Solutions to Final Exam Sample Problems, Math 246, Fall 2013
dy
= (9 y 2)y 2 .
dt
(a) Identify its stationary points and classify their stability.
(b) Sketch its phase-line portrait in the interval 5 y 5.
(c) If y(0) = 1, how does the solution y(t) behave
Solutions to Final Exam Sample Problems, Math 246, Fall 2012
dy
= (9 y 2)y 2 .
dt
(a) Identify its equilibrium (stationary) points and classify their stability.
(b) Sketch how solutions move in the interval 5 y 5 (its phase-line portrait).
(c) If y(0) = 1
MATH 246 - Quiz 1
Name:
Wednesday, June 4th, 2014
You have 10 minutes to complete this Quiz. No calculators or notes are to be used.
(1) [2pts] For the dierential equation below, state the order and whether it is linear or
nonlinear.
dg 2x 3
d2 g
+ g = 0.
Final Exam Sample Problems, Math 246, Fall 2012
dy
= (9 y 2)y 2 .
dt
(a) Identify its equilibrium (stationary) points and classify their stability.
(b) Sketch how solutions move in the interval 5 y 5 (its phase-line portrait).
(c) If y(0) = 1, how does th
Math 246 - Final Exam Solutions
Friday, July 11th, 2014
(1) Find explicit solutions and give the interval of denition to the following initial value
problems
(a) (1 + t2 )y + 2ty = et , y(0) = 0.
Solution: In normal form, this equation is
y +
et
2t
y=
.
1
Final Exam, Math 246/246H
Monday, 16 December 2013
Closed book. No electronics. Answer only one question on each answer page.
Write your name and which question is being answered on each answer page.
Sign the Honor Pledge on the rst answer page only. Indi
MATH 416
Extra credit
The signal given in the txt le represents the blood ow measurements of a patient. It is a part of a
long sequence of measurements; its beginning corresponds to the time moment when the blood pressure
cu was released (assuming it had
MATH 416
HOMEWORK 5
due April 5th, in class
Problem 1
2
(a) Find the Fourier transform of the function f (x) = ex ex ;
(b) Find the Fourier series of the following function f (x) = x2 on [1, 1].
Problem 2
1
Show that for functions from Lipper [0, 1)(perio
MATH 416
HOMEWORK 4
due Tue, March 27th in class
Problem 1
Find the Fourier transforms of the following functions:
(a) f (x) = ex [0,+) (x) (here [0,+) (x) = 1 if x 0 and 0 otherwise);
(b) f (x) = e|x| ;
(c) f (x) = sinc2 (x) (same as f (x) = (sinc(x)2 ).