At the end of the course, each student should be able to…
- C01: LogExpDerInt. Find derivatives and integrals involving logrithmic and exponential functions.
- C02: HypDerInt. Find derivatives and integrals involving hypberbolic functions.
- C03: IntSub. Use integration by substitution.
- C04: IntParts. Use integration by parts.
- C05: IntTech. Identify appropriate integration techniques.
- C06: AreaBtCurv. Express an area between curves as a definite integral.
- C07: WashShell. Use the washer or cylindrical shell method to express a volume of revolution as a definite integral.
- C08: Work. Express the work done in a system as a definite integral.
- C09: Param. Parametrize planar curves and sketch parametrized curves.
- C10: Polar. Convert and sketch polar and Cartesian coordinates and equations.
- C11: SeqLim. Compute the limit of a convergent sequence.
- C12: PartSum. Find the value of a convergent series by expressing it as a limit of partial sums.
- C13: SerTech. Identify series as convergent or divergent along with appropriate techniques to determine convergence or divergence.
- C14: PowSer. Identify the domain of a function defined as a power series.
- C15: TaySer. Generate a Taylor or Maclaurin series from a function.
- C16: Approx. Use Taylor’s formula to approximate values within appropriate margins of error.
- S01: LogExpPrf. Derive properties of the logarithmic and exponential functions from their definitions.
- S02: HypPrf. Prove hyperbolic function identities.
- S03: TrigId. Integrate products of trigonometric functions by applying trigonometric identities.
- S04: TrigSub. Use trigonometric substitution.
- S05: PartFrac. Use partial fractions to integrate rational functions.
- S06: CrossSect. Use cross-sectioning to express a volume as a definite integral.
- S07: WorkDiff. Use the work differential to express the work done in pumping a tank of liquid as a definite integral.
- S08: ParamAppl. Parametrize a curve to find arclengths, surface areas, and slopes.
- S09: PolarAppl. Use polar coordinates to express an arclength or area as a definite integral.
- S10: SeqForm. Define and use explicit and recursive formulas for sequences.
- S11: GeoAlt. Determine if a geometric series or alternating series is convergent or divergent.
- S12: IntTest. Use the integral test to determine series convergence.
- S13: RatioRoot. Use the ratio and root tests to determine series convergence.
- S14: CompTests. Use the comparison tests to determine series convergence.
- S15: PowSerConv. Find a power series converging to a function.
- S16: TaySerConv. Prove the convergence of a Taylor or Maclaurin Series using Taylor’s Formula.
Each standard is due at the end of the second week following its coverage in class according to the class calendar. For example, C02 is covered during Week 1, so it is due by the end of Week 3.