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MAT 250

I.     TITLE:   Calculus and Analytic Geometry I

II.    CATALOG DESCRIPTION:   Inequalities, absolute value, plane analytic geometry, limits, derivatives, beginning integration and applications.

III.    PURPOSE:   This course enhances the student's mathematical abilities through such fundamental concepts as inequalities, limits, and rates of change.  In order to do this thoroughly, the course embodies several aspects.  Communication through oral presentations  and written mathematical composition is pertinent  to effectively and efficiently encourage precise, independent thought.  The logical processes envelop serious analysis of techniques and applications relating to motion problems in physics, population growth in biology, algorithmic concepts in computer science, mixing problems in chemistry, and profit analysis in economics, to name a few.  Also, the student must investigate the validity of solutions in various applications.  This may involve computer software, graphing calculators, or just diligent study with pencil and paper.  In a sense, this course helps the student to understand his/her responsibility to himself/herself and to the class in being an active participant in group activities or open discussions.  Consequently, one can develop skills not only involving manipulation of derivatives and integrals, but also involving comprehension of the usefulness of these calculus tools in other fields of study.

IV.     COURSE OBJECTIVES:
A.  Fundamental Concepts
The student should gain understanding of basic calculus ideas that they   can master by building on their algebra and geometry expertise.     Throughout the process of helping students bridge the gap between abstract   terminology to concrete ideas, various objectives become apparent.  The   student should
  1)  understand functions graphically, numerically, analytically, and    verbally,
  2)  have a strong intuitive grasp of the limit and the derivative,
  3)  ascertain a solid analytical understanding of continuity,
  4)  and understand Riemann sums and their connection to integration.
B.  Application of Content
     In this course, the student can visualize the connection through
  1)  modeling a written description of a mixing or population growth problem with functions, differential equations, integrals,
       and other tools,
  2) using graphing calculators and computer software to visually work with such ideas concerning the derivative of an area
      curve reproducing the original function under which the area occurred,
  3) and communicating the students’ ideas orally through presentations discussing the reasonableness of a solution in other
      settings.
C.  International Perspectives
      The students attain an inside look at the history of calculus and its    international background through prescribed reading
      assignments.

V.     CONTENT OUTLINE:
A.  Review
  1.  Algebraic operations, function, coordinate systems, graphing
  2.  Angles, trigonometric functions and relationships
B.  Limit
  1.  Basic concept and definition of the limit
  2.  Computation of limits at a point and at infinity
C.  Continuity of Functions
D.  Derivative
  1.  Physical motivation for and definition of the derivative
  2.  Derivatives of basic algebraic and trigonometric functions
  3.  Chain rule, implicit differentiation, related rate applications
  4.  Tangent line, linear approximation, and differentials
  5.  Graphing using the first and second derivatives
  6.  Optimization, Newton’s method, and other applications
E.  Integral
  1.  The antiderivative and the indefinite integral
  2.  Basic differential equations
  3.  Riemann sums and area
  4.  Fundamental Theorem of Calculus
  5.  Are of regions, volumes of solids of revolution, and surface area
  6.  Work, pressure, and other applications

VI.     INSTRUCTIONAL ACTIVITIES:
A.  This course is designed to give students an appreciation for various   concepts in calculus.  There exists a multitude of possibilities in    order to relay the information.  Instructors lecture in various capacities and  require students to put problem solutions on the board and to explain   orally the procedure.  Indeed, other strategies as group discussions,    individual and team projects, and technology work have managed to   engage students actively in the learning process.  In some     sections, the students are encouraged to discuss problem solving techniques  within a group setting in order to enhance their abilities in critically    evaluating and comprehending the material.  Group homework and   projects provide new sources of cooperative learning.
  1.  Specifically, two to three students are placed or are allowed to self-  select themselves to be in a group.   The group
       decides on a scribe to take   careful notes and to finalize the written work ,and  it also decides on a   mediator to make
       final  decisions if there is any dissension among the   participants.  Moreover, it is the responsibility of  the mediator and
       each of   the group members to insure  that everyone participates and that everyone   understands the concepts.  If one
       member is not active or if one is too   vivacious, then the peer group is responsible for encouraging one or for calming
       the other.  Also, each person in the  group is given the same grade   for the work.  Grading is based on thoroughness  of
       answers and proficiency   in the mathematical concepts.
  2.  Group homework assignments are completed in class.  They    involve problems from the material and word problems of
       which the   group must strategically solve.  Each question contains a comprehensive,   written response that explains the
       steps and cohesively answers the    question.  In -class group work will count as part of daily work.  In addition,  group
       projects are assigned for a combined effort outside of class.  They may  encompass a computer lab assignment, a carefully
       designed experiment   with graphical analysis, or a problem designed to be explored via a graphing  calculator.  Indeed,
       several problems cross various curricular borders.  For   example, a project may involve discussing the connection
       between    derivatives and velocity or acceleration within a physical setting.   In    general,  each report is to be neatly
       written in the form of a small essay.    Also, group projects will be included in the project portion of the grading in  which
       the  same grade is given to each group member.

B.  Each student has at least two main responsibilities for class daily.  These are to work the assigned problems as thoroughly as possible and to read the material that is to be discussed on that day.  Consequently, homework or a quiz may be given in which the student’s work  is carefully reviewed and graded as daily work.  In addition, the student must be able to critically   analyze such concepts as instantaneous velocity and related rates through visual manipulation of pictures via pencil and paper or by means of a computer or calculator display.  Furthermore, they need to logically take the picture and model it using correctly written mathematical  language.  A student may be asked to present  such a problem on the board.   That person must verbally expound on his/her solution and explain what technology he/she used to arrive at the result.  This rather informal presentation may count as a daily grade or as extra credit.  The grade will be assigned based on clarity of work, ability of the student to answer questions, and the correctness of the result.  Also, a student may be required to prepare a speech of variable length discussing the applicability of a calculus concept to physics, biology, architecture, etc.  This will be graded similar to the board  work.  However, it will be included within the project component of the grading.  Necessarily, the ability of the student to openly discuss his/her conclusions through a prepared verbal address or an impromptu comment only increases the assimilation of applicable knowledge.

C.  Each student has the opportunity to further investigate his/her mathematical understanding on various computers located in the math   laboratory.  Several instructors plan sessions in the laboratory to better illustrate the limit processes, Riemann sums, function manipulation, and other concepts.  In addition, some instructors coordinate listservs so that class can receive information and homework via email.

VII.     FIELD, CLINICAL, AND/OR LABORATORY EXPERIENCES:   Several instructors choose to meet in the computer laboratory in FH 109 to illustrate a concept or to have the computer do complicated calculations so that the students can concentrate on the concept at hand.  Also, instructors may designate homework assignments to be done using Maple or some other computer software available in the laboratory.

VIII.     RESOURCES:  In addition to the textbook, a graphing calculator can be beneficial.  The instructor is one of the best assets for the student.  Several instructors issue handouts to aid in the understanding and the organization of the material.

IX.     GRADING PROCEDURES:
A.  Performance on exams, quizzes/projects, computer assignments, textbook assignments, and the final exam will be considered in determining  the student’s grade.  The exams will test the comprehension of concepts and skill not covered on a previous exam.  Exams may contain essay questions as well as procedure-based problems.  The final exam is comprehensive, covering any material addressed that semester.  The quizzes/projects involve reading assignments from the text and requires   the connection of core concepts with some applications.  The grade is based on content and the effectiveness of the written communication to explain the reasoning and appropriate logic behind the mathematics.  Computer and other homework assignments are tailored to the material at hand.   They involve relatively short investigations of significant calculus terms.    Cumulatively, the following percentages represent the composition of the   graded work.

 Exams   55%
 Final Exam  25%
 Daily Work  15%
 Projects   5%

B.  Important dates involve the last day to drop a course without receiving   a “W”, the last day to change from audit to credit, and the last day to    withdraw completely from the university.  The student should realize that   these dates are firm.
C.  Auditing is strictly based on the permission of the instructor.  Several   instructors require all exams and assignments to be completed in order to   receive an audit.
D.  The following scale is used to determine the letter grades for the course.
     A      90-100
     B      80-89
     C      70-79
     D      60-69
     E      0-50

X.    ATTENDANCE POLICY:    While attendance is not graded, the student is responsible for attending all classes.  Attendance is taken for each class period.  Any missed work must be completed within a reasonable time frame.  Missed exams are administered differently depending on the instructor.

XI.     ACADEMIC HONESTY:  Graded individual assignments and examinations must entirely be the student’s work. Any instance of academic dishonesty, as determined by the instructor, in compliance with the Board of Regents policy on Academic Integrity as of February 1975, will result in zero points for the assignment and possibly a grade of “E” for the course.

XII.   TEXT AND REFERENCES:  Current

XIII.     PREREQUISITES:  A math ACT score of at least 26 , or  MAT 150 (or MAT 140 and 145).

Last updated February 14, 2000. Designed and maintained by Kyosung Koo