STANDARD COMPETENCIES:

 

 1.     Demonstrate algebraic knowledge of vectors and the geometry of space.

 2.    Demonstrate the calculus concepts of vector-valued functions and their applications.

 3.     Apply the concepts of function, limit continuity to domains of more than one variable.

 4.      Use the techniques of partial differentiation to solve problems involving functions of two or more variables.

 5.     Develop the techniques of double and triple integration and their applications.

 6.    Demonstrate a knowledge of vector fields, line integrals, Green¿s and Stokes¿ Theorem and their applications.

 TOPICAL OUTLINE:

 

 I.      Perform vector algebra and apply to the geometry of vector spaces.

         A.      Recognize vectors in the plane and in space and resolve them into components.

         B.      Perform vector addition and subtraction.

         C.      Perform dot and cross products.

         D.      Construct parametric equations of lines and planes

         E.      Construct surfaces in space.

         F.      Translate problems to cylindrical and spherical coordinates.

 II.     Perform calculus on vector-valued functions

         A.      Recognize vector-valued functions.

         B.      Differentiate and integrate vector-valued functions.

         C.      Determine tangent and normal vectors to a curve.

         D.      Examine applications of vector-valued functions.

 III.    Apply the concepts of function, limit and continuity to domains of more than one variable.

         A.      Describe the domain and range of a given function.

         B.      Use definitions and/or theorems to find limits.

         C.      Determine where functions are continuous.

 IV.     Use the techniques of partial differentiation to solve problems involving functions of two or more variables.

         A.      Compute the partial derivatives and directional derivatives.

         B.      Compute the gradient of a given function.

         C.      Compute the equations of the tangent plane and normal line to a given surface at a given point.

         D.      Apply the chain rule for partial derivatives.

         E.      Apply partial derivatives to find maxima and minima of surfaces.

         F.      Examine Lagrange Multipliers (optional).

 V.      Develop the techniques of multiple integrals.

         A.      Compute double integrals and examine their applications.

         B.      Translate double integrals to polar coordinates

         C.      Compute triple integrals and examine their applications.

         D.      Translate triple integrals to cylindrical and spherical coordinates.

 VI.     Develop the techniques Vector Analysis.

         A.      Examine Vector Fields.

         B.      Compute line integrals and apply them.

         C.      Examine conservation of vector fields and independence of path.

         D.      Apply Green¿s Theorem.

         E.      Examine parametric surfaces and compute a surface integral.

         F.      Analyze the Divergence Theorem and apply Stokes¿ Theorem.