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
+
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
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 ch
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.