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MATH 222. Calculus II

Credits: 4
Department: Mathematics & Statistics
Description: Integration techniques and applications, inverse functions, topics in analytic geometry, sequences and series, improper integrals, plane curves.
Prerequisites: MATH 221
Semester Offered:
  • Fall
  • Spring
  • Summer
Grading Method: ABCDF
Lab: Lab

Student Learning Outcomes

1. Use integration to find volumes of solids described via cross-section and solids of revolution, to find the lengths of curves, to find the surface area of a surface of revolution and to solve physical problems involving concepts such as work, hydrostatic force, and center of mass.
2. Calculate integrals exactly by integration by parts, inspection of powers of trigonometric functions, trigonometric substitution, and partial fractions. Approximate integrals by using the Trapezoidal Rule, Simpson’s Rule, and Taylor series.
3. Use analytic methods to evaluate integrals whose integrands have asymptotes or whose interval of integration is infinite.
4. Convert points and equations from polar coordinates to Cartesian coordinates, and vice versa.
5. Calculate areas, tangents, and lengths related to curves given by parametric or polar equations. Calculate limits of sequences by algebraic and numerical methods and the Squeeze Theorem.
6. Identify geometric series, telescoping series, and the harmonic series and test series for convergence by using the integral test, the comparison tests, methods for working with alternating series, the ratio test, and the root test.
7. Represent a given function as a power series over a suitable interval and find the interval of convergence of a given power series.
8. Give the formulas and intervals of convergence for selected Taylor series such as the ones for the sine, cosine, inverse tangent, and natural exponential functions.
9. State and apply named theorems of calculus (Bounded Monotonic Sequence Theorem, Taylor’s Theorem).
10. Communicate their knowledge of the principles of Calculus II, both orally (e.g. class discussions) and in writing (e.g. written assessments).

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