University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #8 This assignment is due March 17 March 20, 2009. A. Suggested reading: 1. 2. 3. B. Problems: 1. Let S be the cone with vertex (3, 2, 1) and base the cir

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2009/2010
Assignment #10
This assignment is
April 1 April 5, 2010.
due
at
the
start
of
your
tutorial
in
the
period
This assignment contains material to be covered ov

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2010/2011
Assignment #9
This assignment is
March 31 April 1, 2011.
due
at
the
start
of
your
tutorial
in
the
period
A. Suggested Reading: Marsden & Tromba, Chapter 8,

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2010/2011
Assignment #10
This assignment is
April 7 April 8, 2011.
due
at
the
start
of
your
tutorial
in
the
period
This assignment contains material to be covered ov

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #5
The Term Test will take place on Friday, March 7, 7:00 pm 9:00 pm in SW128.
This assignment is due at
February 25 February 28, 2008.
the
star

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #4 This assignment is due at February 11 February 14, 2008. the start of your tutorial in the period 2007/2008
A. Suggested Reading: Marsden & Tromba, Cha

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #3 This assignment is due February 4 February 7, 2008. A. Suggested reading: 1. 2. 3. B. Problems: 1. A particle following the curve (t) = (sin et , t, 4

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #2 This assignment is due January 28 January 31, 2008. B. Problems: 1. (a) Find the Fourier series of the sawtooth function f (x) of period 2 whose values

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #1 This assignment is due January 21 January 24, 2008. B. Problems: 1. Show that
2007/2008
at
the
start
of
your
tutorial
in
the
period
(a)
(b)
sin(kx) cos

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2005/2006
Assignment #11
This assignment will not be collected. The solution set should be available at the end of the
term.
Problems:
40
1. Consider the counterc

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #6
The Term Test will take place on Friday, March 7, 7:00 pm 9:00 pm in SW128.
This assignment is
March 3 March 6, 2008.
due
at
the
start
of
you

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #7
This assignment will NOT be graded since the Term Test will take place on
Friday, March 7, 7:00 pm 9:00 pm in SW 128. The term test will incl

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #6 This assignment will NOT be graded since the Term Test will take place on Saturday, February 28, 1:00 pm 3:00 pm in the GYM. The term test will include

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #5 The Term Test will take place on Saturday, February 28, 1:00 3:00 pm in the GYM. This assignment is due at February 24 February 27, 2009. the start of

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #4 This assignment is due at February 10 February 13, 2009. the start of your tutorial in the period 2008/2009
A. Suggested Reading: Marsden & Tromba, Cha

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #3 This assignment is due February 3 February 6, 2009. A. Suggested reading: 1. 2. 3. B. Problems: 1. A particle moving on the curve (t) = (2t3 , cos t, e

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #2 This assignment is due January 27 January 30, 2009. B. Problems: 1. Find F3 (x), the Fourier polynomial of degree three, for the periodic function, wit

University of Toronto Scarborough Department of Computer & Mathematical Sciences
MAT B42H Assignment #1 This assignment is due January 20 January 23, 2009. B. Problems:
2008/2009
at
the
start
of
your
tutorial
in
the
period
1. Show that
sin(kx) sin(nx) dx

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #11
This assignment will not be collected. The solution set should be available at the end of the
term.
Problems:
4 2
3 2
1. Consider the counte

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #10
This assignment is
March 31 April 3, 2008.
due
at
the
start
of
your
tutorial
in
the
period
This assignment contains material to be covered o

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #9
This assignment is due
March 24 March 27, 2008.
at
the
start
of
your
tutorial
in
the
period
A. Suggested Reading: Marsden & Tromba, Chapter 8

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2007/2008
Assignment #8
This assignment is due
March 17 March 20, 2008.
A. Suggested reading:
at
the
start
of
your
tutorial
in
1.
Marsden & Tromba, Chapter 4, sectio

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2005/2006
Assignment #10
This assignment is
April 4 April 6, 2006.
due
at
the
start
of
your
tutorial
in
the
A. Suggested reading:
period
1. Marsden & Tromba, Chap

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2005/2006
Assignment #9
This assignment is due
March 28 March 30, 2006.
at
the
start
of
your
tutorial
in
the
period
A. Suggested Reading: Marsden & Tromba, Chapte

To look at the rate of change in a function f at a point a along the
line p + t v, t R we have
Definition:
The directional derivative of f at a in direction
v, denoted by Dv f (a) , is given by
f (a + tv) f (a)
Dv f (a) = lim
.
t0
tkvk
In the special case

Definition.
A function, whose partial derivatives exist and are
continuous, is said to be of class C1.
If the partial derivatives of a C1 function f have, in
Definition.
turn, continuous partial derivatives, we say f is of class C2 (twice
continuously dif

Definition: Let v = (v1, v2, v3), w = (w1, w2, w3) R3. We
define the cross product v w by
v w = (v2 w3 v3 w2, v3 w1 v1 w3, v1 w2 v2 w1) .
Properties:
1. v w v, w
2. v w = w v
3. v (u + w) = v u + v w
(v + u) w = v w + u w
4. k v w k = kvk kw k | sin |, wh

Theorem: If B is bounded and f is continuous over B, then f is integrable
over B.
Definition The graph of a polar equation (equation in r and ) is the set
of points that corresponds to the polar coordina tes (r, ) that satisfy the
equation.
Theorem Suppos