STANDARD COMPETENCIES:

 

 1.   Solve problems involving curves defined parametrically which involves slope and area.

 2.   Describe the difference between scalars and vectors geometrically and algebraically.

 3.   Demonstrate the ability to work with vector valued functions.  This includes limits, continuity, derivatives, and integrals.

 4.   Solve problems involving velocity and acceleration.

 5.   Solve problems involving the unit tangent and unit perpendicular vector, the unit binomial vector, curvature and tangential and normal components of acceleration both in two space and three space.

 6.   Demonstrate the ability to graph in three dimensions, and know the formulas of basic three dimensional objects such as spheres and planes.

 7.   Work problems involving the dot and cross product.

 8.   Work problems of the line in three space both symmetrically and parametrically.

 9.   Identify the 6 basic different surfaces in three dimensions.  These surfaces are the ellipsoid, hyperboloid of one and two sheets, elliptic paraboloid, hyperbolic, paraboloid ,and elliptic cone.

 10. Relate problems in the rectangular coordinates to the cylindrical coordinates and spherical coordinates.

 11. Apply the concept of the partial derivative.

 12. Apply the concept of differentiability and its relationship to the gradient.

 13. Demonstrate an understanding of the directional derivative, level curves and level surfaces.

 14. Solve problems involving the chain rule for many variables.

 15. Demonstrate the ability to work problems involving maxima and minima both with the second partials test and Lagrange's method.

 16. Demonstrate the ability to work with the double and triple integral and understand applications.  The student will also understand the use of the surface area integral.

 17. Demonstrate knowledge of vectors fields, the potential function, and the divergence and curl of a vector field.

 18. Show proficiency with the line integral and independence of path.

 19. Demonstrate ability to do problems involving surface integrals.

 20. Demonstrate knowledge of the theorems of Green, Gauss, and Stokes and applying the theorems.

 

 TOPICAL OUTLINE:

 

 I.      Geometry in the plane, vectors

 II.     Geometry in space, vectors

 III.    The derivatives in n - space

 IV.     The integral in n-space

 V.      Vector calculus

 VI.     Green's, Gauss's and Stokes Theorem

 VII.    Linear Algebra