Day 07

Tuesday, Feb 21, 2017

Ch 2 Method of separation of variables, cont'd

2.4 Some more examples of heat equation by separation of variables

Sunrise this morning


2.4.2 Circular bar

2017_02_21/20170221_131456.jpg 2017_02_21/20170221_131502.jpg 2017_02_21/20170221_131509.jpg

I neglected to mention that also L − Lcos((nπx)/(L))sin((nπx)/(L))dx = 0 for all integers n, m.


2.5 Laplace's equation in 2D

2.5.1 Rectangle


Decomposition trick

2017_02_21/20170221_134501.jpg 2017_02_21/20170221_134507.jpg 2017_02_21/20170221_134514.jpg

Here is the solution u4(x, y) for some random f1(y) that I chose, with temperature u(x, y) indicated by color.


got to here

2.5.2 Disk

2.5.3 Flow outside a cylinder

2.5.4 Qualitative properties