Real Analysis, course outline
Measure theory I
1. Sigma algebras. Let A be a collection of subsets of some xed set .
It is called a -algebra with the unit element if
(a) , A ;
(b) E A = c E A ;
(c) Ej A , j = 1, 2, . . . =
Ej A .
SECTION 7.1 | NonlineurSystems 375
In extending phaseplane analysis to nonlinear systems, we encounter mul-
tiple equilibrium points and limit cycles. Analysis is facilitated by studying
nullclines and the regions into which they sepa
MID-TERM PRACTICE PROBLEMS
(1) Find the general solution of
(a) 2y 5y 3y = 0,
(b) y + 3y 4y = 0,
(c) y (4) + 2y + y = 0.
(2) Find the general solution of
(a) y 5y + 4y = 8 ex ,
(b) y + 4y = x cos(x),
(c) y 9y + 14y = x e2x + x,
(d) y +
Self-Assessment 1 Math 5A, Winter 2008
Answer the following questions without looking in the book. If you do not
feel comfortable doing this, read the corresponding sections in the book, and
then solve the problems, again without looking in the book.
Math 5A - Solutions to Final Exam Review Problems
Solving 2x2 Homogeneous, Linear Systems of DEs. Details on nding the eigenvalues
and eigenvectors have been left out. Of course, on the exam you will be expected to show
the work for these calc
Match the following systems of differential equations with their respective phase
portraits. Below each portrait, classify the stability of the system, and explain
your answer. '
-1 _ -U5 O 0.5 1
A B SEETION 7.] l Nonlinear Systems 375
WeBWorK assignment number Homework7 is due : 12/01/2011 at 11:20am PST.
(* replace with url for the course home page *)
for the course contains the syllabus, grading policy and other information.
This le is /conf/snipp