University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #5
1. (a) = y exy dx + x exy dy . Put F1 (x, y ) = y exy and F2 (x, y ) = x exy . Since
F1
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
FINAL EXAMINATION
MATB42H Techniques of the Calculus of Several Variables II
Examiner: E. Moore
Date: April 26, 2012
Du
UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF COMPUTER AND MATHEMATICAL SCIENCES MATB42H Examiner: P. Selick Date: August 16, 2007 Duration: 3 hours Question 1. a) [ 7 points] Find the volume of the
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2012/2013
Assignment #3
This assignment is due
February 4 February 8, 2013.
A. Suggested reading:
at
the
start
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2012/2013
Assignment #4
This assignment is due at
February 11 February 15, 2013.
the
start
of
your
tutorial
in
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2012/2013
Assignment #5
The Term Test will take place on Wednesday, March 6, 5:00 7:00 pm .
This assignment is
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2012/2013
Assignment #1
This assignment is due
January 21 January 25, 2013.
at
the
start
of
your
tutorial
in
t
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2012/2013
Assignment #2
This assignment is due
January 28 February 1, 2013.
at
the
start
of
your
tutorial
in
t
The Eclipse Conspiracy
Something doesnt add up.
Yannis Behrakis / Reuters
JAMES HAMBLIN

AUG 16, 2017

SCIENCE
Like The Atlantic? Subscribe to The Atlantic
Daily, our free weekday email newsletter.
Object Recognition: TopDown Pr
ocesses
The Nature of Perception
Perception is Associated with Action
Perception is goal oriented
Perception is an act of interpretation
The Brain is more like a pa
PSYCHOLOGICAL SCIENCE
Research Report
WHEN MORE PAIN IS PREFERRED TO LESS:
Adding a Better End
Daniel Kahneman,' Barbara L. Fredrickson,^ Charles A. Schreiber,' and
Donald A. Redelmeier^
^University o
Chapter 2
Quality and Quality of Experience
Alexander Raake and Sebastian Egger
Abstract The chapter discusses the processes of human perception and experiencing, and of quality formation. In this con
Attention: What is it?
Attention is like Picking a Sandwich
2
Guided Perception
Sometimes, to see something, we have to kno
w what we are looking for
3
What you hear in the other ear
Gender of the v
RSVP and the Attentional Blink
Does the Brain Blink?
See the Attentional Blink Reading
Attentional Blink Demo
You will get a chance to experience the
Attentional Blink in the lab 3 experiment
Eye Bli
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2012/2013
Term Test Solutions
0 , x <
2
1 , x < , we will rst nd the Fourier coecients.
1. Given f (x) =
2
2
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
FINAL EXAMINATION
MATB42H Techniques of the Calculus of Several Variables II
Examiner: E. Moore
Date: April 18, 2011
Du
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #3
1. We are given that the path followed is (t) =
(t) =
et ,
1
,
sin
t2 6
t
6
t
1
et ,
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #4
1. (a) Since T (t) = 1, we have T (t) 2 = T (t) T (t) = 1. Dierentiating w.r.t.
d
t giv
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #1
1. Recalling that sin A sin B =
1
2
cos(A B ) cos(A + B )
we have
1
sin(k x) sin(n x) d
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #6
1. (a) (i) We are given that = 1 so the curve lies on
=
8 , so we can parametrize
(usin
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #2
1. f (x) = x (x 2 ) = x2 2x on [0, 2 ].
Since the periodic extension is even bk =
1 2 2
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
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
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #8
1. (a) In the xz plane the line segment from (3, 0) to (2, 1) can be given by (3 t, t),
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #7
1. (a) The surface S is given by (u, v ) = (u2 +
v, v, u + v 2 ). Now u = (2u, 0, 1), v
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Assignment #2
This assignment is due
February 2 February 3, 2012.
at
the
start
of
your
tutorial
in
t
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #11
1. We can parametrize by (t) = t2 cos t +
, t2 sin t +
2
2
2
(t) = 2t cos t +
t sin
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Assignment #3
This assignment is due
February 9 February 10, 2012.
A. Suggested reading:
at
the
star
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Assignment #1
This assignment is due
January 26 January 27, 2012.
at
the
start
of
your
tutorial
in
t
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B42H
2011/2012
Solutions #10
f
f
f
dx +
dy +
dz .
x
y
z
f
f f f
f
f
f =
f=
=
,
,
,
,
e1 +
e2 +
e3 .
x y z
x y z
x
Object Recognition: What and W
here Pathways
The Problem
We need to be able to describe things and reason a
bout them
We need to be able to operate things and use them
Describe what things are invo