MATH443
PARTIAL DIFFERENTIAL EQUATIONS
FINAL EXAM SOLUTIONS
January 11, 2012 WEDNESDAY 15:30-17:30, SAZ04
QUESTIONS: Solve any four of the following ve problems. WARNING:
1. In each problem explain what you are doing.
2. The way you solve, not the answers
MATH.443
PARTIAL DIFFERENTIAL EQUATIONS
MAKEUP EXAM 2
January 13, 2010 Wednesday 10.00-12.00
QUESTIONS: Solve any four of the following ve problems
[25]1. Reduce the equation
xuxx (x + y)uxy + yuyy =
x+y
(ux uy )
xy
to canonical form, and hence solve it.
MATH443
PARTIAL DIFFERENTIAL EQUATIONS
FIRST MIDTERM EXAM WITH SOLUTIONS
November 2, 2011 WEDNESDAY 10:40-12:30, SAZ01
QUESTIONS: Solve any four of the following ve problems
[25]1. A Pfaan dierential equation
ydx xdy + u(x, y, z)dz = 0
is integrable, wher
MATH.443
PARTIAL DIFFERENTIAL EQUATIONS
FINAL EXAM
December 30, 2009 Wednesday 15.30-17.30 , SAZ18
QUESTIONS: Solve any four of the following ve problems
[25]1. (25)25. .a. If there exists one integrating factor of a Pfaan dierential equation prove that t
MATH 443: PARTIAL DIFFERENTIAL EQUATIONS
PROBLEMS:
[25]1. Solve the following problem with separation of variables.
ut k (uxx + uyy )
u(x, y, 0)
u(0, y, t)
u(x, 0, t)
=
=
=
=
q(x, y, t),
f (x, y),
u(a, y, t) = 0,
u(x, b, t) = 0,
(t > o, 0 < x < a, 0 < y <
MATH 443: PARTIAL DIFFERENTIAL EQUATIONS
Final Exam: 29 December 2005 Thursday 09.00-12.00(SAZ19)
QUESTIONS: Solve ve problems out of the following seven problems
[25]1. Find the equation of the integral surface of the equation
2y(z 3)p + (2x z)q = y(2x 3
MATH.443
PARTIAL DIFFERENTIAL EQUATIONS
MAKEUP EXAM
December 31, 2009 Thursday 10.00-12.00
QUESTIONS: Solve any four of the following ve problems
[25]1. Find the integral surface of the of the equation
(y + xz)
z
z
+ (x + yz)
= z2 1
x
y
passing through th
MATH 443: PARTIAL DIFFERENTIAL EQUATIONS
Second Midterm Exam: 24 November 2005 Thursday 10.00-12.30
(SAZ19)
QUESTIONS: Solve four problems out of the following ve problems
[25]1. Reduce the equation
y 2 zxx 2xy zxy + x2 zyy =
x2
y2
zx +
zy
x
y
(1)
to its
MATH 443: PARTIAL DIFFERENTIAL EQUATIONS
First Midterm Exam: 20 October 2005 Thursday 10.00-12.30 (SAZ18)
QUESTIONS: You will solve four problems. The last three problems are compulsory. Choose any one out of the rst three problems
[25]1. Find the integra
MATH443
PARTIAL DIFFERENTIAL EQUATIONS
SECOND MIDTERM EXAM SOLUTIONS
December 14, 2011 WEDNESDAY 10:40-12:30, SAZ01
QUESTIONS: Solve any four of the following ve problems. WARNING:
1. In each problem explain what you are doing.
2. The way you solve, not t
MATH.443
PARTIAL DIFFERENTIAL EQUATIONS
MAKEUP EXAM 2
January 13, 2010 Wednesday 10.00-12.00
QUESTIONS WITH SOLUTIONS: Solve any four of the following ve
problems
[25]1. Reduce the equation
xuxx (x + y)uxy + yuyy =
x+y
(ux uy )
xy
to canonical form, and h