Georgia flagGeorgia: Multivariable Calculus Math Standards

30 standards · 5 domains

MVC.AQR

  • MVC.AQR.3.1 Approximate the partial derivatives at a point of a function defined by a table of data.
  • MVC.AQR.3.2 Find expressions for the first and second partial derivatives of a function.
  • MVC.AQR.3.3 Use the total differential to approximate mathematical models.
  • MVC.AQR.3.4 Represent the partial derivatives of a system of two functions in two variables using the Jacobian.
  • MVC.AQR.3.5 Find the partial derivatives of the composition of functions using the general chain rule.
  • MVC.AQR.3.6 Apply partial differentiation to problems of optimization, including problems requiring the use of the Lagrange multiplier.
  • MVC.AQR.3.7 Find the family of solutions and the envelope of the family of solutions to differential equations, including Clairaut equations.
  • MVC.AQR.3.8 Define and apply the gradient, the divergence, and the curl in terms of differential vector operations.
  • 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.
  • 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.

ABSTRACT & QUANTITATIVE REASONING – PARTIAL DIFFERENTIATION

  • MVC.AQRa.3 Define, describe, and represent the differentiation of functions of two independent variables and differential vectors to solve contextual, mathematical problems and to explain real-life phenomena.

ABSTRACT & QUANTITATIVE REASONING – INTEGRATION

  • MVC.AQRb.4 Interpret integrals of functions of two independent variables and of vector functions to solve contextual, mathematical problems and to explain real-life phenomena.

MATHEMATICAL MODELING

  • MVC.MM.1.1 Explain contextual, mathematical problems using a mathematical model.
  • MVC.MM.1.2 Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.
  • MVC.MM.1.3 Using abstract and quantitative reasoning, make decisions about information and data from a contextual situation.
  • MVC.MM.1.4 Use various mathematical representations and structures with this information to represent and solve real-life problems.

PATTERNING & ALGEBRAIC REASONING – VECTORS, FUNCTIONS, AND ANALYTIC GEOMETRY IN THREE DIMENSIONS

  • MVC.PAR.2.1 Represent equations of lines in space using vectors.
  • MVC.PAR.2.2 Express the analytic geometry of three dimensions in terms of the dot product and cross product of vectors.
  • MVC.PAR.2.3 Use a linear system of equations to determine whether two planes intersect in a single point or a line, or whether they do not intersect at all.
  • MVC.PAR.2.4 Evaluate functions of two independent variables at a point in the plane.
  • MVC.PAR.2.5 Graph the level curves of functions of two independent variables.
  • MVC.PAR.2.6 Investigate the continuity of functions of two independent variables in terms of the limits of such functions as (x, y) approaches a given point in the plane.
  • MVC.PAR.2.7 Determine points or regions of discontinuity of functions of two independent variables.