Series Part 2 - Testing for Convergence (more Ch 10)

Here is another bit of Ch 9 which introduces the idea of convergence and divergence for functions. Three nights of homework on this and then on to the rest of Ch 10 - Convergence of Series.

3/18  Horizontally Infinite Improper Integrals
3/21  Vertically Infinite Improper Integrals

Homework: By the end of the 2 days, you should have done p.475-477/1 - 44, 55, and 59-61.

The last unit is on Convergence Tests.  There are several - all with their own plusses and minuses.  The challenge is to choose the correct test in each situation.

(Note: D-Block will meet in room 408 on 3/22 and 3/23 due to MCAS)
3/22  Recap of Infinite Sequences and Series, n^th term, Integral Test

         HW p.521/29, 30, 34, 38  and  p.534/1-5, 7, 8, 10-14,17, 19, 21
3/24  Half Day F C A H  (End of Term 3)

3/28  Limit and Direct Comparison Test

         HW p.521-522/3, 4, 49, 51, 53  and  p.534-535/9, 15, 16, 22, 59  

               also try some of the previous problems using these tests

3/29  Ratio Test and the Radius of Convergence         

         HW p.521/9-27 by 3's, 31-47 odd

3/30  Alternating Series, Liebniz Error Bound
         HW p.534-535/27-32, 55, 56, 58, 63-65

4/01  Absolute and Conditional Convergence

         HW p.534-535/23-26, 35-47 odd, 54, 61, 66-71

4/04  Fourier Series, Gamma Functions, Review and many AP Problems

         HW p.537-538/1-16, 41-51 odd (evens are optional but helpful)

4/05  Test of Series Convergence (9b) - NO CALCULATORS

Important Dates

3/22  MCAS Day 1 (E B A Hr G H D)

3/23  MCAS Day 2 (A H D E F C B)

3/24  MCAS Day 3 (F C A H)

3/24  End of Term 3 and Half Day

3/25  Good Friday - no school

4/16-4/24 April Vacation (includes Passover)

5/05  AP Calculus BC Exam

Series Part 1 - Modeling functions with Series (Ch 10)

We are starting Chapter 10 - the study of infinite series. The first test is on sections 10.1-10.3 plus two handouts of sections from the Hughes-Hallett Calculus book. 

3/02  10.1  Infinite series, power series, intervals of convergence
                  HW p.489-490/1, 2, 3-35 odd, 48-53

3/04  10.1  Finding series that represent functions

                  HW p.490-491/54-61, 63-65, 72;  read p.492-496; do Explorations 1 and 2

3/07  10.2  Taylor and Maclaurin series
                  HW p.500-502/1, 3, 5-18, 20-24, 26, 27, 32, 33, 36, 43

3/09  HH  10.3  Finding and using Taylor series
                  HW handout/1-22

3/10  10.2  More with Taylor series

                  HW p.501-502/25, 28, 31, 34-36, 44  and p.509/1 - 10

3/12  HH 10.4 The Error in Taylor Polynomial Approximations/1 - 14 except 3

3/14  Extra Problems  HW finish handout (answer key)
3/15  Review (more extra problems plus 2 AP problems - answer key)

3/16  Series Approximation Test (NO CALCULATOR)

         HW read pp.467-470 (Horizontally Improper Integrals)

MCAS on Tues, 3/22 - Thur, 3/24 (D-Block will meet in room 408)
Thur, 3/24 Half Day - F C A H, and End of Term 3

Fri, 3/27 Good Friday, no school