- Draw parametric and space curves (practicing 3D drawing).
- Compute velocity, acceleration, a_T and a_N, both 2 and 3D. This just projections and orthogonal components.
- Compute derivatives of space curves, and use them to obtain tangent lines and approximations.
- Compute TNB for a space curve.
- Compute curvature, radius of curvature, and center of curvature.
- Use integrals to find the length of a parametric curve, the work done by a nonconstant force along a curve, and the center of mass of a uniform wire lying along a curve.
- Projectile motion questions (get position from acceleration, compute total displacement, etc.) - Maybe skip this...
- Relationships between curvature and components of acceleration. Not sure on this one - Maybe we'll just tackle this out of class.
- Plotting functions, level curves, etc.
- Partial Derivatives
- linearization, approximation, differentials
- chain rule
- Second Derivative Test
- Lagrange Multipliers
- Double integrals
- Polar integrals
- Average Value, Centroid, Center-of-mass, moment of inertia (applications)
- Swap order of integration
- Cylindrical coordinates??
- Spherical Coordinates
- Div, Grad, Curl
- Verify Fundamental Theorem of Line integrals, and compute potentials
- Calculus with Parametric Surfaces, including flux
- Verify Green's Theorem
- Verify Stokes's Theorem
- Verify Divergence Theorem
Mini Projects
3-5 hours on a topic. The student can define their own. I will provide some options too.
Chapter 13
- Build animation in Mathematica/Python to visualize the TNB frame, circle of curature, etc.
- Prove Kepler's 3rd law of planetary motion (see https://openstax.org/books/calculus-volume-3@7650bff/pages/3-4-motion-in-space).
- Complete the student project at the end of https://openstax.org/books/calculus-volume-3@7650bff/pages/3-4-motion-in-space, exploring navigating a banked turn.
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.