The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2011
D. Galloway
Tutorial 1
For the week beginning Monday 1st August
1.
Using the method of undetermined coecients, solve the following 2nd order
linear cons
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 5
For the week beginning Monday 2nd September
1.
Put the following dierential equations into the Sturm-Liouville form
dy
d
p(x)
+
The University of Sydney
APPLIED MATHEMATICS 2
MATH2965
Introduction to PDEs (Advanced)
2013
Lecturer: C. Cresswell
Tutorial 11
For the week beginning Monday 21st October
1. Waves on a circularly symmetric membrane (see Haberman section 7.7.9)
Waves on a
The University of Sydney
APPLIED MATHEMATICS 2
MATH2965
Introduction to PDEs (Advanced)
2013
Lecturer: C. Cresswell
Tutorial 10
For the week beginning Monday 14th October
1. Solve the following ODEs using Laplace transforms:
(i ) y + 16y = 4(t ),
y(0) = 2
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 7
For the week beginning Monday 16th September
1.
Dene the Laplace transforms
2
I = L t3/2 ea
(a)
(b)
(c)
/4t
and
2
J = L t1/2 ea
The University of Sydney
APPLIED MATHEMATICS 2
MATH2965
Introduction to PDEs (Advanced)
2013
Lecturer: C. Cresswell
Tutorial 12
For the week beginning Monday 28th October
1. Consider the following rst order PDE
+
=0
t x
with (x, 0) = f (x) given. Write
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 2
For the week beginning Monday 12th August
1.
Show that in the case where the procedure for solving the Euler-Cauchy equation
x2
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 1
For the week beginning Monday 5th August
1.
Using the method of undetermined coecients, solve the following 2nd order
linear con
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 3
For the week beginning Monday 19th August
1.
Use the method of Frobenius to nd a solution to
xy + (x 2)y 3y = 0 .
Use reduction
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 8
For the week beginning Monday 23rd September
1.
Solve Laplaces equation inside the quarter-circle of radius 1 (0 /2, 0
r 1 ) su
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 9
For the week beginning Tuesday 8th October
1.
If
f (x) =
0 |x| > a
1 |x| < a,
determine the Fourier transform of f (x).
(Haberma
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2013
C. Cresswell
Tutorial 4
For the week beginning Monday 26th August
1.
Calculate the Fourier series for the function
f (x) = 0 (L x < 0)
= x (0 x < L) .
N
The University of Sydney
Applied Mathematics 2
MATH2965
Lecturer:
Introduction to PDEs (Advanced)
2011
D. Galloway
Tutorial 2
For the week beginning Monday 8th August
1.
Show that in the case where the procedure for solving the Euler-Cauchy equation
x2 y
The University of Sydney
APPLIED MATHEMATICS 2
MATH2965
Introduction to PDEs (Advanced)
2011
Lecturer: D. Galloway
Tutorial 10
For the week beginning Monday 10th October
1. Solve the following ODEs using Laplace transforms:
(i ) y + 16y = 4 (t ),
y (0) =
The University of Sydney
The School of Mathematics and Statistics
Assignment Solutions
Longen Lan 440351423
MATH2965: Introduction to Partial Differential Equations (Advanced)
Lecturer: Clio Cresswell
Semester 2, 2015
1. Consider the following ODE for y(t