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MA 227 Standards

Calculus III - 2017 Summer
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  6. MA 227 Standards

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.

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