MATH 18B - Support Topics for Calculus II

Student Learning Outcomes (SLOs)

1. Students feel that Math 18B has improved their overall mathematical understanding and ability in Math 181 (measured by survey provided by corequisite committee).
2. Math 18B students will be able to integrate Riemann integrable functions using a variety of techniques.
3. Math 18B students will be able to construct integrals to determine work, hydrostatic force, and center of mass.
4. Math 18B students will be able to apply tests for convergence/divergence of sequences and series using a variety of techniques.
5. Math 18B students will be able to construct Taylor series of C^infty functions.

Course Measurable Objectives (CMOs)

1. Evaluate integrals using integration by parts, trigonometric integrals, trigonometric substitution, and integration using partial fractions.
2. Find the volume and surface area of surface of revolution.
3. Find the arc length of a function in Cartesian coordinates, in polar coordinates, and a function in parametric form.
4. Use integrals to determine work, hydrostatic force, and center of mass.
5. Find an equivalent Cartesian equation of a parametric equation and sketch the resulting graph.
6. Use the tests for convergence or divergence of sequences and series using a variety of techniques.
7. Find the power series representation of a function and the interval of convergence.
8. Find the Maclaurin and Taylor series representation of a function.