Math 426 Final: Due Wed. Dec 17 before
2:00P.M. (No Extensions!)
C. Chicone
December 16, 2003
1. The system x = x y + 2 sin(x), y = x + y + x2 y has a rest point at
the origin. Draw (with explanation)
Math 426 Homework 1
C. Chicone
September 7, 2003
Hand in problems 5,7,9,13 on Sept. 1.
Prepare the rest of the problems to present to the class starting Aug. 27.
General rules: Please do not consult b
Math 426 Homework 4
C. Chicone
September 21, 2003
1. Prove that the phase portrait of the 2nd-order ODE x x + x2 = 0 has
a homoclinic orbit.
2. Let H (x, y, z ) = xyz . Does XH := grad H 3H , where de
Math 426 Homework 3
C. Chicone
September 23, 2003
1. Exercise 1.34 p. 26 of the book. Consider a Newtonian particle of
mass m moving under the inuence of the potential U . If the position
coordinate i
Math 426 Homework 2
C. Chicone
September 4, 2003
1. Construct innitely many dierent solutions of the initial value problem
x = x 1/3 ,
x(0) = 0.
Why does the Existence and Uniqueness Theorem for diere
Math 426 Homework 5
C. Chicone
October 12, 2003
1. Draw the phase portrait of Newtonian system x = x x3 . Give a qual
itative description of solution of the system for the initial condition
the
(x(0),
Math 426 Homework 7
C. Chicone
November 4, 2003
1. Prove that the system
x = x y x3 ,
y = x + y y3
has a unique globally attracting limit cycle on the punctured plane;
that is, the plane with the orig
Math 426 Homework 6
C. Chicone
October 21, 2003
1. Find an explicit formula for the ow of the dierential equaton
x = y + x(1 x2 y 2 ),
y = x + y (1 x2 y 2 ).
Show that all orbits except the rest point
Math 426 Homework 8
C. Chicone
October 27, 2002
1. 2.2
2. The linearized Hills equations for the relative motion of two satellites
with respect to a circular reference orbit about the earth are given
Math 426 Homework 10
C. Chicone
December 9, 2002
1. Find the principal fundamental matrix solution at t = 0 for the MarkusYamabe system: x = A(t)x, where A(t) is given on page 171. Write
the principal
Mechanical Engineering degree requirements for students entering MU FS16 or later.
Name: _
Solid lines indicate a prerequisite
Student Number: _
Dashed Lines indicate co-requisites
Date Entered: _
14