MATH 18B - Support Topics for Calculus II
Student Learning Outcomes (SLOs)
- Students feel that Math 18B has improved their overall mathematical understanding and ability in Math 181 (measured by survey provided by corequisite committee).
- Math 18B students will be able to integrate Riemann integrable functions using a variety of techniques.
- Math 18B students will be able to construct integrals to determine work, hydrostatic force, and center of mass.
- Math 18B students will be able to apply tests for convergence/divergence of sequences and series using a variety of techniques.
- Math 18B students will be able to construct Taylor series of C^infty functions.
Course Measurable Objectives Effective through Summer 2024 (CMOs)
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Evaluate integrals using integration by parts, trigonometric integrals, trigonometric substitution, and integration using partial fractions.
- Find the volume and surface area of surface of revolution.
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Find the arc length of a function in Cartesian coordinates, in polar coordinates, and a function in parametric form.
- Use integrals to determine work, hydrostatic force, and center of mass.
- Find an equivalent Cartesian equation of a parametric equation and sketch the resulting graph.
- Use the tests for convergence or divergence of sequences and series using a variety of techniques.
- Find the power series representation of a function and the interval of convergence.
- Find the Maclaurin and Taylor series representation of a function.
Course Measurable Objectives Effective Beginning Fall 2024 (CMOs)
- Use definite integrals to calculate areas between curves and volumes - including solids of revolution, work, the mean value of functions, arc lengths, areas of surfaces of revolution, moments, centers of mass, and other physics applications.
- Evaluate indefinite and definite integrals (proper and improper) using integration by parts, trigonometric identities and substitutions, partial fractions, tables, computer algebra systems, and numerical techniques.
- Solve separable differential equations with applications.
- Plot curves parametrically and in polar coordinates, using calculus to compute associated areas, arc-lengths, and slopes.
- Test for convergence for sequences and series using the integral, comparison, alternating series, ratio, and root tests.
- Determine representations of functions as power series including Taylor and Maclaurin series.
- Use power series in applications.