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
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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 of
January 11th, 2016. You may ask questions about this
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 of
January 25th, 2016. You may ask questions about this
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: Marsden & Tromba, Vector Calculus, 6e.
Ch 7.4,7.5
B. P
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 of
February 1st, 2016. You may ask questions about this
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 of
February 8th, 2016. You may ask questions about this
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 of
January 18th, 2016. You may ask questions about this
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University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2014/2015
Solutions #9
1. We can parametrize S by (u, v)
=
(u cos v, u sin v, u), 0
v
2,
1 u 2. Now u = (cos v, sin v, 1),
v = (u sin v, u cos v, 0) and u u =
(u cos
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 on
the base circle. This point P has the
form P = (cos
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 cos t +
t2 sin t +
, 2t sin t +
+
4 2
2
2
2
t2 cos t