MA 227 Standards

Calculus III - 2017 Summer

At the end of the course, each student should be able to…

Core Standards

• C01: SurfaceEQ. Identify and sketch surfaces in three-dimensional Euclidean space.
• C02: VectFunc. Model curves in Euclidean space with vector functions.
• C03: VectCalc. Compute and apply vector function limits, derivatives, and integrals.
• C04: VectFuncSTNB. Compute and apply the arclength parameter and TNB frame for a vector function.
• C05: MultivarCalc. Compute and apply the partial derivatives, gradient, and directional derivatives of a multivariable real-valued function.
• C06: ChainRule. Apply the multivariable Chain Rule to compute derivatives.
• C07: DoubleInt. Compute and apply double integrals.
• C08: TripleInt. Compute and apply triple integrals.
• C09: PolCylSph. Apply polar, cylindrical, and spherical transformations of variables.
• C10: VectField. Analyze vector fields, including computing curl and divergence.
• C11: LineInt. Compute and apply line integrals.
• C12: FundThmLine. Apply the Fundamental Theorem of Line Integrals.

Supporting Standards

• S01: 3DSpace. Plot and analyze points and vectors in Euclidean space.
• S02: DotProd. Compute and apply the dot product of two vectors.
• S03: CrossProd. Compute and apply the cross product of two vectors.
• S04: Kinematics. Compute and apply position, velocity, and acceleration vector functions.
• S05: MulivarFunc. Sketch and analyze the domain, level curves, and graph of a two-variable real-valued function.
• S06: Lineariz. Compute the linearization of a two-variable real-valued function at a point and use it for approximation.
• S07: Optimiz. Use the first-derivative test and Lagrange multipliers to optimize a real-valued multivariable function.
• S08: TransVar. Compute and apply a transformation of variables.
• S09: ParamSurf. Parametrize surfaces in three-dimensional Euclidean space.
• S10: SurfInt. Compute and apply surface integrals.
• S11: GreenStokes. Apply Green’s Theorem and Stokes’s Theorem.
• S12: DivThm. Apply the Divergence Theorem.