MIT 1803 lecture 5

This lecture started with noting that equations of the form y' = f(y) where there is no dependence in the RHS on t are known as autonomous, and can be dealt by separation of variables (so I realized that I use separation of variables all the time without realizing it, in these simpler dy/dx formulas.)

Critical points are y_0 s.t. f(y_0) = 0 , creating bounding integral curves.

The logistic equation y'=ky where k=a-by and demonstrated critical points which are when y'=0 and what they can tell you.  Plot the y’ vs y and y vs. t for quick intuition about what the system is doing.

Advertisements
Explore posts in the same categories: Math

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: