New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Differential Equations

by: Kaylin Wehner

Differential Equations MATH 33B

Kaylin Wehner
GPA 3.55


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Kaylin Wehner on Friday September 4, 2015. The Class Notes belongs to MATH 33B at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 102 views. For similar materials see /class/177836/math-33b-university-of-california-los-angeles in Mathematics (M) at University of California - Los Angeles.


Reviews for Differential Equations


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/04/15
Math 33B Final Exam Review Sheet 1 Classi cation of the Equilibria of y Ay where A is a 2 gtlt 2 matrix with trace T and determinant D Generic Cases 0 Real eigenvalues one positive one negative D lt 0 Saddle o Distinct real e values both negative D gt 0 T2 7 4D gt 0 T lt 0 Nodal Sink o Distinct real e values both positive D gt 0 T274D gt 0 T gt 0 Nodal Source 0 Complex e values with negative real part T2 7 4D lt 0 T lt 0 Spiral Sink 0 Complex e values with positive real part T2 7 4D lt 0 T gt 0 Spiral Source Degenerate Cases 0 Purely imaginary eigenvalues D gt 0 T 0 Center 0 Negative e value of multiplicity two T2 7 4D 0 T lt 0 Degenerate Sink Like a nodal sink but a solution may curve signi cantly as it approaches the origin like its almost77 a spiral 0 Positive e value of multiplicity two T2 7 4D 0 T gt 0 Degenerate Source Like a nodal source but a solution may curve signi cantly as it leaves the origin like its almost77 a spiral 0 One of the eigenvalues is 0 D 0 No Catchy Name In this case there are in nitely many equilibria arranged along a line in the plane If T lt 0 they are all stable If T gt 0 they are all unstable If T 0 they are neither All other solutions are straight lines 96 may 2 Qualitative Analysis of Autonomous Nonlinear Systems y 9mg 0 The znullcline is the set of points Ly where fy 0 ie where the arrows all point straight up or down The ynullcline is the set of points Ly where gxy 0 ie where the arrows all point straight left or right 0 A point xmyo is an equilibrium if f0y0 0 and gxoy0 0 ie if it is on both nullclines Q Q o The Jacobian of the system is the matrix J lt3 3 E E o The linearization of the system at an equilibrium zoy0 is the homogeneous linear system y J07yoY o If the linearization at zoy0 is one of the ve generic types saddle nodal sink nodal source spiral sink spiral source then the equilibrium at zoy0 is of the same type


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.