Math 421 - 1
Analysis II
Course Information
| Dr. Keith Promislow | kpromisl AT math.msu.edu |
| Wells Hall 212D | Office phone: 432-7135 |
| Office Hours Th 10-11, W 4-5pm | Office Fax: 432-1562 |
The course Syllabus is available.
As are Sections 5.1 and 5.2 of Wade
Homework Assignments
Partial Homework Answers
Images From Class
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Image of the function
f(x,y)= (|x|^\alpha |y|^\beta)/(|x|^2+|y|^3)
On the left, alpha/2+beta/3<1 and the function grows to
infinity along the ridge-line.
In the center image, alpha/2+beta/3=1 and the function tends
to a non-zero value along the ridge line y= a x^(2/3)
with a=(1.2/1.8)^(1.3)=0.8736,
but to zero along any straight line.
On the right, alpha/2+beta/3> 1 and f tends to zero as
(x,y) tends to zero.
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The function
f(x,y)= (x^3 /(|x|^2+|y|^2)
Has a cusp at (0,0)