MA252 Calculus II Learning Targets for Spring 2022

Core Learning Targets

1. Compute antiderivatives of functions. (S4.10 of Volume 1, Ch 1 of Volume 2)
2. Evaluate an integral using only basic techniques (power rule, linearity properties, etc.) (S1.2)
3. Evaluate an integral using substitution. (S1.5)
4. Set up an integral to compute the area between curves. (S2.1)
5. Set up an integral to compute volume of a solid of revolution (S2.2 and S2.3)
6. Evaluate an integral using integration by parts. (S3.1)
7. Demonstrate familiarity with paremetric equations and derivatives. (S7.1 and S7.2)
8. Demonstrate familiarity with polar coordinates. (S7.3)
9. Evaluate a geometric series. (S5.2)
10. Determine the radius of convergence of a power series. (S6.1) Done via WeBWorK: 24 S6-1PowerSeries. 50% on the set gets completion, 80% on the set gets mastery. (time spend in class on this set)

Supplemental Learning Targets

1. Use a finite summation to approximate the area under a curve. (S1.1)
2. Calculate an integral to find net area under a curve. (S1.2)
3. Calculate a derivative using FTC. (S1.3)
4. Set up an integral to compute volume using the disk or washer method. (S2.2)
5. Set up an integral to compute volume using the shell method. (S2.2)
6. Set up an integral to find the mean of a continuous random variable. (S3.7 and supplemental section)
7. Set up an integral of a probability density function to find probabilites. (S3.7 and supplemental section)
8. Evaluate a trigonometric integral. (S3.2)
9. Evaluate an integral using trigonometric substitution. (S3.3)
10. Evaluate an integral using partial fractions. (S3.4)
11. Identify and apply a proper method(s) to evaluate an integral when not given a specific method. (Chapter 3)
12. Determine whether an improper integral over an infinite interval converges or diverges, and evaluate if possible. (S3.7)
13. Determine whether an improper integral with a discontinuous integrand converges or diverges, and evaluate if possible. (S3.7)
14. Solve a challenging problem that combines different skills and/or presents material from Chapters 1-3 + Pre-Reqs in a different way.
15. Calculate or set up an integral to calculate area under a parametric curve. (S7.2)
16. Calculate or set up an integral to calculate arc length of a parametric curve. (S2.4 and S7.2)
17. Calculate or set up an integral to calculate area of a region bounded by a polar curve. (S7.4) (updated April 7)
18. Calculate or set up an integral to calculate arc length of polar curves. (S2.4 and S7.4)
19. Demonstrate an understanding of the underlying concept of an infinite series. (S5.2)
20. Use the integral test to determine the convergence of a series. (S5.3)
21. Use the divergence test to determine the divergence of a series. (S5.3)
22. Use the direct comparison test to determine the convergence of a series. (S5.4)
23. Use the alternating series test to determine the convergence of a series. (S5.5) (readded May 4)
24. Use the ratio test to determine the convergence of a series. (S5.6)
25. Identify and apply a proper method to determine the convergence of a series when not given a specific method. (Chapter 5)
26. Determine the interval of convergence of a power series. (S6.1)
27. Compute terms of a Taylor series using differentiation or integration. (S6.3)
28. Compute a Taylor series from a known series. (S6.3 and/or S6.4)
29. Calculate the average value of a continuous function over an interval. (S1.2)
30. Set up an integral to calculate arc length of a function. (S2.4)
31. Demonstrate an understanding of infinite sequences. (S5.1) (updated April 22)