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)-243-8541  (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 2414-902  (CRN 20081),   CALCULUS II                      M, Tu, W, Th    8- 8:50 A.M.                      Room  SU 308
     2:  MATH 1314-902  (CRN 20040),   COLLEGE ALGEBRA          M,W,F             10 A.M. - 10:50 A.M.         Room SU308
     3:  MATH 2312-901  (CRN 21092),   PRECALCULUS                   M,W,F             12 NOON - 12:50 P.M.     Room SU 306
     4:  MATH 1316-901  (CRN 20068),   TRIGONOMETRY               Tu,Th                9:25 - 10:40 A.M.               Room SU 407
     5:  MATH 1325-902  (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 5-9, 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 1316TRIGONOMETRY    [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 2413-2414, 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 two-semester "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 two-semester 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 re-examine 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!
 
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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 two-semester 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 2414CALCULUS II    [4 Hours, 4 Credits]
This is the second of a two-semester 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 credit-bearing 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!"
 
 

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