University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2013/2014
Solutions #1
1. (a) Recalling that sin A cos B = 1 sin(A + B) + sin(A B) we have
2
1
sin(k x) cos(n
1
y
1
x2
-1
1
-1
y 1 x2
-1 1
y 0
1
z
0
-1 -1 0 x 1
y
z
x
1 z 0 -1 0 x 1 -1 0 1 y
y 1 6 z 4 2 0
2
S
D
1 x 2 3
3 y 1 2 z 2
1
0 x 1
y 1 2 z 1
2
0 2 x 4
y 0.5 0 1
1
z 0.5
0 0.5 x 1
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B42
Winter 2016
Assignment # 3
You are expected to work on this assignment prior to your tutorial in the week
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B42
Winter 2016
Assignment # 6
Due the week of February 22nd.
A. Readings:
1. Lecture notes: LW6.
2. Readings:
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B42
Winter 2016
Assignment # 4
You are expected to work on this assignment prior to your tutorial in the week
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B42
Winter 2016
Assignment # 5
You are expected to work on this assignment prior to your tutorial in the week
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B42
Winter 2016
Assignment # 2
You are expected to work on this assignment prior to your tutorial in the week
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B42
Winter 2016
Assignment # 1
You are expected to work on this assignment prior to your tutorial in the week
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University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2014/2015
Solutions #8
1. (a) We view the cone as a collection of line
segments joining (3, 2, 1) to a point P
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2014/2015
Solutions #11
2
, t sin t +
, 0 t 2. Now
1. We can parametrize by (t) = t2 cos t +
2
2
(t) = 2t
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2014/2015
Solutions #10
1. (a) d
2 ) dz dx =
= (dF3 ) dx dy + (dF1 ) dy dz + (dF
F3
F3
F3
F1
F1
F1
dx +
dy +
Definition : An oriented surface is a 2-sided regular (smooth)
surface to which we have attached, at each point, a unit normal
vector (which varies continuously from point to point).
An orientable sur
Divergence Theorem or Gauss Theorem
Let S be a closed surface in R3 oriented by the outward pointing
unit normal n and let R be the region enclosed by S (i.e., R = S).
Suppose F is a smooth vector fie