Dave Tompkinss Awesome CPSC 121 Handout. Version 7 (2013.01.22)
and
^
or
_
not
p
T
T
F
F
q
T
F
T
F
p^q
T
F
F
F
p_q
T
T
T
F
p
F
F
T
T
p
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Logical Equivalence () Laws: (and accepted [SHORT] name)
Commutative: [COM]
p^q q^p
Associative: [ASS]
(p ^ q)
HtDW
(require 2htdp/image)
(require 2htdp/universe)
!
!
!
!
; My world program (make this more specific)
; =
; Constants:
; =
; Data definitions:
!
!
!
!
; WS is . (give WS a better name)
; =
; Functions:
!
; WS -> WS
; start the world with .
Rearrangements:
Integral Calculus
Math 101 Section 209
If we mul)ply this series by we get
Inser)ng zeros between the terms of this series, we have
Now we add the series in and :
No)ce that
Integral Calculus
Math 101 Section 209
Warm-up Problem
When is 99 more than 100?
99
Integral Calculus
Math 101 Section 209
Sequence vs Series:
A sequence is a list of
numbers wri>en in a
denite order:
(a n ) = a1 , a2 , a
MATHIOI
MIDTERM 2
IS COMING
UP!
REVIEW SESSION: Thurs March 5. 4:30 - 7pm LOCATION: TBA
OUR EXAM-AID SESSION
WILL HELP YOU ACE IT!
SOS Exam-AID sessions are run by senior students who have aced the
course. 8095 3 hour Exam-AID and extensive review packa
If-then statements:
Integral Calculus
Math 101 Section 209
Given: If the worker is injured, then the family sues.
Which of the following is logically equivalent to the given statement:
A. If the worker is not injured, th
Integral Calculus
Math 101 Section 209
Warm-up Problem
Given that sequence converges, nd its limit.
1
2
an+1 =
an +
,
a1 = 1
2
an
The following sequence was known to the Babylonians ~ 3,500 years ago!
The technique is that both an and an+1 will converge
Warm-up Problem
Integral Calculus
Math 101 Section 209
Connect the circles with four line segments linked at the ends to form a closed route,
passing through the centers of the circles and visi8ng each circle just once. The
Warm-up Problem
Warm up Problem: "
"
Find the sum of the following series:
Integral Calculus
Math 101 Section 209
1 1
1
1
1+ + +
+
.
3 6 10 15
This was the problem that Leibniz was given as an entrance exam to study analysis.
Announce
Math 101: Warm-Up Problem
Integral Calculus
Math 101 Section 209
An ocer thinks a car may be speeding, in a 60 km/h zone, but didnt have is radar
gun with him, so he doesnt pull over the car. The ocer calls up the road
Department of Mathematics
The University of British Columbia
Math 101, section 209!
Integral Calculus
Instructor: Dr. Shawn Desaulniers
Department of Mathematics
The University of British Columbia
Todays schedule
1. Welcome
2. Your Instructor?
3. What is
Math 101: Warm-Up Problem
Integral Calculus
Math 101 Section 209
On the Island of Knights and Knaves there are two kinds of inhabitants:
Knights always tell the truth, and knaves who always lie.
You bump into the three
Volume:
Integral Calculus
Math 101 Section 209
In trying to nd the volume of a solid we face
the same type of problem as in nding areas.
We have an intui;ve idea of what volume
means, but we must make this idea p
Warm-Up Problem
The Facts:
A test for a serious illness is reliable 96% of the 7me.
1 out of 200 people suer from the illness.
Your doctor tells you that tested posi7ve for the illness!
i.e. the 96% accur
Clicker Problem 3-1
Integral Calculus
Math 101 Section 209
Consider a con,nuous func,on f (x) such that the the le2 endpoints
always yield a larger approxima,on than the right endpoints on the
interval [a,b]. Th
Integral Calculus
Math 101 Section 209
Math 101 Warm-up
Let =
1
101,000,000
, A1 =
Z
1
1
1
x1
dx, and A2 =
A. Then A 1 is nite, but A2 is innite.
B. Then A 2 is nite, but A is innite.
Warm-up Problem
Department of Mathematics
The University of British Columbia
Integral Calculus Lecture 2
Math 101 Section 209
Main Ideas from Last class
1. Experts understand the basic concepts deeply.
2. Understand why, dont just memorize
3. Learn from
Math 101 Warm-up
Integral Calculus
Math 101 Section 209
If a rota(onal volume is nite, then its surface area must also be nite.
A. TRUE
B. FALSE
False: Gabriels Horn is obtained by rota(ng y=1/x about the x-
axis. It