Calculus III

1. Vectors and the Geometry of Space 1: I can
   • express vectors with appropriate notation,
   • add vectors,
   • subtract vectors,
   • scale vectors,
   • find the magnitude of a vector,
   • find the direction of a vector.
2. Vectors and the Geometry of Space 2: I can
   • compute the dot product of two vectors,
   • find the angle between two vectors,
   • determine whether two vectors are orthogonal,
   • compute the orthogonal projection of one vector onto another.
3. Vectors and the Geometry of Space 3: I can
   • compute the cross product of two given vectors to find a third vector orthogonal to each of the given vectors.
4. Vectors and the Geometry of Space 4: I can
   • find the equation of a line in space given a point and a vector in space,
   • find the equation of a line in space given two points in space,
   • express a line in space as a vector equation,
   • express a line in space as using parametric equations.
5. Vectors and the Geometry of Space 5: I can
   • find the equation of a plane given a point and a normal vector in space,
   • find the equation of a plane given three points in space.
6. Vectors and the Geometry of Space 6: I can
   • match standard quadric surfaces and their standard equations,
   • place the equation of a quadratic surface into standard form.
7. Vector-Valued Functions 1: I can
   • sketch the graph of a vector-valued function of a single variable,
   • compute limits involving vector-valued functions,
   • determine whether a vector-valued function is continuous at a point.
8. Vector-Valued Functions 2: I can
   • use the derivative rules to compute the derivative of a vector-valued function,
   • use the derivative rules to find the vector tangent to a point on a space curve,
   • compute the unit tangent vector at a point on a space curve,
   • compute definite and indefinite integrals involving vector-valued functions.
9. Vector-Valued Functions 3: I can
   • represent the path of an object moving in space using a vector-valued function,
   • compute the velocity, speed, and acceleration of an object moving in space,
   • find the vector-valued function representing the path of an object moving in space given either the acceleration or velocity vector and appropriate initial conditions,
   • recognize straight-line and circular motion.
10. Vector-Valued Functions 4: I can
    • compute the length of a space curve on a closed interval,
    • parameterize a curve by arc length under appropriate conditions.
11. Vector-Valued Functions 5: I can
    • compute the curvature of a smooth space curve,
    • compute the principal unit normal vector for a smooth space curve,
    • compute the tangential and normal components of the acceleration,
    • compute the binormal vector for a smooth space curve and interpret the TNB frame,
    • compute the torsion for a smooth space curve.
12. Functions of Several Variables 1: I can
    • find the domain and range of a function of two real variables,
    • sketch the level curves of a function of two real variables,
    • sketch the level surfaces of a function of three real variables.
13. Functions of Several Variables 2: I can
    • use the limit laws for functions of two real variables to compute limits,
    • determine whether a function of two real variables is continuous at a point in the domain,
    • define interior point, boundary point, open set, and closed set.
14. Functions of Several Variables 3: I can
    • compute the partial derivatives for functions of two or more variables,
    • determine whether a function of two variables is differentiable.
15. Functions of Several Variables 4: I can
    • use the chain rule on functions with one or more independent variables,
    • use implicit differentiation on a function of two variables.
16. Functions of Several Variables 5: I can
    • compute the directional derivatives of a function of two or more variables,
    • compute the gradient of a function of two or more variables.
17. Functions of Several Variables 6: I can
    • compute the plane tangent to a surface at a point,
    • approximate a surface near a point using the tangent plane.
18. Functions of Several Variables 7: I can
    • identify critical points of functions of two variables,
    • use the second derivative test to classify critical points,
    • find maximum/minimum values on closed and bounded sets.
19. Functions of Several Variables 8: I can
    • use Lagrange Multipliers to find absolute extrema on closed and bounded constraint curves.
20. Multiple Integration 1: I can
    • use iterated integrals to compute double integrals over a region in the plane,
    • identify when to use polar coordinates to simplify iterated integrals.
21. Multiple Integration 2: I can
    • use iterated integrals to compute triple integrals over a region in space,
    • identify when to use cylindrical to simplify iterated integrals,
    • identify when to use spherical coordinates to simplify iterated integrals.
22. Multiple Integration 3: I can
    • compute the center of mass of an object.
23. Multiple Integration 4: I can
    • use a change of variables in two and three dimensions to simplify an integral.
24. Vector Calculus 1: I can
    • match vector fields with their graphs,
    • parameterize curves,
    • evaluate line integrals,
    • interpret line integrals as mass, work, flux, and circulation.
25. Vector Calculus 2: I can
    • determine whether a vector field is conservative,
    • find the potential function of a conservative vector field,
    • use the Fundamental Theorem for Line Integrals to evaluate line integrals of conservative vector fields.
26. Vector Calculus 3: I can
    • use Green's Theorem to evaluate line integrals of vector fields.
27. Vector Calculus 4: I can
    • compute the divergence and curl of a vector field.
28. Vector Calculus 5: I can
    • parameterize a given surface,
    • compute surface integrals.
29. Vector Calculus 6: I can
    • use Stoke's Theorem to evaluate integrals.
30. Vector Calculus 7: I can
    • use the Divergence Theorem to evaluate integrals.