For REQUIRED SYLLABUS information that is to be included on all syllabi starting Spring 2018, 201830 go to https://internal.cccs.edu/wp-content/uploads/documents/GT-MA1-Required-Syllabus-Info.docx.

 REQUIRED COURSE LEARNING OUTCOMES:

 1.  Apply vector algebra to the geometry of space.

 2.  Analyze 2 and 3 dimensional curves given as vector valued functions using calculus techniques.

 3.  Examine surfaces/multivariable functions and their graphs using calculus techniques.

 4.  Construct multiple integrals for regions in the plane and space using rectangular, polar, cylindrical, and spherical coordinates to measure areas, volumes, and other applications.

 5.  Evaluate double and triple integrals.

 6.  Determine vector field properties.

 7.  Apply theorems of vector calculus, such as Fundamental Theorem of line integrals, Green’s Theorem, Stokes’ Theorem, and Divergence Theorem.

 8.  Apply multivariable Calculus techniques to engineering and physics problems.

 RECOMMENDED TOPICAL OUTLINE:

 I.    Apply vector algebra to the geometry of space

         A.  Vector addition and subtraction, geometrically and algebraically

         B.  Properties of Vectors in 2 and 3 dimensional space

         C.  Dot product, cross product, and projection

         D.  Applications of the dot and cross products

         E.  Distances in 3-space

 II.   Analyze 2 and 3 dimensional curves given as vector valued functions using calculus techniques

         A.  Graph curves given in vector valued form

         B.  Construct a vector valued function for a given curve

         C.  Evaluate limits

         D.  Determine continuity and smoothness

         E.  Differentiate and integrate vector valued functions

         F.  Parametric and symmetric forms of a line

         G.  Find the unit tangent and unit normal vectors of a curve

         H.  Examine applications of vector valued functions

         I.  Find arc length and curvature

         J.  Projectile motion

 III.  Examine surfaces/multivariable functions and their graphs using calculus techniques

         A.  Construct the equation of a surface of revolution

         B.  Construct a vector valued function for a given surface, with the necessary domain restrictions

         C.  Graph cylinders and quadric surfaces

         D.  Graphs of lines and planes in 3 dimensional space

         E.  Graph cylindrical and spherical coordinates and surfaces

         F.  Construct level curves and level surfaces

         G.  Graph a surface given in parametric form

         H.  Limits and continuity of surfaces

         I.  Find the domain of surfaces/multivariable functions

         J.  Evaluate limits using the definition and theorems

         K.  Find partial derivatives and directional derivatives

         L.  Use the chain rule

         M.  Use implicit differentiation

         N.  Differentials

         O.  Find the gradient

         P.  Find the tangent plane and normal line

         Q.  Optimization of surfaces using calculus

         R.  Show differentiability of a multivariable function

 IV.   Construct multiple integrals for regions in the plane and space using rectangular, polar, cylindrical, and spherical coordinates to measure areas, volumes, and other applications

         A.  Transform equations of surfaces between rectangular, cylindrical and spherical forms

         B.  Transform double integrals between rectangular and polar

         C.  Transform triple integrals between rectangular, cylindrical and spherical

 V.    Evaluate double and triple integrals

         A.  Evaluate iterated integrals

         B.  Change the order of integration in a double or triple integral

 VI.   Determine vector field properties

         A.  Conservative vector fields

         B.  Find curl

         C.  Find divergence

 VII.  Apply theorems of vector calculus, such as Fundamental Theorem of Line Integrals, Green’s Theorem, Stokes’ Theorem, and Divergence Theorem.

         A.  Evaluate a line integral

         B.  Evaluate a line integral in a vector field

         C.  Use the Fundamental Theorem of line integrals

         D.  Use independence of path

         E.  Use Green’s Theorem

         F.  Use Stokes’ Theorem

         G.  Use Divergence Theorem

         H.  Evaluate a surface integral

         I.  Evaluate a surface integral in a vector field

         J.  Find work done in a vector field using theorems related to line integrals

         K.  Find flux in a vector field using theorems related to surface integrals

 VIII. Apply Multivariable Calculus Techniques to Engineering and Physics problems

         A.  Use the Jacobian

         B.  Lagrange Multipliers

         C.  Find center of mass using iterated integrals

         D.  Work (as a projection of a vector)

         E.  Torque

         F.  Static force system

         G.  Moments of Inertia