Text only

MAT 230

 I.  TITLE:  Technical Math II

II.  CATALOG DESCRIPTION:
Analytic geometry, differential and integral calculus with applications from technical fields.

III.  PURPOSE:
Math 230 is a first course in calculus that is meant to develop a feeling for mathematical methods and applications associated with analytic geometry and differential and integral calculus.  The approach used is basically an intuitive one.  Numerous applications  from many fields of study are included.  However, it is not necessary that the student have a specific knowledge of the area from which any given problem is taken.
    Math 230 contributes to the knowledge and skills necessary to develop many of the desired characteristics of the Murray State graduate.  Students in this course are encouraged to engage in mature, independent thought as they complete written assignments, participate in class discussion and present their work in both oral and written form to the instructor and their fellow classmates.  As students complete their assignments they are employing mathematical methods to discover solutions to various problems. They  also use reasoning skills to verify their conclusions.  By carefully analyzing and evaluation the situation the problem presents, students use mathematical procedures to reach logical decisions.  Math 230 develops the students understanding of the role and applications of technology and science through use of graphing calculators and through the applied problems that are  assigned and discussed.
    As students learn that class attendance and good study habits lead to success in the classroom, they are developing the dedication and discipline necessary to become responsible citizens.  Since the topics covered in Math 230 relate to many fields of study, students who complete this course will be better able to demonstrate mastery in their chosen field of study.  In general, the analytical and logical approach of mathematics will instill in students thought  processes that will help them as they prepare for a successful, productive life.

IV. COURSE OBJECTIVES:
A.  Students will be introduced to the following fundamental concepts and ways of knowing
  1.  Solve linear and nonlinear inequalities.
  2.  Understand the relationship of an algebraic equation and geometric properties of the curve (straight line, circle, parabola,
       ellipse, hyperbola) that represents the equation.
  3.  Become familiar with trigonometric identities and inverse trigonometric functions.
  4.  Develop a basic understanding of the derivative as a rate of change of one quantity with respect to another.
  5.  Determine the derivative of algebraic functions (differentiation).
  6.  Use analytical thinking to solve problems involving applications of the derivative of algebraic functions.
  7.  Perform the process of integration (reversing the process of differentiation).
  8.  Use analytical thinking to solve problems involving applications of the process of integration.
B.  The content and methods covered in Math 230 relate to many  fields of study other than mathematics.  Following are some examples of the interdisciplinary understanding and the functional use in society of the topics covered in this course.
   1.  Inequalities are uses in business to set production levels for maximizing profits or minimizing cost, in electricity to for the
        values of a current that is less than a given value, in computer programming to switch from one part of a program to
        another based on a result that is greater than (or less than) some programmed value and in many other fields of study.
   2.  The concepts developed from studying the line, parabola, circle, ellipse, and hyperbola have many technical and scientific
        applications, which include projectile motion, planetary orbits, and fluid motion.  Also, the design of gears, airplane wings
        and automobile headlights as well as construction of bridges and nuclear cooling towers are some other applications.
   3.  Trigonometric identities are used to develop expressions and solve equations in physics, electronics, chemistry, surveying
        and other technical fields.
   4.  The methods of differential calculus has applications in fields of study such as physics, business, electricity, and other
        technical fields.  Examples of rates of change are velocity, the rate of change of the length of a metal rod with respect
        to temperature, the rate of change of light intensity with respect to the distance from the source, the rate of change of
        electric current with respect to time, and the rate of change of production costs with respect to the number of units a
        business produces. Other applications of the derivative include finding the maximum possible income from production or
        the least amount of material needed to make a product or even the dimensions of a beam with the greatest strength.
   5.  Integral calculus has important applications in electricity, mechanics, hydrostatics, architecture, machine design, business,
        and physics.  It can be applied to finding areas and volumes, as well as to the physical concepts of work, pressure, and
        the center of mass.
C.  This course does not lend itself to international perspectives.

V.    CONTENT OUTLINE:
A.  Logarithms and applications
      laws of logarithms, common and natural logarithms, exponential and logarithmic equations
B.  Solving inequalities including absolute value inequalities
C.  Plane analytic geometry
      Circles, parabolas, ellipses, and hyperbolas
D.  Introduction to derivatives
      Limits and continuity, average rate of change, the derivative, derivatives of    polynomials, instantaneous rate of change,
      product and quotient rules, chain   rule, implicit differentiation, higher-order derivatives
E.  Applications of derivatives
     Tangents and normals, curve sketching, applied maximum and minimum    problems, related rates, curvilinear motion,
     differentials
F.  Introduction to integration
     Antiderivatives, indefinite integral, area under a curve, fundamental theorem   of integral calculus, numerical integration
G. Applications of integration
     Area between two curves, volumes of revolution using disk and washer    methods
H. Trigonometric identities and additional trigonometric formulas
     Basic identities, sum and difference of two angles, double-angle and
     half-angle formulas

VI.  INSTRUCTIONAL ACTIVITIES:
A.  There are several instructional activities used to assist the student in learning the material.  The instructor presents lectures on the material.  This might include interaction between students and the teacher in a discussion format.  As in  any math course, students are assigned homework problems to work outside
class that are pertinent to each lecture.  In class, instructors might assign
problems to be worked in groups to encourage interaction among students or worked by the individual students in more of a quiz format.  Group work is treated differently by various instructors but usually is considered similar to a quiz with all members of the group receiving the same grade.  In some sections, students are  asked to put problems on the board and explain their work.

B.  As is typical of any math course, students will be using critical thinking in all their problem solving from basic homework problems to actual exam questions.  In mathematics, critical thinking takes place when a student reads  a problem, analyzes the situation, organizes the information, and determines appropriate procedures.  The homework assignments, quizzes,  group work, and exams provide the students with opportunities to test their understanding of the concepts and effectively explain in writing how they arrived at the solution.  Also, students who are assigned problems on the board must verbally explain their work and may be given a grade based on their presentation.  This grade would probably be considered in conjunction with their homework grades.  Students might  be required to give oral presentations from three to ten times during the course.

C.  Students are required to purchase a graphing calculator to aid in homework and on exams.

VII.    FIELD AND CLINICAL EXPERIENCES:  None

VIII.   RESOURCES:   The resources that the student has access to are the text, lectures, the instructor, and a graphing calculator.

IX.   GRADING PROCEDURE:
The student's grade is determined by the performance on exams, homework, quizzes, the comprehensive final exam, and other in class activity set forth by the instructor.  The breakdown for the different components of the course grade might be as follows:
        homework, quizzes and
        other in class activities:  10%-20%
        exams (except final exam):  55%-65%
        comprehensive final exam:  15%-25%

Grades are assigned based on the following grading scale:
         A 90 - 100%
         B 80 - 89%
         C 70 - 79%
         D 60 - 69%
         E below 60%

 A student must have the consent of the instructor to audit the course.

X.   ATTENDANCE POLICY:  Regular attendance is expected of the student.  The instructor determines how attendance will be reflected in the grade.  The student is responsible for any missed work.  Make-up work and exams are given at the discretion of the instructor.

XI.   ACADEMIC HONESTY POLICY:  Any instance of academic dishonesty as determined by the instructor (in compliance with Board of Regents policy on Academic Integrity - Feb. 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:  MAT 130

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