1. I can draw parametric curves in 2D and 3D.
  2. For a given parametrization, I can compute velocity, acceleration, speed, and give a vector equation of the tangent lines to the curve at a specified point.
  3. I can decompose a vector into parallel and orthogonal components.
  4. I can use integrals to find the length of a parametric curve and the work done by a nonconstant force along a parametric curve.
  5. I can compute the TNB frame for a space curve.
  6. I can compute curvature, radius of curvature, and center of curvature for a vector-valued function at a given point.
  7. I can construct contour plots, surface plots, and gradient field plots for functions of the form $f(x, y)$, and I can construct level surface plots for functions of the form $f(x, y, z)$
  8. I can compute differentials, partial derivatives, gradients, and total derivatives.
  9. For functions of several variables, I can compute directional derivatives, tolerances (using differentials), and equations of tangent planes (linearizations).
  10. I can obtain and use appropriate chain rules to compute derivatives for compositions of functions.
  11. I can use Lagrange multipliers to locate and compute extreme values of a function $f$ subject to a constraint $g = c$.
  12. I can apply the second derivative test, using eigenvalues, to locate local maximum and local minimum values of a function $f$ over a region $R$.
  13. I can set up and compute iterated single, double, and triple integrals to obtain lengths, areas, volumes, and mass, connecting these to the differentials $dx$, $ds$, $dA$, $dV$, and $dm$.
  14. I can appropriately use polar coordinates $dA = |r| dr d\theta$ to setup and compute iterated integrals.
  15. I can find the average value of a function over a region, and use this to compute the center-of-mass (varying density) and centroid (uniform density) of a wire, planar region, or solid object.
  16. I can draw regions described by the bounds of an integral, and then use this drawing to swap the order of integration.
  17. I can appropriately use cylindrical coordinates $dV = |r|drd\theta dz$ and spherical coordinates $dV = |\rho ^2 \sin\phi |d\rho d\phi d\theta$ to setup and compute iterated integrals.
  18. For a given change-of-coordinates, I can compute and appropriately use the Jacobian to change an integral from one coordinate system to another.
  19. I can use the del operator to compute the divergence and curl of a vector field, as well as the gradient of a function.
  20. I can determine whether or now a vector field has a potential, and verify the Fundamental Theorem of Line integrals for vector fields that have a potential (computing the work done by a vector field along a curve).
  21. I can verify Green's Theorem given a simple closed curve and vector field (computing the circulation of vector field along closed curve).
  22. For a parametric surface, I can draw the surface, as well as set up appropriate integrals to compute the surface area, mass, center-of-mass,
  23. I can verify Stokes's Theorem for a given parametric surface and vector field.
  24. I can verify the Divergence Theorem for a given closed surface and vector field, obtaining the flux of a vector field across the surface.

Mini Projects

3-5 hours on a topic. The student can define their own. I will provide some options too.

Chapter 13

Syllabus/Grading

There are 24 objectives. How many to demonstrate mastery of? Should it always be twice? Or maybe 2/3 of the objectives need double demonstration. I'm happy with 2/3. Should I use CORE learning targets? Should I change the name to learning targets?

  • A - 21/14
  • B - 18/12
  • C - 15/10
  • D - 12/8

Projects. For every grade above C, complete 1.

  • C+ - 1 projects
  • B- - 2 projects
  • B - 3 projects
  • B+ - 4 projects
  • A- - 5 projects
  • A - 6 projects

Daily work/participation/ IBL presenting to class.

  • B- or higher - 80% of median

Final exam

  • Above 70% causes grade to go up half a letter.
  • Below 30% causes grade to go down half a letter.