MVC.AQR.4Multivariable and Vector Integrals

Expectations

• Evaluate and apply double and triple integrals.

  • MVC.AQR.4.1

    Integrate functions of the form $z = f(x, y)$ or $w = f(x, y, z)$ through various techniques.

  • MVC.AQR.4.2

    Use, evaluate, and interpret double and triple integrals in terms of volume and mass.

  • MVC.AQR.4.3

    Represent and evaluate integrals of vector functions as double and triple integrals.

• Evaluate and interpret line and surface integrals.

  • MVC.AQR.4.4

    Apply line and surface integral to functions representing real-world phenomena.

  • MVC.AQR.4.5

    Solve first-order exact differential equations.

  • MVC.AQR.4.6

    Use Green’s Theorem to evaluate line integrals in the plane; use Stokes’ Theorem to evaluate line integrals in space.

  • MVC.AQR.4.7

    Determine whether a line integral is independent of path and use line integrals in context.

  • MVC.AQR.4.8

    Use Gauss’ Divergence Theorem to evaluate surface integrals.

  • MVC.AQR.4.9

    Define and apply the gradient, the divergence, and the curl in terms of integrals of vector functions.

Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.