Introduction Chapter 12
MATH 2433 - 12631
Aarti Jajoo
ajajoo@math.uh.edu
Office : PGH 606
Lecture : MoWeFre 10-11am in SR 116
Office hours : MW 11:30-12:30pm and BY APPOINTMENT
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Introduction Chapter 12
Course website
http://www.math.uh.edu/∼ajajoo/Math2433
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Introduction Chapter 12
Key Points
1
CASA Account
2
Textbook
3
Homework
4
Daily class quizzes(poppers)
5
Weekly online quizzes
6
Weekly lab quizzes
7
Exams
http://www.math.uh.edu/∼ajajoo/Math2433
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Introduction Chapter 12
1) CASA Account
http://www.casa.uh.edu/
Open your CASA account as soon as possible!
You will find your textbook, the weekly online quizzes, and
the exam scheduler here.
In order to access all of the above, you need to purchase an
Access Code from the Book Store in the University Center.
http://www.math.uh.edu/∼ajajoo/Math2433
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Introduction Chapter 12
2) Textbook
CALCULUS, 9th edition, by Salas/Hille/Etgen. Publisher: John
Wiley & Sons, Inc.
You do not need to purchase this textbook. With the Access
Code you can access the text electronically by logging into CASA
at
http://www.casa.uh.edu.
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Introduction Chapter 12
3) Homework
Homework will be collected each Monday in lab starting the
third week of class.
The list of problems will be posted on the course website by
the previous Monday.
Late homework will NOT be accepted.
Your homework will NOT be returned.
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Introduction Chapter 12
4) Daily class quizzes(Poppers)
Daily poppers will be given in lecture starting the third week
of class.
Purchase a course pack of custom bubbling forms from the
Book Store in the University Center.
Make sure you get the correct packet. They are sold by
Section Number:
Section 12631 - 10-11am MWF
Do NOT punch holes in the page, do NOT use ink, do fill all the
required bubbles or you will NOT receive credit.
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Introduction Chapter 12
5) Weekly Online Quizzes
Online quizzes will be available at
http://www.casa.uh.edu, starting the first week of class.
You can take them up to 20 times and only the best score is
used for the grade.
Check the weekly quizzes calendar at the course website to
know when they close.
http://www.math.uh.edu/∼ajajoo/Mah2433
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Introduction Chapter 12
6) Weekly Lab Quizzes
Quizzes will be given every week in lab, starting the second
week of class.
Quizzes will be given either on Monday or on Wednesday and
will be collected in lab the same day.
There are NO make-up quizzes. If you miss a quiz, you will
receive a zero, and the two lowest quiz grades will be dropped.
http://www.math.uh.edu/∼ajajoo
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MATH 2433
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Introduction Chapter 12
7) Exams
Three tests during the semester and one final exam.
Exams are given at CASA. You will schedule the time of your
exam at http://www.casa.uh.edu.
The scheduler will be available two weeks prior to the exams
(I will inform you).
Exam 1
Exam 2
Exam 3
Final exam
Feb 13-14
Match 27-28
April 24-25
May 7-9
There are NO make-up exams!
Plan on arriving early so if you are stuck in traffic etc. you don’t
miss the exam.
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Introduction Chapter 12
Grades
Lab Quiz
Online Quiz
Homework and poppers
Exam 1
Exam 2
Exam 3
Final exam
10
10
10
15
15
15
25
90 % and above
above 80% and below 90%
above 70% and below 80%
above 60% and below 70%
above 60%
%
%
%
%
%
%
%
A
B
C
D
F
http://www.math.uh.edu/∼ajajoo/Math2433
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Introduction Chapter 12
Classroom behavior
Come to class on time.
Attendance is NOT mandatory. If you have something to do
more exciting than cal 3, do it outside the classroom and do
not disturb other students. However, be aware that you will
miss the points from the daily poppers.
ASK QUESTIONS. If there is something you do not
understand in what I am saying or working on, do not hesitate
to raise your hand.
ANSWER QUESTIONS.
All the info about the course are available at the course website.
Check info under Course Organization.
http://www.math.uh.edu/∼ajajoo/Math2433
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Introduction Chapter 12
Sect. 12.1
Cartesian Space Coordinates
Section 12.1
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Introduction Chapter 12
Sect. 12.1
Three dimensional space
The z-axis
is perpendicular to the xy -plane
oriented to form a right-handed system
Now we have 3 coordinate planes: xy -plane, xz-plane, yz-plane.
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Introduction Chapter 12
Sect. 12.1
Plotting points
The position of a point in 3D is given by its 3 coordinates (x, y , z).
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Introduction Chapter 12
Sect. 12.1
Planes
Example:
write the equation of a plane that passes through (3, 1, -2) that is
parallel to the xz-plane.
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Introduction Chapter 12
Sect. 12.1
Take two points P1 (x1 , y1 , z1 ) and P2 (x2 , y2 , z2 ):
Distance formula
The distance between P1 and P2 is given by
q
d(P1 , P2 ) = (x2 − x1 )2 + (y2 − y1 )2 + (z2 − z1 )2
Midpoint formula
The midpoint of the line segmente P1 P2 is given by
x1 + x2 y1 + y2 z1 + z2
,
,
2
2
2
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Introduction Chapter 12
Sect. 12.1
Example
Given A(2, 0, −1) and B(2, 1, 3), find the distance between A and
B and the midpoint of the line segment AB.
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Introduction Chapter 12
Sect. 12.1
Sphere
The sphere of radius r centered at P0 (a, b, c) is the set of all the
points P(x, y , z) with d(P, P0 ) = r :
(x − a)2 + (y − b)2 + (z − c)2 = r 2 .
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Introduction Chapter 12
Sect. 12.1
Example
Find the center and radius of
x 2 + y 2 + z 2 + 4x − 8y − 2z + 5 = 0.
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Introduction Chapter 12
Sect. 12.1
Vectors
Section 12.3
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Introduction Chapter 12
Sect. 12.1
Vectors
Definition
A vector is an ORDERED triple of real numbers where addition
and multiplication by scalars hold:
(a1 , a2 , a3 ) + (b1 , b2 , b3 ) = (a1 + b1 , a2 + b2 , a3 + b3 )
α(a1 , a2 , a3 ) = (αa1 , αa2 , αa3 ).
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Introduction Chapter 12
Sect. 12.1
Vectors
We depict vectors with arrows. To depict the vector (a1 , a2 , a3 ),
you can choose any initial point and use the arrow
−→
−→
Notation: QR and OP or a = (a1 , a2 , a3 ).
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Introduction Chapter 12
Sect. 12.1
Example
−→
−→
Given P(1, −2, 5) and Q(5, −1, −3), find PQ and QP.
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Introduction Chapter 12
Sect. 12.1
To Do
Open your CASA account.
Buy the Access Code.
Syllabus is posted on the course website.
Read Sections 12.1 and 12.3.
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