Mr. Rizzi - Stoney Creek High School
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  • AP Calculus BC
    • Parametric and Polar (Ch 10)
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      • Limits (Ch. 1)
      • Differentiation (Ch. 2)
      • Applications of Derivatives (Ch. 3)
      • Integration (Ch. 4)
      • Logs, Exponentials, and Other Transcendentals (Ch. 5)
      • Differential Equations (Ch. 6)
      • Applications of Integration (Ch. 7)
      • Integration Techniques, L'Hopital's Rule, and Improper Integrals (Ch. 8)
      • Infinite Series (Ch. 9)
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Chapter 9
Infinite Series

Week of February 28
Monday, February 28 - 
Series and Convergence (UT #1-11)​
  • Extra Notes

Tuesday, March 1 - The Integral Test and p-Series (UT #12-14)
  • Extra Notes​

​Wednesday, March 2 - Review 
  • Watch Direct Comparison Video: https://youtu.be/oZtAgihok5s
  • 9.2 #7-19 odd, 25-35 odd, 41-49 odd
  • 9.3 #1, 3, 7, 13, 25-37 odd, 71-81 odd

Thursday, March 3 - Limit Comparison Test (UT #15-23)
  • 9.4 #3-29 odd
  • Extra Notes
​
Friday, March 4 - Alternating Series Introduction (UT #24-30)
  • Review 9.2-9.4 - Answer Key
  • 9.5 #37-53 odd, 63
  • Extra Notes

Week of March 7
Monday, March 7 - Alternating Series Error Bound
  • 9.5 #27, 29, 31, 35​

Tuesday, March 8 - The Ratio Test (UT #31-36)
  • 9.6 #13-33 odd
  • Extra Notes

Wednesday, March 9 - Review
  • Review Ratio Test
  • 9.2-9.6 Practice Quiz + Answer Key
  • UT Quest Due Tonight at Midnight

Thursday, March 10 - Quiz
  • Quiz 9.2-9.6
​
Friday, March 11 - TBD
  • TBD

Week of March 4
Monday, March 4 - Taylor Polynomials (UT #1-8)
  • Go Over Quiz
  • Taylor and Maclaurin Polynomials Investigation - In Class

Tuesday, March 5 - Continue Taylor Polynomials
  • In Class: Taylor and Maclaurin Polynomial Homework - Answer Key​

Wednesday, March 6 - Lagrange Error Bound of a Taylor Polynomial
  • Lagrange Error Bound Worksheet - Answer Key​​

Thursday, March 7 - Maclaurin Series and Manipulation Involving Substitution (UT #20-27) 
  • AP Problems - Answer Key​
​
Friday, March 8 - Manipulation of Taylor Series Involving Integration and Differentiation
  • Taylor and Maclaurin Series Worksheet (#1-12) - Answer Key

Week of March 11
Monday, March 11 -  Manipulation of Taylor Series Involving Integration and Differentiation
  • Taylor and Maclaurin Series Worksheet (#13-17)

Tuesday, March 12 - Geometric Power Series and Interval of Convergence (UT #13-19) 
  • Geometric Power Series Worksheet - Answer Key​
  • Geometric Power Series AP FRQ + Answer Key (Just Question #6)

Wednesday, March 13 - Radius and Interval of Convergence Using Ratio Test (UT #9-12)
  • ​Interval of Convergence Investigation

Thursday, March 14 - Review​​​
  • ​Interval of Convergence Worksheet - Answer Key

​Friday, March 15 - Review
  • ​​AP Free Response Questions (#1-3) + Answer Key​

Week of March 18
Monday, March 18 -
Review
  • ​​AP Free Response Questions (#4-6) + Answer Key​

Tuesday, March 19 - Review
  • Ch. 9 AP MC Review + Answer Key
  • UT Quest Due at Midnight Tonight

Wednesday, March 20 - Test
  • Ch. 9 Test (10 MC and 2 FRQ from ALL of chapter 9)

AP Standards for Chapter 9
Concept of series (Section 9.2)
  • A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence and divergence.
Series of constants (Sections 9.2-9.6)
  • Motivating examples, including decimal expansion.
  • Geometric series with applications. (9.2)
  • The harmonic series. (9.3)
  • Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series. (9.3)
  • Comparing series to test for convergence or divergence. (9.4)
  • Alternating series with error bound. (9.5)
  • The ratio test for convergence and divergence. (9.6)
Taylor series (Sections 9.7-9.10)
  • Taylor polynomial approximation with graphical demonstration of convergence (for example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve).
  • Lagrange error bound for Taylor polynomials.
  • Maclaurin series and the general Taylor series centered at x = a.
  • Maclaurin series for the functions sin, cos, e^x, and 1/(1-x)
  • Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series.
  • Functions defined by power series.
  • Radius and interval of convergence of power series.
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