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MTH 132 (sec 201)
Syllabus
Spring 2011
CRN 3170
Prerequisites: A good high school algebra background together with a Math ACT of 24 or higher,
or completion of MTH 127 or 130 with a C or higher
Course Objectives : To learn about functions used in calculus including polynomial, rational,
exponential, logarithmic, and trigonometric. To be able to solve systems of equations and inequalities,
to study conic sections, polar parametric equations, sequences and series and the binomial Theorem.
( 5 credit hours )
Meeting time : M – F 8– 8:50 am Room 514 Smith Hall
Instructor : Dr. Alan Horwitz
Office : Room 741 Smith Hall
Phone : (304)696-3046
Email : [email protected]
Text : College Algebra and Trigonometry , Narasimhan, Houghton Mifflin
Grading : attendance
5% (34 points )
surprise quizzes
15% (100 points)
probably 4 major exams
60% (400 points)
Note:
If we have a 5th exam, then I will count the highest four exam scores
final( comprehensive ) exam 20% (133 points)
Final exam date: 8 - 10 am on either Monday May 2 or Thursday May 5, 2011( we'll discuss in class )
General Policies :
Attendance is required and you must bring your text and graphing calculator (especially on quizzes and exams ). You
are responsible for reading the text, working the exercises, coming to office hours for help when you’re stuck, and being
aware of the dates for the major exams as they are announced. The TI-83 will be used in classroom demonstrations and is
the recommended calculator, but you are free to use other brands (although I may not be able to help you with them in
class).
Exam dates will be announced at least one week in advance. Makeup exams will be given only if you have an
acceptable written excuse with evidence and/or you have obtained my prior permission.
I don’t like to give makeup exams, so don’t make a habit of requesting them. Makeups are likely to be
more difficult than the original exam and must be taken within one calendar week of the original exam date. You can’t
make up a makeup exam: if you miss your appointment for a makeup exam, then you’ll get a score of 0 on the exam.
If you anticipate being absent from an exam due to a prior commitment, let me know in advance so we can schedule
a makeup. If you cannot take an exam due to sudden circumstances, you must call my office and leave a message or
email me on or before the day of the exam!
Surprise quizzes will cover material from the lectures and the assigned homework exercises. These can be given at
any time during the class period. No makeup quizzes will be given, but the 2 lowest quiz grades will be dropped. The sum
of your quiz scores ( after dropping the two lowest) will be scaled to a 100 point possible maximum, that is, to 15% of the
667 total possible points in the course.
In borderline cases, your final grade can be influenced by factors such as your record of attendance, whether or not
your exam scores have been improving during the semester, and your class participation. For example, if your course point
total is at the very top of the C range or at the bottom of the B range , then a strong performance on the final exam can
result in getting a course grade of B, while a weak performance can result in getting a C.
Attendance Policy :
This is not a DISTANCE LEARNING class!
Attendance is 5% of your grade( 34 points total). If your grade is borderline, these points can be important
in determining the final result. Everyone starts out with 34 points, then loses 2 points for each class missed. Doing
boardwork problems (see below) is a way to win back those lost points. Your attendance score will be graded on a stricter
curve than your exam scores.
Having more than 3 weeks worth of unexcused absences (i.e., 15 of 70 lectures ) will automatically result in a
course grade of F! Being habitually late to class will count as an unexcused absence for each occurrence. Carrying on
conversations with your neighbor , as well as engaging in other forms of disruptive behavior, could be counted as an
unexcused absence. Walking out in the middle of lecture is rude and a distraction to the class ; each occurrence will count
as an unexcused absence. If you must leave class early for a doctor’s appointment , etc., let me know at the beginning and
I’ll usually be happy to give permission. Absences which can be excused include illness, emergencies, or official
participation in another university activity.
MTH 132 (sec 201)
Syllabus
Spring 2011
( continued )
Documentation from an outside source ( eg. coach, doctor, court clerk…) must be provided. If you lack documentation,
then I can choose whether or not to excuse your absence.
HEED THIS WARNING:
Previously excused absences without documentation can, later, instantly change into the unexcused type if you accumulate
an excessive number ( eg. more than 2 weeks worth ) of absences of any kind, both documented and undocumented :
You are responsible for keeping track of the number of times you’ve been absent. I won’t tell you when you’ve reached the
threshold. Attendance will be checked daily with a sign-in sheet. Signing for someone other than yourself will result in
severe penalties!! Signing in, then leaving early without permission will be regarded as an unexcused absence.
Sleeping in Class :
Habitual sleeping during lectures can be considered as an unexcused absence for each occurrence. If you are that
tired, go home and take a real nap! You might want to change your sleeping schedule, so that you can be awake for class.
Policy on Cap Visors :
During quizzes and exams, all cap visors will be worn backward so that I can verify that your eyes aren’t roaming to
your neighbor’s paper.
Cell Phone and Pager
Policy :
Unless you are a secret service agent, fireman, or paramedic on call, all electronic communication devices such as
pagers and cell phones should be shut off during class. Violation of this policy can result in confiscation of your device and
the forced participation in a study of the deleterious health effects of frequent cell phone use.
Policy on Cheating :
Don't. Don't even help your neighbor cheat. If I suspect you are, then you'll get a 0 on that quiz or exam, and worse.
Addendum to MTH 132 Syllabus :
I would like to motivate greater participation in class. Frequently, I will be selecting a few homework
problems so that volunteers can post their solutions immediately before the start of the next lecture. For each
solution that you post on the board ( and make a reasonable attempt on ) , I will ADD 2 points to your total score
in the course. Boardwork points can help determine your final grade in borderline cases and can help you to recover
points lost from your attendance score. ( They will not cancel your accumulation of unexcused absences, which can
result in failing the course if you have too many ) Rules for doing boardwork follow:
RULES FOR DOING BOARDWORK :
1.
I’ll assign a selection of homework exercises to be posted for the next lecture.
2.
Arrive early!! Have your solutions written on the board by the beginning of the class period.
Be sure to write the page number of the problem. Read the question carefully and be
reasonably sure that your solution is correct and that you have showed the details in your
solution.
3.
Don’t post a problem that someone else is doing. On choosing which problem you do,
remember : The early bird gets the worm !
4.
Write small enough so that your neighbors also have space to write their problems.
I don’t want territorial disputes. Also write large enough for people in the back rows to see.
5.
Work it out, peaceably among yourselves, about who gets to post a problem.
Don’t be greedy: if you frequently post problems, give someone else an opportunity
if they haven’t posted one recently. On the other hand, don’t be so considerate that
nobody posts any problems.
6.
Circle your name on the attendance sheet if you’ve posted a problem that day.
Use the honor system: don’t circle for someone else. The number of problems on the board
should match the number of circled names on the attendance sheet. Make sure you also keep
a record in your notes, just in case I lose the attendance sheet.
TOPICS IN NARASIMHAN BOOK( darker font topics will be covered in MTH132 )
P.1. interval notation for open, closed, half-open & unbounded intervals
P.2. laws of exponents, rewriting expressions to have positive exponents
P.3. radical notation, simplifying radical expressions
rational exponents, simplifying expressions with rational exponents
rationalizing denominators
P.6. simplifying rational expressions, multiplying rational expressions
using LCD to help add/subtract rational expressions
simplifying complex fractions
1.1
relations & functions
domain and range
evaluating functions
1.2
graphing by plotting points
vertical line test
judging domain and range from a graph
x and y intercepts
1.3
linear functions and slope of a line
equations of horizontal and vertical lines
point slope form and slope intercept form
parallel and perpendicular lines
1.5
solving linear equations
finding point of intersection for two lines
solving linear inequalities, solving compound inequalities
2.5 solving absolute value equations
solving absolute value inequalities
2.6 graphing piecewise functions
3.1
vertex, axis of symmetry and shape of parabolas
vertex form & standard form for quadratic functions
graphing parabolas
3.2 solving quadratic equations by factoring, quadratic formula
importance of the discriminant
solving quadratic equations by using principle of square roots
completing the square
dividing one complex number by another
3.3 adding, subtracting, multiplying complex numbers
complex conjugates
division of complex numbers
powers of i
4.3
long division of polynomials
division algorithm
Remainder Theorem and Factor Theorem
synthetic division
4.4 using known zeros to help factor a polynomial
using the Rational Zeros Theorem to find candidates for zeros
4.5 Fundamental Theorem of Algebra and the Factorization Theorem
multiplicity of a factor, of a zero
factoring polynomials with real and complex zeros
designing a polynomial to have given real zeros
TOPICS IN NARASIMHAN BOOK(continued)
4.7 using sign charts and test points to solve polynomial and rational inequalities
5.1
concept of inverse function
verifying two functions are inverses
solving for the inverse function
one to one functions have inverses
horizontal line test for checking "one to oneness"
how to sketch the graph of an inverse function
5.2 graphing exponential functions
properties of exponential functions
base e
5.3 definition of logarithm base a, evaluating logarithms without a calculator
natural and common logarithms
converting logarithmic form to exponential form and vice versa
solving simple logarithmic equations
using the change of base formula
graphs of logarithmic functions
5.4 algebraic properties of logarithms
expanding a single logarithm into sums/differences of logarithms
combining sums/differences of logarithms into a single logarithm
5.5 solving exponential equations
using algebraic properties to help solve logarithmic equations
how to avoid extraneous solutions: check answers in original equation
5.6 exponential growth models and doubling time
radioactive decay models and half life
6.1 positive and negative angles, coterminal angles
measuring angles in degrees, minutes and seconds
converting degrees to radians and vice versa
arclength formula
how linear speed is related to angular speed
6.2 "right triangle" definitions of sine, cosine and tangent for
acute angles:SOH CAH TOA
using cofunction identities to find trig function values of complementary angles
sines and cosines of special acute angles
6.3 definitions of trig functions for angles on a circle of radius r
reciprocal trig functions: cosecant, secant, cotangent
using reference angles to find trig functions for non-acute angles
using the value of one basic trig function and the quadrant of the terminal edge
to find the value of the other five basic trig functions
TOPICS IN NARASIMHAN BOOK(continued)
6.4 unit circle definitions of the basic trig functions
sines and cosines of special angles in 1st quadrant of unit circle
using reference angles to help find sines and cosines of special angles
outside of the 1st quadrant
the three Pythagorean Identities
negative angle identities
6.5 properties of graphs of cosine and sine: domain and range,
period and amplitude
hand sketching graphs of transformed sine and cosine functions:
phase shift and starting point, period and ending point of one cycle,
axis of periodicity, basic shape of graph, amplitude
given a picture of a transformed sine or cosine graph, figure out what
the equation is
6.6 sketching graphs of tangent and cotangent, secant and cosecant
6.7 using concept of restricting the domain to define
inverse functions for sine, cosine, tangent
definition of arcsine, arccosine, arctangent : know their domains
and ranges
simplifying compositions of trig functions with inverse trig functions:
sometimes a picture of a right triangle helps
7.1 proving trig identities: using trig identities and substitution to make one side
look like another
7.2 identities for sine , cosine and tangent of sum/difference of angles
co-function identities
how to rewrite a sum of sine and cosine terms as a single sine term
7.3 double angle identities and power reducing identities
using half angle identities to evaluate trig functions at half the value of a
familiar angle
product to sum identities
7.4 solving trigonometric equations
8.1
Law of Sines
solving AAS and ASA triangles
solving SSA triangles: one solution, two solutions or no solution
finding area of an oblique triangle
8.2 using the Law of Cosines to solve SSS triangles
8.3 converting rectangular to polar coordinates and vice versa
8.4
hand graphing polar equations
TOPICS IN NARASIMHAN BOOK(continued)
8.5 standard position of a vector
writing a vector in component form
computing magnitude of a vector
finding the direction angle of a vector
addition, subtraction and scalar multiplication:
algebraic computation and parallelogram law method
finding a unit vector in the direction of a given vector
applications to net velocity and net force
8.6 computing dot product of vectors
using dot product to compute angle between vectors
testing if vectors are orthogonal
using dot products to compute work done by a force vector
computing projection of one vector on another vector
orthogonal decomposition of vectors
8.7 plotting a complex number in the coordinate plane
converting a complex number from standard form
to polar form and vice versa
using polar form to multiply, divide complex numbers
using DeMoivre’s Theorem to raise complex numbers to powers
finding roots of complex numbers in polar form
9.1 solving system of two equations and two unknowns:
substitution and elimination methods
solving systems of linear inequalities by graphing
9.2 solving systems of three equations by Gaussian elimination
9.3 augmented matrix for a system of linear equations
elementary row operations
recognizing row reduced echelon form
Gauss-Jordan method of solving systems of equations
9.4 addition, subtraction, and scalar multiplication of matrices
additive inverse of a matrix, the zero matrix
knowing when you can multiply matrices together
computing a product of matrices
9.5 the identity matrix
definition of the multiplicative inverse of a square matrix
Gauss-Jordan method of finding an inverse, if it exists
using inverses to solve matrix equations
9.6 determinants of 2x2 & 3x3 matrices
Cramer’s Rule
9.7 partial fraction decompositions
9.8 techniques for solving systems of non-linear equations
TOPICS IN NARASIMHAN BOOK(continued)
10.1
directrix and focus, axis of symmetry and vertex of parabola
equations of parabolas with vertex at (0,0), at (h,k)
10.2 foci, major axis and minor axis of ellipse
standard equation of ellipses centered at (0,0), at (h,k)
10.3 foci and transverse axis of hyperbola
standard equation of hyperbolas centered at (0,0), at (h,k)
10.4
change of coordinates by rotation of x and y axes
general equation of conic section
rotating axes to rewrite conic section equation in new variables to
eliminate mixed variable terms
graphing rotated conics
10.5 focus-directrix definition(eccentricity) of ellipses, parabolas, and hyperbolas
deriving polar equations of ellipses, parabolas and hyperbolas
identifying a polar equation as an ellipse, parabola or hyperbola
10.6 graphing parametric equations of plane curves by plotting points,
by converting to rectangular form
parametric equations of circles, ellipses, projectile motion
11.1 forms of arithmetic sequences and geometric sequences
11.2 formulas for sum of 1st n terms of an arithmetic sequence, of a
geometric sequence
summation notation
formula for sum of an infinite geometric series
11.3 using a rule to define a sequence
finding a rule to describe terms of a sequence
generating terms of a recursively defined sequence
Fibonacci sequences
nth partial sum of a sequence
11.4
Multiplication Principle of counting
factorial notation
formulas for counting permutations and combinations
combinations of objects selected from different sets
11.5
directly computing the probability of an outcome in an event
probabilities of mutually exclusive events, of complement of an event
11.6
binomial expansions: ith binomial coefficient and ith term of binomial expansion
Binomial Theorem
11.7
principle of mathematical induction
proving formulas by mathematical induction
MTH 132 (sec 201)
Syllabus
Spring 2011
The following brisk schedule optimistically assumes we will cover a multitude of topics at a rapid pace:
approximately 4 sections per week! Realistically speaking, we may surge ahead or fall somewhat behind,
but we can’t afford to fall too far off the pace. The major exams will be roughly on the 3rd, 6th, 9th, and
13th weeks, plus or minus one week. Their precise dates will be announced at least one week in advance
and the topics will be specified ( and may possibly differ from what is indicated below).
Come to class regularly and you won’t be lost.
.
Week
1
2
Dates
Spring
2011
1/101/14
1/181/21
MLK
day on
1/17
3
1/241/28
4
1/312/4
5
2/72/11
6
2/122/16
7
2/212/25
Approximate schedule : Sections covered and topics
P.6
1.2
1.3
1.5
4.4
4.5
4.7
5.1
5.2
5.3
5.4
EXAM 1
5.5
5.6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
7.1
EXAM 2
7.2
7.3
7.4
Actual
date
covered
Week
8
Dates
Spring
2011
2/283/4
9
3/73/11
10
3/143/18
(Last day
to drop
on 3/18)
SPRING
BREAK
next
week
11
3/284/1
12
4/44/8
(ASSessment day
on 4/6 )
13
Approximate schedule : Sections covered and topics
Actual
date
covered
8.1
8.2
8.3
8.4
8.5
8.6
EXAM 3
8.7
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
10.1
10.2
10.3
EXAM 4
4/114/15
10.4
10.5
10.6
11.1
4/1811.2
4/22
11.3
11.4
4/2511.5
4/29
11.6
Week of 11.7
the
Review if we have time, or we may schedule it outside class hours
Dead
14
15
Student Support Services:
0.
1.
2.
3.
4.
Office Hours. Schedule to be announced.
Math Tutoring Lab, Smith Hall Room 526. Will be opened by the start of 2nd week of classes
Tutoring Services, in basement of Community and Technical College in room CTCB3.
See http://www.marshall.edu/uc/TS.shtm for more details.
Student Support Services Program in Prichard Hall, Room 130.
Call (304)696-3164 for more details.
Disabled Student Services in Prichard Hall, Room 120.
See http://www.marshall.edu/dss/ or call (304)696-2271 for more details
MTH 132 (sec 201)
Syllabus
Spring 2011
Keeping Records of Your Grades and Computing Your Score
Quiz#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
score
Raw Quiz Score= sum of all, but the two lowest quiz scores
Adjusted Quiz Score =
Exam #
score
100
 Raw Quiz Score
10  ( # of quizzes  2)
1
2
3
4
Exam Total = sum of all exam scores(not including the final exam)
grade range for
Exam 1
Exam 2
Exam 3
average of range values
for all four exams
Exam 4
A
B
C
D
Absence #
Date absent
Excused? Y or N?
Attendance Score
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Attendance Score = 34 – 2  (# of days you were absent or extremely late)
Boardwork #
Date done
Boardwork Score
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
Boardwork Score = 2  ( # of boardworks you did , not counting the ones you really did badly )
Total % of Points = (Attendance Score
+Boardwork Score
+Adjusted Quiz Score
+Exam Total
+Final Exam Score)/667