I have one rule in life: when Robert Talbert issues me a personal challenge, I respond. I have created learning outcomes for my Calculus II course, which are below.

There are a couple of things to note. First, this might seem to imply that I have thrown out the work I did on Dee Fink’s Significant Learning planning. This is not the case, though. Doing Fink’s exercise helped prep me for these learning outcomes. More importantly, Fink’s exercise was focused on “What do you want your students to remember several years from now?” I clearly could not assess such long-term goals in Fall 2020, so I needed to approximate the goals from the Fink exercise to something that I can assess this semester. This is the result.

Second, I intend to focus much more on applications than I normally do. I will couch differential equations in terms of Covid 19 modeling, and I will do much of integration in terms of probability (improper integrals and double integrals) and applied work/density problems. Series are then motivated by trying to solve differential equations and integrals that have no “nice” solution. I additionally will focus on successive approximations and estimating error—starting with a rough solution, and working toward a better one.

Third, we are on the block system this year, so I am intensively teaching this course over the course of four weeks. The advice I have gotten is that you must cut content in such situations, which is why I am missing your favorite convergence test for series (although there are some that are hidden in other outcomes).

I haven’t thought much about my assessments yet, so the implied modules below (Integration, Optimization, Series, Approximation, and Error) might change. In particular, I suspect that I might have several projects, and the modules might change to match the needs of the project rather than the more conceptual categorization below. I don’t know for sure, though.

Below are my learning outcomes for Calculus II. I welcome all comments, compliments, and criticisms.

- Group I: I can use integrals to solve authentic real-life application problems.
- I1: I can solve separable differential equations.
- I2: I can compute integrals using integration by parts.
- I3: I can solve real-world problems by slicing and integrating.
- I4: I can compute improper integrals.
- I5: I evaluate a double integral over a general region.

- Group O: I can find optimal solutions to multivariable functions.
- O1: I can optimize a 3D function.

- Group S: I can determine whether series, including power series, converge.
- S1: I can define what it means for a series to converge.
- S2: I can show con(di)vergence of a series using the Direct Comparison Test.
- S3: I can show con(di)vergence of a series using the Integral Test
- S4: I can find the interval and radius of convergence of a power series.
- S5: I can prove a sequence converges using an -$N$ argument.

- Group A: I can find good approximations to functions, values of integrals and solutions to differential equations.
- A1: I can approximate the value of an integral using the Trapezoidal Rule, Midpoint Rule, or Simpson’s Rule.
- A2: I can approximate the value of a solution to a differential equation using Euler’s Method.
- A3: I can approximate a function with a Taylor polynomial

- Group E: I can bound the error associated with the above approximations.
- E1: I can bound the error when using the Trapezoidal Rule, Midpoint Rule, or Simpson’s Rule.
- E2: I can bound the error when using Euler’s Method.
- E3: I can bound the error of a Taylor polynomial using Taylor’s Theorem.