Description:

This is the second course in a two-semester series on calculus that covers five techniques of integration, differentiation and integration of trigonometric functions, differential equations, and functions of several variables as applied to business, statistics, biology and the social sciences. 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. Differentiate trigonometric and multivariable functions.
2. Integrate trigonometric and multivariable functions.
3. Solve differential equations.
4. Use calculus to solve probability problems.
5. Use calculus to solve business application problems, e.g., Cobb-Douglas production function.

Content Outline & Competencies:

I. Additional Integration Techniques
   A. Calculate definite and indefinite integrals using integration by
parts.
   B. Calculate definite and indefinite integrals using the Integration
Tables.
   C. Determine value of definite integrals using numerical integration.
   D. Determine whether improper integrals converge.
   E. Apply l’Hôpital’s Rule to find limits.

II. Multivariable Calculus
   A. Discover the need for and the use of functions of several
variables.
   B. Discover how to compute the first and second partial derivatives of
functions of several variables.
   C. Compute the value of double integrals.
   D. Locate the coordinates of any relative extrema of a function of two
variables.
   E. Utilize Lagrange Multipliers to compute the maximum or minimum of a
function subject to constraints.
   F. Find the best fitting line through three points using the method of
least squares. (Optional)
   G. Use total differentials to obtain an approximation of an expression.
(Optional)

III. Differential Equations
   A. Identify differential equations.
   B. Solve differential equations using the method of separation of
variables.
   C. Calculate approximate solutions to differential equations using
Euler’s method. (Optional)
   D. Determine the qualitative behavior of solutions to differential
equations. (Optional)
   E. Apply differential equations to problems, e.g. logistic growth.

IV. Calculus and Trigonometric Functions
   A. Review the sine and cosine functions.
   B. Discover the derivatives of the sine and cosine functions.
   C. Discover the integrals of the sine and cosine functions.
   D. Extend the derivatives and integrals of the sine and cosine
functions to the other trigonometric functions.

V. Calculus and Probability Theory
   A. Define discrete probability
   B. Identify continuous probability density functions.
   C. Compute expected value and variance of a continuous random variable
and compare to discrete probability.
   D. Convert a normal distribution function to a standard normal
distribution function.
   E. Use the standard normal distribution function to calculate the
probabilities of a random variable.

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.