# Toronto Math Forum

## MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Daniel Clark on October 12, 2018, 03:43:18 PM

Title: Behold, MAT244 in flowchart form!
Post by: Daniel Clark on October 12, 2018, 03:43:18 PM
So I had this idea of putting all of the lecture material of MAT244 in a giant flowchart. So I did.

A few notes:
Dotted lines means the question is reduced to the smaller one

For the partial derivatives I used notation not used in class, the curly "d" with a subscript just means a derivative with respect to the variable in the subscript

I tried to keep it on one page and have all the notation as general as possible, which might have made it nigh impossible to read.  Sorry about that.

I don't have EVERYTHING, and I'm planning to update it as the class goes on.  Constrictive criticism welcome.
Title: Re: Behold, MAT244 in flowchart form!
Post by: Victor Ivrii on October 12, 2018, 04:04:52 PM
Wowzers!!!

But you forgot in integrating factor case of $\mu= \mu (xy)$.

And somehow relevant
https://www.nytimes.com/2010/04/27/world/27powerpoint.html?hp (https://www.nytimes.com/2010/04/27/world/27powerpoint.html?hp)
Title: Re: Behold, MAT244 in flowchart form!
Post by: Kathryn Bucci on October 12, 2018, 06:00:41 PM
I think that if you had a non-exact homogeneous equation and you can't easily find an integrating factor, you could also solve it by making a substitution y=vx.. then it would be reduced to a separable equation.
Title: Re: Behold, MAT244 in flowchart form!
Post by: Daniel Clark on October 14, 2018, 09:33:11 PM
RE: Kathryn Bucci
Incorrect, counterexample x +(x^2-y^2)y' = 0
using the substitution gives us x +(x^2-v^2x^2)v' =0 which is arguably worse.
That would work if the derivative is a function of the ratio, which i covered in my unholy diagram on the left.
Title: Re: Behold, MAT244 in flowchart form!
Post by: Victor Ivrii on October 15, 2018, 07:24:24 AM
Daniel, Kathryn

The word "homogeneous" is overused. Kathryn is right if equation is homogeneous which means $y'=f(y/x)$. Daniel meanwhile thinks about linear homogeneous, which is a completely different story.
Title: Re: Behold, MAT244 in flowchart form!
Post by: Kathryn Bucci on October 15, 2018, 11:57:23 AM
Daniel, Kathryn

The word "homogeneous" is overused. Kathryn is right if equation is homogeneous which means $y'=f(y/x)$. Daniel meanwhile thinks about linear homogeneous, which is a completely different story.

Yes that is what I was referring to - sorry, I should have been more clear.