

and

The boundary condition implies

and