Methods of Applied Mathematics 311-2
Practice Problems For Midterm
Winter 2016
Hermann Riecke
Friday, February 5, 2016
due Monday, February 8, 2016
1. Consider again the bacteria problem from Fridays class:
t u = x2 u + u
u(0, t) = 0 = u(L, t)
u(x, 0) = f
Methods of Applied Mathematics 311-2
Winter 2016
Hermann Riecke
Problem Set 3
Tuesday, February 2, 2016
due Monday, February 8, 2016
1. Solve Laplaces equation
2 u = 0
inside the circular, semi-innite cylinder 0 < z, 0 < r < 1 with boundary conditions
u(r
Methods of Applied Mathematics 311-2
Winter 2016
Hermann Riecke
Problem Set 2
Monday, January 25, 2016
due Monday, February 1, 2016
1. Solve Laplaces equation
2 u = 0
on the circular annulus 1 < r < 2 with boundary conditions
u(r = 1, ) = 1
u(r = 2, ) = s
Methods of Applied Mathematics 311-2
Winter 2016
Hermann Riecke
Problem Set 1
Monday, January 11, 2016
due Monday, January 18, 2016
1. Solve Laplaces equation
2 u = 0
on the domain 0 < x < 1, 0 < y < 2 with boundary conditions
u(x, 0) = u(x, 2) = u(0, y)
ESAM 252 Midterm Solutions
Fall 2013
1. As shown in the diagram, the vectors u and v are
E
E
drawn from the center of a circle to the circumference, so that jE j D jEj. Use vector operations to show
u
v
that AC is perpendicular to CB .
C
v
A
B
u
-u
!
!
1.
Miscellaneous Integrals (Answers)
Instructions: For each of the following, you should be able to perform each of the integrations and
dierentiate the result to get back to the original integrand without any errors.
1.
1
dx = 2 tan1 ( x) + C
(1 + x) x
2.
Honors Engineering Calculus Assignment 4
EE
1. Solve for x in the vector equation b x D x a and give a vector diagram that includes a,
E
EE
E
E, b x and x a. Why is it true that jb x j D jx aj?
EE
EE
b
EE
EE
1. Answer:
xD
E
1
aCb :
EE
2
b-x
x-a
b
x
a
The
Honors Engineering Calculus Assignment 3
1. Assume the earth is a perfect sphere of radius R. If the z axis is the polar axis and the
zOx plane has zero longitude, show that a point P having latitude (positive in the northern
hemisphere) and longitude (me
Honors Engineering Calculus Assignment 2
1. A methane molecule, CH4 , arranges itself with the four hydrogen atoms at the vertices of
a regular tetrahedron and with the carbon atom at its center. Demonstrate that the points
.0; 0; 0/, .1; 1; 0/, .1; 0; 1/
Honors Engineering Calculus Assignment 1
!
!
!
E
1. If OA D a, OB D b and P represents a point on the line AB, show that in general OP D
E
EE
E
EE
a C .b a / D b
E
.b a/ where , are constants. Show that
E
aC b
E
C
!
OP D
and consider the location of P in