AMath 231
ASSIGNMENT # 1: Review and Curves
Spring 2011
Due on or before Wednesday, May 11th at 9:30am in drop box 6, slot 11 or 12 across from
MC4066.
Comment: The rst two problems are review. If you
AMath 231
ASSIGNMENT # 2: Vector Fields
Spring 2011
Due on or before Wednesday, May 18th at 9:30am in drop box 6, slot 11 or 12 across from
MC4066.
1. Given that the Euclidean norm is dened as |x|2 =
AMATH 231: Assignment 3 (Line Integrals)
Due Wednesday 5 October at the beginning of tutorial. Write your solutions clearly and concisely.
Marks will be deducted for poor presentation and incorrect no
AMath 231
ASSIGNMENT # 3*: Line integrals, cons. elds
Spring 2011
Due on or before Wednesday, June 1st at 9:30am in drop box 6, slot 11 or 12 across from
MC4066.
*Note that this assignment is a 2-week
AMATH 231 COURSE SUMMARY
Curves & Vector Fields
- Curves in Rn:
[Ch. 1]
g : [ a, b] R
g (t ) = ( g1 (t ), g 2 (t ),., g n (t )
n
(ie path of a particle through space with parameter time t)
- Expressin
Question 1, ll marks.
Consider the function/(x) = x. 0 5 x 5 I., for some: rcol number L > 0.
I) Find the Fourier cosine series Uf/(X). and sketch the function to which it converges on R.
4.
r l k
.
Assignment 5 - Circulation, Flux and Divergence theorem.
Due Noon February 05, 2016.
1. Compute the area enclosed by the hypocycloid of four cusps
~ : [0, 2] 7 R2 and ~ (t) = (a cos3 t, a sin3 t),
wh
Assignment 10 - Fourier series.
Due Noon Monday March 28, 2016.
1. A function f (x) is defined in the interval 1 < x < 1 by,
0 1 < x < ,
1
< x < ,
f (x) =
2
0
< x < 1.
where 0 < < 1.
(a) Sketch th
Assignment 6 - Surfaces and surface integrals.
Due February 12, 2016.
~ Find an orthonormal basis set lying on the surface.
1. Sketch the following surfaces S.
(u, v) [0, ] [0, 2]
~ = (cos v sin u)i
Assignment 7 - Stokess and Divergence theorem.
Due Noon March 04, 2016.
1. The surface integral of a scalar function can be given in a particularly
simple form when the surface is the graph of a funct
Assignment 1 - Review material.
Not to be handed in
Linear algebra
are the unit basis vectors of the Cartesian coordinate system.
Notation: (i, j, k)
~ of a particle of mass m is defined by H
~ = ~r
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Mk 5? d " Ow: )
DMWAWCAWC .2 _
f g N "r; " (0W '3 COLLAHEGW
A f, x A
MC;,\ q/ \ x \ m, 1,
"a: ,3 \ \ (1/ (q,"\/"7[/+l 1-1)
W \Qfm: a123, :2 5 A0 cfw_3 1:;
mxwya
W WW/ W: [UL/L' ,
gaw
Assignment 5 - Circulation, Flux and Divergence theorem.
Due on Friday, October 20, 2017 (in-class).
1. Compute the area enclosed by the hypocycloid of four cusps
~ : [0, 2] 7 R2 and ~ (t) = (a cos3
Assignment 1 - Review material.
Due on Friday September 15, 2017 (in-class).
Linear algebra
are the unit basis vectors of the Cartesian coordinate system.
Notation: (i, j, k)
~b = qi + 1j + 1k and ~
Assignment 4 - Conservative fields and Greens theorem.
Due on Friday, October 6, 2017 (in-class).
1. A force F~ acts on a particle that is moving in the plane along the semi-circle C parameterized by
Assignment 4 - Conservative fields and Greens theorem.
Due Noon January 29, 2016.
1. A force F~ acts on a particle that is moving in the plane along the semi-circle ~ (t) = ( cos t)i+(sin t)j; t [0, ]
Assignment 3 - Path integrals and gradient fields.
Due on Friday September 29, 2017 (in-class).
Compute the work done by F~ in moving a
1. A force field F~ : R3 R3 is given by F~ (x, y, z) = xi + yj
Assignment 6 - Surfaces and surface integrals.
Due on Friday, November 3, 2017 (in-class).
~ Find an orthonormal basis set of vectors lying
1. Sketch the surfaces parameterized by the following mappin