ASSIGNED EXERCISES OF MATH544 February, 2001
CALCULUS OF VARIATIONS
1. Find the shortest distance between two points A and B on the plane
using the polar coordinates.
2. Find the shortest distance between two points A and B on a sphere.
3. Find the shorte
ASSIGNED EXERCISES OF MATH544: PDE set 4 March, 2001
INITIAL AND BOUNDARY VALUE PROBLEMS OF
SOME HYPERBOLIC TYPE OF EQUATIONS
Ronald B Guenther and John W Lee, Partial Dierential Equations of Mathematical Physics and Integral Equations
1. Homogeneous wave
ASSIGNED EXERCiSES4:
PDE Set 2
February, 2001
PDE Problems
Copson:
See also Ch.4 of the lecture notes.
1. Find the types of the following dierential equations, and reduce them to
normal form:
y 2 r t = 0,
(1)
(ii)
y 2 r + 2ys + t = p,
(2)
(iii)
y 2 r + t
ASSIGNED EXERCISES OF MATH544: PDE set 6 April, 2001
THE HEAT EQUATION
Ronald B Guenther and John W Lee, Partial Dierential Equations of Mathematical Physics and Integral Equations
1. Solve the following initial value problem
x [0, L],
(1)
u(0, t) = u(L,
ASSIGNED EXERCISES OF MATH544: PDE set 5 March, 2001
THE METHOD OF RIEMANN
Ronald B Guenther and John W Lee, Partial Dierential Equations of Mathematical Physics and Integral Equations
1. Solve the following initial value problem
uxy yux = 1,
y > x, x ,
(