COLLEGE

This page is for my students at
Wharton County Junior College for the Spring, 2007 Semester. Content includes
General Information, Course Descriptions and Topic
Outlines, Class Schedules, Instructor's Office Hours and Contact Data, and anything
else I forgot. 
(PAGE
UNDER CONSTRUCTION)

INSTRUCTOR 
William Heierman, Office: Sugar Land,
SU118, Cubicle #12 
Telephone: (281)2438541 (Campus Ext. 8541) 
Email
(cc both, please):
wheierman@corunduminium.com

williamh@wcjc.edu

Office Hours: Monday
7:30  8:00 A.M., 9:00  9:50 A.M., 11:00  11:50 A.M. (after 1 P.M.
by appointment) 
Tuesday 7:30 
8:00 A.M., 12:15  1;00 P.M. (later by appointment) 
Wednesday 7:30  8:00 A.M., 9:00  9:50
A.M., 11:00  11:50 A.M. (after 1 P.M. by appointment) 
Thursday 7:30  8:00
A.M., 12:15  1;00 P.M. (later by appointment) 
Friday
7:30  9:50 A.M., 11:00  11:50 A.M. 




COURSES 
1: MATH 2414902 (CRN 20081), CALCULUS II
M, Tu, W, Th 8 8:50 A.M.
Room SU 308 
2: MATH 1314902
(CRN 20040), COLLEGE ALGEBRA M,W,F
10 A.M.  10:50 A.M. Room
SU308 
3: MATH 2312901 (CRN 21092), PRECALCULUS
M,W,F
12 NOON  12:50 P.M. Room SU 306 
4: MATH 1316901 (CRN 20068), TRIGONOMETRY
Tu,Th
9:25  10:40 A.M.
Room SU 407 
5: MATH 1325902 (CRN 20078), "BUSINESS CALCULUS"
Tu,Th
10:50 A.M.  12:05 P.M. Room SU 307 

SPRING TERM
CALENDAR 
First
day of classes: January 16
(Tuesday) 
No
classes:
February 23
(Friday)
TCCTA Meetings (Austin) 
Spring Break:
March 12  16 (Monday  Friday) 
No classes:
March 30
(Friday)
University Interscholastic League Competition (Wharton) 
No classes:
April 5  6
(Thursday  Friday) Easter Holiday 
Drop Date:
April 13
(Friday) 
Last day of classes: May 8
(Tuesday) 
Final Exam Schedule: [Exams are
in the regular class meeting rooms; special Finals Week office hours will be
announced.] 
1: Calculus II
May 15 (Tuesday), 8:00  10:00 A.M. 
2: College Algebra May 14
(Monday), 10:15 A.M.  12:15 P.M. 
3: Precalculus
May 14 (Monday), 12:30  2:30 P.M. 
4: Trigonometry
May 10 (Thursday), 8:00  10:00 A.M. 
5: Business Calculus May 15 (Tuesday),
10:15  12:15 A.M. 

WHAT'S
NEW 
During the week of Fabruary 59, I will be in Tucson, Arizona, and have
arranged for class coverage by colleagues. Here are some of the
details. 
CALCULUS II: Prof. Pastora will cover for me. Tentative schedule
is Exam Review Monday, Exam Tuesday, Comments about Exam Wednesday (key
handed out), lecture Thursday. Where time allows, the new topic under
discussion will be "Work" (a physical quantity). 
COLLRGE ALGEBRA: Prof. Brink will cover. Monday is Exam Review,
Wednesday is exam, Friday is Comments about Exam (keys handed out), and more
word problems solved. 
PRECALCULUS: I am working on this one. Expect Exam Review and
Exam 1, and a third class, but schedule is uncertain at this time. 

TRIGONOMETRY: Prof. Brink will cover. Tuesday is Exam Review and
Trig Identities, Thursday is last questions and Exam. 
BUSINESS CALCULUS: I think Prof. Neaderhouser will cover.
Tuesday will be Exam Review and limits, Thursday will be llast questions and
exams. 
All graded Exams will be returned as soon as possible, but I will not get
them until Monday. I hope to have them by the next class (Tuesday or
Wednesday). 

GENERAL REMARKS (See Update in your Course
Outline) 
The courses are
presented the usual lecture format with regularly assigned Homework,
occasional pop quizzes, periodic Exams, and a comprehensive two hour Final Examination. For note taking, I recommend
business size loose leaf paper (lined or unlined), punched and in a ring
binder. Pencils (2 or 3 colors) with eraser are preferable, and a
straightedge is often useful. 
There will be a series
of Homework Sheets
should be filled out and turned in on due dates. They may be
resubmitted once if they were submitted by the deadline and are in need of correction. After due dates,
solutions will be inserted in a set of Library notes for your course, which
can be obtained at the front desk. Other assignments
(text exercises) should be done but will not ordinarily be turned in. A cumulative Homework score will be included in the Final
Grade, having the weight of one regular Examination. 
There will
probably be four Exams, each an "hour" in length, announced in advance, and
preceded by a class set aside for your review questions. Usually,
there will be a Sample Exam or Exam Review Sheet, given out in advance, from
which to fine tune your understanding. See also the Worked Exams
from past semesters in the Library note
sets for
additional materials. Calculators will not be allowed on Tests unless
explicitly permitted in the Test instructions. 
The Final
Examination will be comprehensive and will have a two hour time limit. It is the last and most
important statement of competence in the subject matter of the course, and
it will carry weight somewhere between 25% and 35% in determination of
the Course Average. The schedule for Final Exams is above. 
Though no relevant
facts are ignored in determining final grade, the Course Average will be the
determining factor in most cases. Borderline decisions may involve
other considerations, such as class attendance (which is required  maximum
15% cuts) and other forms of involvement. 
If you have difficulty
with something and need help beyond the class experience, see me for an
office visit. If you miss a class, I recommend you get a hold of a
fellow student's notes and study them before asking anybody to reproduce the
entire lecture you missed. Also, check the Library note sets to see if
there is anything that will help you there. You can always email me
for suggestions; but I cannot reply with detailed solutions involving
lengthy arguments or math symbolism  see me in my cubicle for those! 

Please email me also if
you must be absent for two or more classes. If you don't, failure to
meet attendance requirements may result in technical failure of the course. I
can assist with study plans, or the withdrawal process if that becomes
necessary. Notify your counselor and all your instructors if you find
yourself in this situation. 
The "Drop Date" (last
day to withdraw without penalty) for the Spring, 2007 Semester is Friday,
April 13, 2007. 
Check this
page ("WHAT'S NEW", above) frequently for any newsworthy items, such as Test dates. These
items will also be announced in class. You are responsible for this
knowledge, even if you are absent or asleep when the announcement is made! 

COURSE
OUTLINES AND TEXTS 

MATH 1314,
COLLEGE ALGEBRA [3 Hours, 3 Credits]
TEXT: Sullivan, College Algebra
(Seventh Ed.) 
This course continues investigation
of the ideas and processes begun in Intermediate algebra. 
1: Review
polynomial algebra, showing some special methods useful in treatment of high
degree polynomials; 
2: Examine set
algebra, and its application to "or" and "and" compound
statements; 
3: Discuss
solutions of linear and polynomial equations (including inconsistent
equations and identities) and apply them to verbal problems; 
4: Describe
properties of fractions, roots, and absolute values and solution of equations and inequalities
involving these; 
Success in this course
is highly dependent on logical understanding and attention to details.
You may find the methods more "analytical" and less "procedural" than in the
past  it is often "the thinking that goes on before the writing begins"
that determines the algebraic procedure that solves a problem.


MATH
1316, TRIGONOMETRY [3
Hours, 3 Credits] TEXT:
Lial, Hornsby, Schneider, Trigonometry (Eighth Ed.) 
This course describes the basic
methods and concepts of both "Theoretical" and "Practical" Trigonometry,
with emphasis on knowledge required for 
the Calculus sequence. Math
24132414, and beyond. After a brief review of algebraic methods, we will 
1: Describe basic
geometric ideas associated with parallel and perpendicular lines and
triangles (especially, right triangles); 
2: Define the six
Trigonometric Functions for acute angles in terms of sides of right
triangles; 
3: Apply these ideas to calculate values of the Trigonometric
Functions, prove some Basic Identities, "solve" right triangles, and 
compute distances using "remote
measurement" techniques; 
4: Extend the definitions of the Trigonometric Functions to
"arbitrary" angles (sometimes the results are called the "Circular
Functions") , and 
show different
computational techniques; 
5: Prove the
"Basic Identities" for the Trigonometric Functions (these equations must be
memorized); 
6: Examine the
relationship between different units of angle measurement (degrees, radians,
revolutions); with application to problems involving 
rotating objects, and to the American Revolution; 
7: Examine
features of the Trigonometric Functions (domains, ranges, graphs, ...) and
their Inverse Functions; 
8: Use the
Fundamental Identities and algebraic trickery to prove other Identities and
to solve Trigonometric Equations; 
9: Derive the
"Law of Sines" and the "Law of Cosines", and apply to "solving"
triangles of arbitrary shape; and 
10: Apply
triangle solution methods and "Heron's Formula" to surveying (calculating
land areas). 
Many of the problems in this course require the
use of calculators ("Scientific", but not "Graphing"). I will be using
a "TI30X IIS", and will be describing 
"Button Sequences" in class for this or others identically programmed.
Others will be allowed, but users are responsible for knowing modifications. 
When a
calculator is used on a Test, written specification of button sequence
should be presented. 
Trigonometry requires more memorization than
most math courses  be prepared for this! 

MATH
1325, MATH ANALYSIS FOR BUSINESS ("BUSINESS
CALCULUS") [3
Hours, 3 Credits] TEXT:
Lial, Greenwell, Ritchey, CALCULUS with Applications
(Eighth Ed.) 
This is an introductory calculus course for
business majors which stresses the functions and processes of calculus
applied to business and economic problems. We shall 
1: Briefly review
the concepts and procedures of precalculus algebra, 
2: Introduce the
concept of limit, and learn how to find limits by visual and computational
methods, 
3: Define the
derivative, look at its geometrical interpretation, and learn how to compute
derivatives of algebraic, exponential, and logarithmic functions, 
4: Apply
derivatives to problems of curve sketching and extremization (maxima,
minima), 
5: Do some cost
analysis, including treatment of marginal cost, revenue, and profit as derivatives, 
6: Examine the
mathematics of simple and compound interest (including continuous
compounding), accumulation of annuity value, and loan amortization, 
7: Introduce the
concept of integral as antiderivative, limit of a sum, and area (with some
basic applications). 
This course is
intensive, but not as much so as the twosemester "Engineering Calculus"
sequence, partially because trigonometric functions are not involved. Further,
emphasis here is on applications in business and finance rather than
physics, cardiac output, and engineering. 

MATH 2312,
PRECALCULUS [3 Hours, 3 Credits] Text: 
This course refreshes the skills and concepts from algebra and trigonometry
needed for the effective study of elementary calculus. We shall 
1: Review polynomial algebra, including division, factoring, and
solution of equations and inequalities, 
2: Do the same for fractions, roots, and absolute values, 
3: Express reciprocals and roots using negative and fractional
exponents 
4: Graph polynomials, rational functions, and the general quadratic
equation (case B=0), 
5: Discuss logarithmic and exponential functions, and solve equations
involving them, 
6: Discuss right triangles and the six trigonometric ratios, 
7: Extend to define trigonometric functions of arbitrary angles and
examine methods for evaluating them, 
8: Derive the basic trigonometric identities and verify others, 
9: Solve several types of trigonometric equations, 
10: Examine the graphs, domains, ranges, etc. of the trigonometric
functions, and 
11: Define the inverse trigonometric functions and look at their
graphs. 

Beware: this is
a refresher course, accelerated so that all topics mentioned may be reviewed
in the allotted time. If you have not had College Algebra and a full
course in Trigonometry, you should take MATH 1314 and/or MATH 1316; and then
you may go directly into Calculus I (MATH 2413). 

MATH
2414,
CALCULUS II
[4 Hours, 4 Credits] Text: Stewart,
CALCULUS (Fifth Edition), Thomson (Brooks/Cole), 2003. 
This course is the
second half of a twosemester sequence which examines the theory and
practice of "Elementary Calculus". Prerequisite for this course is
MATH2413 (CALCULUS I) or the equivalent. Entering students should have a basic
understanding of precalculus algebra and trigonometry, and a working
knowledge of limits and derivatives of algebraic functions and their
applications. Since people enter this course with different
backgrounds, the first couple of sessions are often devoted to background
summaries so everyone is ready to go forward from the same starting line. 
We will begin by reviewing
the basic concepts of Limit, Derivative, Antiderivative (Indefinite
Integral) and Definite Integral. 
Then, we shall discuss
summation techniques and reexamine the definite integral as a limit of
sums. This will provide the foundation for using integration to
compute such quantities as volumes and surface areas of complicated solids,
work and energy, moments, and coordinates of centroids of plane laminae.
This work will be the subject matter of our first Examination. 
Some of the integrals
constructed will require specialized "Techniques of Integration". We
will look at several classical methods for constructing antiderivatives of
algebraic, trigonometric, inverse trigonometric, exponential, and
logarithmic functions. Some review of these functions (and their
derivatives) will probably be necessary. This will be the subject
matter of our second Examination. 
When these techniques
fail, one may still be able to integrate functions using limits of sequences
of polynomials (called "Power Series") which approximate them. We will
examine how they are constructed, and only begin to deal with the delicate
issues of reliability of results (using the notion of "Absolute
Convergence", this is usually a big deal in "Advanced Calculus" courses).
The related concept of an "Improper Integral" will also come into play.
You can guess what our third Examination will cover. 
This course is intensive and heavily
reliant on detailed knowledge of algebraic processes, as well as properties
and identities associated with trigonometric, logarithmic, and exponential
functions. Do not even think of taking this course if you have not had
a comprehensive course in trigonometry and achieved at least a "C" in
Calculus I or you have permission of the instructor! 


* * *
* * * * * * *
** * * * * **
* * ** * * * **
**** * * * * *** * *** * **
**** * *** *** * ** 

STORAGE BIN:
Everything below this level is kept in storage for future terms. You
may ignore it, or read it for your enjoyment. 

MATH 1342, INTRODUCTION
TO STATISTICS [3 Hours, 3 Credits]
TEXT: Weiss, Introductory
Statistics, Seventh Edition (2005), Pearson (Addison Wesley). 
This is a basic
course in statistics designed to acquaint the student with the concepts and
basic methods of statistics. Emphasis will be on theoretical rather
than technological processes. 
After a brief
description of what "Statistics" tries to do, we shall take a look at some
basic combinatoric (counting) methods and their role in statistics.
The concept of "Probability" is the unifying theme. This will be the
subject of our first Examination. 
Analysis of data will
be our second major topic. Concepts of average (mean, mode, median),
distribution of data (type and how widely spread) 
Sampling, and how
reliability of samples is measured will be the third consideration. 
This will lead
naturally into the fourth, where we discuss the design of experiments for
hypothesis testing (in particular, "cause and effect" analysis), and compute
probabilities that conclusions made from samples are true about the
population. 
With a good understanding of Intermediate
Algebra, you should find the technicalities not too difficult; but to handle
the problems some clear analysis (the thinking that goes on before the
writing begins) is often required. 
5: Look at graphs
in rectangular coordinates for linear functions, polynomials, and rational
functions; 
6: Discuss
"conic sections" and their corresponding equations; 
7: Look at
techniques for finding or estimating roots of higher degree polynomials
with integer coefficients; 
8: Examine
different techniques for solving "2x2" and "3x3" systems of linear
equations; and 
9: Examine the
domains, ranges, and basic properties of exponential and logarithmic functions. 
If you find
you are either underprepared for this course or falling behind in it,
talk to me immediately about a special study program or other options for
catching up with the discussions! 










MATH 2413,
CALCULUS I
[4 Hours, 4 Credits] 
This is the first of a twosemester sequence of
courses in calculus for students in science and engineering. Because I
will not be teaching Calculus II in the Summer II term, I will let your new
instructor know the topics we covered and continue to make the Library note
sets available on the Sugar Land Campus. We shall 
1: Briefly review
the concepts and procedures of precalculus algebra and trigonometry (if you have not had a course in trigonometry, don't
take this course  I will explain the first day), 
2: Introduce the
concept of limit, and examine its visual and computational properties, 
3: Define the
concept of derivative and learn how to compute derivatives of all kinds of
functions, 
4: Examine
applications of derivatives to problems of curve sketching, extremization,
implicit functions, and related rates, and 
5: Introduce the
concepts of indefinite integral (antiderivative) and definite integral. 
This is an intensive
course, requiring understanding of fundamental principles (including some
new ones), skill in algebraic manipulations, and detailed knowledge of properties of the
functions involved. Don't even think of missing a class if it can be
avoided! 

MATH 2414, CALCULUS II
[4 Hours, 4 Credits] 
This is the second of a twosemester sequence
of courses in calculus for students in science and engineering. We will

1: Briefly review
Calculus I: Limits, derivatives and applications, basic indefinite and
definite integrals, 
2: Use integrals
to calculate areas, volumes, work, moments, and centroids; 
3: Investigate
more sophisticated methods for finding antiderivatives; including those for
algebraic, trigonometric, inverse trigonometric, logarithmic, and
exponential functions; 
4: Investigate
infinite sequences and series and the concept of convergence; 
5: Describe
motions and orbits using parametric equations; and 
6: Examine
algebraic, trigonometric, and calculous properties of graphs in the polar coordinate system. 
This is an intensive course, requiring
understanding of fundamental principles, skill in
algebraic manipulations, and detailed knowledge of the properties of the
types of functions involved. Creativity is also very helpful! 


MATH 0312,
INTERMEDIATE ALGEBRA [ 3 Hours, 0 Credits] 
This Developmental
course prepares students to take College Algebra (MATH1314) and several
other creditbearing college math courses (Finite Math, Statistics, maybe
Business Calculus, etc.). 
Topics include algebra
of polynomials, including basic factoring techniques; solving linear
equations and word problems with the use of linear equations; solving
quadratic equations by factoring or by "Quadratic Formula"; algebra of
fractions and square roots; and graphs of lines and quadratic functions.
[This is only a preliminary outline, and it is not complete.]

There will be a lot of exercises, and regular quizzes in this class.
The three words that best describe how one masters this course are:
"Practice, practice, practice!" 
