Math 363, 2006. Assignment 3 Solutions.
Question 1
(a) Given the dierential equation
x = f (x)
nd a conserved quantity.
(b) The relativistic equation for the orbit of a planet around the sun is
d2 u
+ u = + u2 ,
d 2
where u = 1/r and r, are the polar coor
Math 363, 2006. Assignment 4 Solutions
Question 1
Consider the equation
x + bx kx + x3 = 0.
(a) Convert to a rst-order system and nd all the steady states.
(b) The origin is always a steady state. In the b, k plane, sketch the stability
diagram of the ori
Department of Mathematics
Maths 363
Examples of solutions of 1st order PDEs
August 23, 2006
Solve the initial value problems in (1), (2) and (3).
1.
u
u
+ x2
= 0, u(x, 0) = f (x).
t
x
Solution: The characteristic equations are x = x2 , u = 0, with initial
Department of Mathematics
Maths 363
August 8, 2006
Assignment 1 Solutions
Due: Student Resource Centre, 3pm, Friday, 4th August
Attach a copy of all the Matlab les that you wrote for this assignment.
Make sure that all of your graphs have axis labels an