Description:

This is the third course in a three-semester sequence on analytic geometry and calculus. Topics include vector-valued functions, functions of several variables, multiple integration, and vector analysis. 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. Analyze surfaces in space.
2. Differentiate multivariable functions and vector-valued functions.
3. Integrate multivariable functions and vector-valued functions.
4. Analyze vector fields.
5. Utilize the calculus of multivariable functions and vector calculus to solve applied problems.

Content Outline & Competencies:

I. Surfaces in Space
   A. Identify equations of right cylinders and sketch graphs of these
cylinders.
   B. Identify equations of quadric surfaces and sketch graphs of quadric
surfaces.

II. Vector-valued Functions
   A. Define vector-valued functions.
   B. Identify the space curve determined by a vector-valued function.
   C. Define differentiation and integration of vector-valued functions.
   D. Calculate derivatives of vector-valued functions.
   E. Calculate integrals of vector-valued functions.
   F. Identify intervals on which a parametrically defined curve is
smooth.
   G. For a given position vector, calculate the velocity and acceleration
vectors.
   H. Determine the principal unit tangent, unit normal and unit binormal
vectors to a given curve at a given point.
   I. Determine the tangential and normal components of an acceleration
vector.
   J. Calculate the arc length of a curve.
   K. Calculate the curvature of a curve.
   L. Calculate the torsion of a curve. 
   M. Use position, velocity, acceleration, speed, and/or tangential and
normal components of acceleration to analyze motion along a curve.

III. Functions of Several Variables
   A. Determine the domain of functions of several variables.
   B. Graph functions of two variables.
   C. Sketch level curves and level surfaces of multivariable functions.
   D. Define limits and continuity for multivariable functions.
   E. Determine limits or show that the limit does not exist for
multivariable functions.
   F. Determine regions on which a multivariable function is continuous.
   G. Define partial derivatives.
   H. Calculate and interpret partial derivatives.
   I. Compute differentials.
   J. Define differentiability of multivariable functions.
   K. State the chain rule.
   L. Apply chain rule for multivariable functions.
   M. Compute and interpret directional derivatives.
   N. Calculate and interpret gradients.
   O. Find equations of tangent planes and normal lines to surfaces.
   P. Find critical points and classify as relative extrema or saddle
points for functions of two variables.
   Q. Find extrema of functions of two variables.
   R. Solve applied optimization problems using multivariable functions.
   S. Utilize Lagrange multipliers to solve constrained optimization
problems.

IV. Multiple Integration
   A. Define double and triple integrals.
   B. Set up and evaluate iterated multiple integrals in rectangular
coordinates.
   C. Use polar coordinates to evaluate double integrals.
   D. Use cylindrical and spherical coordinates to evaluate triple
integrals. (Note:  Students’ prior familiarity with cylindrical and
spherical coordinates should not be assumed.) 
   E. Use double integrals to compute area in the plane.
   F. Use double and triple integrals to calculate volume.
   G. Use double integrals to compute surface area.
   H. Use double and triple integrals in applications including
calculation of mass, center of mass, and moments of inertia.
   I. Implement a change of variables to evaluate a double integral.

V. Vector Analysis
   A. Define vector fields.
   B. Calculate divergence and curl for a vector field.
   C. Define conservative vector field.
   D. Determine whether a vector field is conservative or not.
   E. Calculate the potential function for a conservative vector field.
   F. Define line integrals.
   G. Evaluate a line integral over a given curve.
   H. Use line integrals to calculate work, circulation, and flow.
   I. Calculate flux of a vector field across a curve.
   J. Define path independence.
   K. Determine if a line integral is path independent.
   L. Apply the Fundamental Theorem of Line Integrals.
   M. Apply Green’s Theorem where appropriate.
   N. Define surface integrals.
   O. Evaluate surface integrals.
   P. Calculate flux of a vector field through a surface.
   Q. Parameterize a surface.
   R. Evaluate surface integrals over parameterized surfaces.
   S. Apply the Divergence Theorem where appropriate.
   T. Apply Stokes’s Theorem where appropriate.

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.