Description:

This is the second course of a three-semester sequence on calculus. The emphasis will be an analytic, numerical and graphical approach to techniques of integration, infinite series and vectors in the plane including scientific applications. 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. Identify and use techniques necessary for integration.
2. Use infinite series to approximate functions.
3. Apply techniques of differential and integral calculus to parametric and polar equations.
4. Use vectors in the plane and in space.
5. Use calculus to model and solve scientific applications.

Content Outline & Competencies:

I. Techniques of Integration 
   A. Evaluate an integral using the method of partial fractions.
   B. Evaluate an integral which involves powers of trigonometric
functions.
   C. Evaluate an integral by using trigonometric substitutions.
   D. Evaluate an integral by using integral tables.
   E. Apply L’Hôpital’s Rule to evaluate limits involving indeterminate
forms.
   F. Determine whether an improper integral converges or diverges.
   G. Test for the convergence or divergence of an improper integral using
an
       appropriate test.
   H. Evaluate a convergent improper integral.
    

II. Infinite Sequences and Series
   A. Determine whether an infinite sequence converges or diverges.
   B. Find the limit of a convergent sequence.
   C. Identify geometric series, telescoping series, harmonic series,
p-series,
       alternating series, and power series. 
   D. Determine whether an infinite series converges or diverges. 
   E. Test for convergence or divergence of an infinite series using an
appropriate 
       test. 
   F. Determine whether an infinite series converges absolutely or
conditionally.
   G. Find the radius and interval of convergence for a power series.
   H. Write a power series which represents a function.
   I. Write a Taylor polynomial which represents a function.
   J. Calculate the error in approximating a function with an infinite
series.
   
 III. Parametric and Polar Equations
   A. Differentiate parametric equations.
   B. Calculate the length of a smooth parametrized curve.
   C. Calculate the surface area from a parametrized curve.
   D. Graph polar equations.
   E. Convert from rectangular to polar coordinates and vice-versa.
   F. Differentiate polar equations.
   G. Integrate polar equations.
   H. Calculate the area in the plane using polar coordinates.
   I. Calculate the area between two curves using polar coordinates.
   J. Calculate the length of a polar curve.
   K. Calculate the surface area of a surface of revolution using polar
coordinates.


IV. Applications of Definite Integrals in physics
    A. Calculate work, moments and centers of mass.
    B. Calculate fluid pressures and forces.
          
V. Vectors in the Plane and in Space
   A. Determine the components of a vector in the plane and in space and
illustrate
       geometrically.
   B. Apply vector operations and properties and interpret them
geometrically.
   C. Calculate the dot product to determine the angle between two
vectors.
   D. Find the magnitude and direction of a resultant vector and
illustrate
       geometrically.
   E. Find tangent and normal vectors to a parametrized curve.
   F. Determine the components of a vector-valued function.
   G. Determine a vector passing through two points.
   H. Determine whether two vectors are orthogonal
   I. Determine whether two vectors are parallel.
   J. Determine the projection of one vector onto another vector.
   K. Calculate the cross product for two vectors and interpret
geometrically.
   L. Write the parametric equations for a line in space.
   M. Determine the equation for a plane.

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%

   Grading scale:
   90 - 100%   A
   80 -  89%   B
   70 -  79%   C
   60 –  69%   D
    0 –  59%   F

**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.