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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Report of the Content Panel for Mathematics (2002) / Chapter Skim
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Appendix D: Topical Outline for AP Calculus BC
Pages 60-64

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.


From page 60...
... (For example, contrasting exponential growth, polynomial growth, and logarithmic growth.)
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From page 61...
... The analysis of planar curves includes those given in parametric form, polar form, and vector form.
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From page 62...
... · Use of implicit differentiation to find the derivative of an inverse · Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration. + Geometric interpretation of differential equations via slope fields and the relationship between slope fields and derivatives of implicitly defined functions.
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From page 63...
... · Finding specific antiderivatives using initial conditions, including applications to motion along a line. · Solving separable differential equations and using them in modeling.
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From page 64...
... + Taylor polynomial approximation with graphical demonstration of convergence. (For example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve.)
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Key Terms

  • differential equations
  • definite integral
  • taylor series
  • including velocity
  • taylor polynomials

  • fundamental theorem
  • maclaurin series
  • basic functions
  • parametric form
  • riemann sums

  • improper integrals
  • slope fields
  • approximate definite
  • using initial
  • examination board

  • including substitution
  • implicit differentiation
  • function approximating
  • numerical approximations
  • partial fractions

  • midpoint evaluation
  • following directly
  • planar curves
  • implicitly defined
  • varied applied

  • graphical analysis
  • sine function
  • initial conditions
  • trigonometric functions
  • distance traveled


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