Description:

This is the first course in calculus as it applies to business; the social, behavioral, and biomedical sciences; and other fields. Concepts include measuring the slope of a curve, writing equations of tangent lines, finding maximum and minimum points, determining the rate of change of a function, and measuring the area under a curve. Algebraic skills and application problems are stressed. Specific calculus topics include finding limits, differentiation of algebraic, exponential and logarithmic functions, and integration of algebraic and exponential functions. Trigonometry (MATH 172) can be taken concurrently with MATH 231 for those students planning to enroll in MATH 232 in subsequent semesters. 3 hrs./wk.

Associated Costs: These are additional (out-of-pocket) expense considerations that students should expect in addition to the course tuition, fees, and textbooks. $0 to $100.

Supplies: Refer to the instructor’s course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

Course Objectives:

Upon successful completion of this course the student should be able to:

1. Evaluate limits of functions using graphs, tables and algebraic methods.
2. Demonstrate the use of limits to determine continuity of a function at a point.
3. Determine differentiability of a function at a point using limits and graphs.
4. Demonstrate the use of the limit definition to find the derivative.
5. Differentiate algebraic, exponential and logarithmic functions.
6. Produce equations of tangent lines.
7. Demonstrate the use of derivatives to describe the behavior of a function.
8. Apply derivatives in applications including economics, physics and social sciences.
9. Antidifferentiate algebraic and exponential functions.
10. Apply the Fundamental Theorem of Calculus to find the area under a curve and between two curves.

Content Outline & Competencies:

I. Demonstrate a knowledge of limits
   A. Evaluating limits.
      1. Evaluate a limit at a point using algebraic techniques or a
table.
      2. Evaluate a limit of a function at infinity using algebraic
techniques or a table.
      3. Evaluate a limit using a graph.
      4. Evaluate left and right hand limits using algebraic techniques or
a graph.
   B. Use of limits
      1. Use of the limit to determine continuity of a function at a
point.
      2. Use a limit to determine differentiability of a function.
      3. Use the limit definition of the derivative to determine
differentiability of a function and to find the derivative of a function.

II. Demonstrate a knowledge of derivatives
   A. Finding and estimating derivatives.
      1. Find the derivatives of algebraic functions using the power rule,
product rule, quotient rule and chain rule.
      2. Find the derivatives of natural exponential and logarithmic
functions.
      3. Find the derivatives using implicit differentiation.
      4. Use a graph to estimate the intervals over which the first
derivative is positive or negative.
      5. Use a graph to estimate the intervals over which the second
derivative is positive or negative.
      6. Find the equation of a tangent line to a curve at a given point.

III. Using derivatives
   A. Apply derivative techniques to curve sketching
      1. Using the first derivative, find critical points.
      2. Determine the behavior of a function using the first derivative.
      3. Using the second derivative, find inflection points.
      4. Determine the concavity of a function using the second
derivative.
      5. Sketch a function using information gathered from the first and
second derivatives.

   B. Apply derivative techniques to physical, economics and social
sciences problems
      1. Use derivatives to predict rates of change.
      2. Use derivatives to determine the maxima/minima (optimization).
      3. Use derivatives to determine outcomes in related rates problems.
      4. Use derivatives to find and explain rates of change for position
functions, including the relationship between position, velocity and
acceleration.
      5. Find extrema of functions with restricted domains.

IV. Finding integrals
   A. Identify the antiderivative for a given function using elementary
techniques.
   B. Identify the antiderivative for a given function using
u-substitution.
   C. Apply the Fundamental Theorem of Calculus.
      1. Evaluate a definite integral using elementary techniques.
      2. Evaluate a definite integral using u-substition.
      3. Calculate the area between two curves.

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

Unit Exams, Unit Papers and/or Unit Projects   40% - 80%
Homework, Quizzes and/or Small Projects         0% - 50%
Final Exam**                                   10% - 40%

**The final exam must count at least as much as any unit exam, unit paper
or unit project. In any course where unit exams are not proctored, the
instructor may require that the student score at least a 70% on the final
exam to earn a ‘C’ for the course. At the instructor's discretion, the
grade on all or any part of the final exam may replace any lower test
score.

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level math course on a space available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.