Description:

This is the first of a three-semester sequence on calculus designed for engineering, physics and math majors. Rates of change, areas and volumes will be studied. To accomplish this, the students will study and apply limits and continuity. Differentiation and integration of algebraic, trigonometric and transcendental functions will also be a major focus of this course. 5 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 the limits of functions.
2. State whether a function is continuous or discontinuous based on both the graph and the definition of continuity.
3. Use limits to describe instantaneous rate of change, the slope of the tangent line and the velocity and acceleration of a moving particle.
4. Differentiate algebraic, trigonometric, and transcendental functions explicitly and, where appropriate, implicitly.
5. Use derivatives for curve sketching.
6. Use and interpret the derivatives of functions to solve problems from a variety of fields, including physics and geometry.
7. Integrate algebraic, trigonometric, and transcendental functions.
8. Compute definite integrals by the Fundamental Theorem of Calculus, by numerical techniques, and by substitution.
9. Use integration results to calculate areas, volumes, and mean values.

Content Outline & Competencies:

I. Using Limits
   A. Evaluation of limits
      1. Evaluate the limit of a function at a point both algebraically
and graphically.
      2. Evaluate the limit of a function at infinity both algebraically
and graphically.
      3. Use the definition of a limit to verify a value of the limit of a
function.
   B. Use of limits
      1. Use the limit to determine the continuity of a function.
      2. Use the limit to determine differentiability of a function.
   C. Limiting process
      1. Use the limiting process to find the derivative of a function.
 
II. Finding Derivatives
   A. Find derivatives involving powers, exponents, and sums.
   B. Find derivatives involving products and quotients.
   C. Find derivatives involving the chain rule.
   D. Find derivatives involving exponential and logarithmic functions.
   E. Find derivatives involving trigonometric and inverse trigonometric
functions.
   F. Find derivatives involving implicit differentiation.
   G. Use the derivative to find velocity, acceleration, and other rates
of change.
   H. Use the derivative to find the equation of a line tangent to a curve
at a given point.
    
III. Using Derivatives
   A. Curve sketching
      1. Use the first derivative to find critical points.
      2. Apply the Mean-Value Theorem for derivatives.
      3. Determine the behavior of a function using the first derivative.
      4. Use the second derivative to find inflection points.
      5. Determine the concavity of a function using the second
derivative.
      6. Sketch the graph of the function using information gathered from
the first and second derivatives.
      7. Interpret graphs of functions.
   B. Applications of the derivative
      1. Solve related rates problems.
      2. Use optimization techniques in economics, the physical sciences,
and geometry.
      3. Use differentials to estimate change.
      4. Use Newton’s Method.
      
IV. Finding Integrals
   A. Find area using Riemann sums.
   B. Express the limit of a Riemann sum as a definite integral.
   C. Evaluate the definite integral using geometry.
   D. Integrate definite integral using numerical approximation.
   E. Evaluate definite integrals using the Fundamental Theorem of
Calculus.
   F. Integrate algebraic, natural exponential, natural logarithm,
trigonometric, and inverse trigonometric functions.
   G. Integrate indefinite integrals. 
   H. Integration by substitution.
   I.  Integration by parts.
   
V. Using the Integral
   A. Utilize the Mean-Value Theorem for Integrals.
   B. Calculate the area between curves using integration.
   C. Calculate the volume of a solid of revolution by the disk method.
   D. Calculate the volume of a solid of revolution by the washer method.
   E. Calculate the volume of a solid of revolution by the cylindrical
shells method.
   F. Calculate the arc length and surface area using integration.

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.