Yangming Xue
Assignment a9 due 03/31/2015 at 11:59pm EDT
dalhousieuniv-math2002
has a period one quarter that of graph (1), we know that equation
(a) must match graph 1, (b) must match 4 and (c) must match 3.
To find the equations for each graph, note tha
MW Ck
Cami LU WA lag/jam:
I
Q
at: f xxm+,(+uv
E
LMM PM pm I
Lecs L0M{th ILL 3mg} :fie. géwéémm.
Mi $0,, M4: 2: 0) am! a
WEEV'PM} u?» VLJWy
2m. - bur oéJr (3ka : 0
21w) * F L 3' |og10(t+1)
10000
8000
6000
4000
2000 gql U
Example of catastrophic regime:
F (r) = er 0.5er/2
r=1.3978
r=1.43535
r=1.44716
N=100
N=400
N=800
Example of h-stable regime:
F (r) = er 0.5er/1.2
r=9.56367
r=13.3742
r=19.3298
N=25
N=50
N=100
1
References:
- M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes
Data from LA police
(2008), A statistical model of criminal behavior, Math. Models. Meth. Appl. Sci., 18, Suppl. pp. 1249-1267.
- T. R
=
Reference:
T. Kolokolnikov, M. Ward and J. Wei,
Self-replication of mesa patterns in reaction-diffusion models,
Physica D, Vol.236(2), 2007, Pages 104-122
Yangming Xue
Assignment a2 due 01/25/2015 at 11:59pm EST
dalhousieuniv-math2002
Correct Answers:
1. (1 pt) Evaluate the integral.
Z 3 Z 3 Z 9x2
1
dy dx dz =
2
2
(x
+
y2 )1/2
0 3 9x
NEGATIVE
ZERO
4. (1
pt)Z Use cylindrical coordinates to evaluate the tri
Yangming Xue
Assignment a1 due 01/18/2015 at 11:59pm EST
dalhousieuniv-math2002
1. (1 pt) Find the volume
of the solid enclosed
by the
paraboloids z = 9 x2 + y2 and z = 2 9 x2 + y2 .
h1 (x, y) =
h2 (x, y) =
Z b Z g2 (y) Z h2 (x,y)
2.
g1 (y)
a
Correct Answ
Yangming Xue
Assignment a5 due 02/22/2015 at 11:59pm EST
dalhousieuniv-math2002
1. (1 pt)
2
2
2
Suppose that f (x, y, z) = 2xyzex i + zex j + yex k.
4. (1 pt) Let C be the positively oriented circle xR2 + y2 = 1.
Use Greens Theorem to evaluate the line in
Yangming Xue
Assignment a7 due 03/17/2015 at 11:59pm EDT
dalhousieuniv-math2002
3. (1 pt)
1. (1 pt)
Calculate Tu , Tv , and n(u, v) for the parametrized surface at
the given point.
Then find the equation of the tangent plane to the surface at that
point.
Yangming Xue
Assignment a3 due 02/01/2015 at 11:59pm EST
dalhousieuniv-math2002
1. (1 pt)
Compute the Jacobian of :
(u, v) = (6u 4v, 4u 9v)
Jac() =
Solution:
Solution: By the Jacobian of linear mappings we get
(x, y) 6 (4)
= 6 (9) (4) 4 = 38
Jac() =
=
4
Yangming Xue
Assignment a10 due 04/09/2015 at 11:59pm EDT
dalhousieuniv-math2002
1. (1 pt) Suppose a spring with spring constant 8 N/m is
horizontal and has one end attached to a wall and the other end
attached to a 3 kg mass. Suppose that the friction of
Yangming Xue
Assignment a4 due 02/08/2015 at 11:59pm EST
dalhousieuniv-math2002
Solution:
1. (1 pt)
Compute the line integral of the scalar function f (x, y) =
1 + 9xy
over
the curve y = x3 for 0 x 6
R
C f (x, y) ds =
Solution:
Solution: The curve is par
Yangming Xue
Assignment a8 due 03/24/2015 at 11:59pm EDT
dalhousieuniv-math2002
Combining with (1) we get
1. (1 pt)
D
E
3
Let I be the flux of G = 3ey , 3x2 ex , 0 through the upper
hemisphere S of the unit sphere.
(a) Find a vector field A of the form h0
Yangming Xue
Assignment a6 due 03/09/2015 at 12:59am EDT
dalhousieuniv-math2002
Solution:
SOLUTION
(a) Cross sections of the vector fields are shown below, for
w = 1 on the left and for w = 1 on the right. In either case
the cross-section is taken in the