A touch of Multivariable Calculus...and the Final

Post AP we start looking at multivariable calculus - though only the function aspect of it.  Here is the syllabus:

5/10  13.1 Introduction to Functions of Several Variables 
         HW problems 31,33,35,37,43 (skip confirming),45-48,49-59 odd,63-66.

5/13  13.3 Partial Derivatives of a Function of Two Variables  (Math MCAS Day 1: C E F D B) (and AP Physics!)      
         HW problems 1-4, 6-27 by 3's, 29, 35, 37-40, 45, 47, 89-91
5/14  13.4  Differentials  (Math MCAS Day 2: A G H B)         
         HW problems 1-9 odd, 11-16, 17, 19, 20, 27, 30-32, 34-36, 40
5/16  13.6 Directional Derivatives and Gradients
         HW problems 1-8, 13-18, 21-24 , 27, 28, 39, 40a-43a
5/17   13.6 Applications of the Gradient  CW problems 71, 72
          HW problems 44-52, 55-63 odd, 64, 73

5/20   13.8 Extrema of Functions of Two Variables
          HW problems 1-13 odd, 21, 23, 26, 31, 33, 41, 42, 45-47
5/21   Catch up on homework questions, start Review packet
5/23   Review 
5/24   Multivariable Test

5/27   Memorial Day
5/28   Last Questions (from you and from me)
5/30   Final Day 1
5/31   Final Day 2

Review for the AP

Here is the complete review schedule.  Note that starting the week of April 22th, an AP problem quiz could be given on any day and will be given at least 1 - 2 times a week.

We will score the 2008 exam on Friday, 4/12.  I will collect the score sheets so make sure you do the test and bring the answers.

4/09  Multiple Choice portion of 2008 AP Exam (1A in class, 1B for HW)
4/11  Open Response portion of 2008 AP Exam (2A in class, 2B for HW)
4/12  Score the 2008 Exam

4/13 - 4/21  April Vacation

4/22  Derivatives of Inverse, Curve Sketching, Linearization
4/23  Differential Equations
4/25  Optimization, Implicit Differentiation, Related Rates

4/26  Integration and the Fundamental Theorem of Calculus

4/29  Integration Applications (Area and Volume, Rates in and out)
4/30  Hard 1998 AP Multiple Choice Questions
5/02  Work on 2003 AP Exam
5/03  Work on 2003 AP Exam - submit questions/topics you would like covered on Monday 5/06

5/06  Topics chosen by you
5/07  Last Questions
5/08  AP Exam at 7:30am
5/09  Half Day C A G F

Tests for Convergence

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.  (Homework listed in red are problems from the old edition of the book.)

3/26  n^th term, Direct Comparison, Absolute Convergence  (2nd night of Passover)
         HW p.508/Exploration1 and  p.511-512/1-5, 9-27 by 3's, 29, 33, 39, 41, 45, 46, 61, 62
3/28  Ratio Test, Integral Test, Limit Comparison 
         HW p.511-512/10, 14, 20-44 even, 49-53odd, 64 and  p.523/1-6

3/29  Good Friday - no school

4/01  Alternating Series, Liebniz Error Bound
         HW p.523-524/7-21 odd, 54, 55, 57-60, 63-65
4/02  Absolute and Conditional Convergence (End of Term 3)
         HW p.523-524/25-32, 35-47 odd, 61
4/04  Review plus 2 AP Problems
         HW p.526-529/1-16, 41-51 odd (evens are optional but helpful)
4/05  5 more AP problems

4/08  Test of Series Convergence (9b)

Improper Integrals

Here is another bit of Ch 8 which introduces the idea of convergence and divergence for functions. Three nights of homework on this and then on to the rest of Ch 9 - Convergence of Series.

3/18  Post-test, Horizontally Infinite Improper Integrals (read pp.459-462)

3/19  SNOW DAY3/21  Vertically Infinite Improper Integrals and the Direct Comparison Test
3/25  Limit Comparison Test


Homework: By the end of the 3 days, you should have done problems 1 - 44, 55, and 59-61.

Important Dates

3/21  MCAS Day 1 (Hr G H A)

3/22  MCAS Day 2 (D E F B C)

3/25  MCAS Day 3 and 1st night of Passover

3/26  2nd night of Passover

3/28  End of Term 3

3/29  Good Friday - no school

Series Part 1

We are starting Chapter 9 - the study of infinite series. The first test is on sections 9.1-9.3 plus two handouts of sections from the Hughes-Hallett Calculus book. 

3/01  9.1  Infinite series, power series, intervals of convergence
               HW p.481-482/1, 2, 3-35 odd, 48-53

3/04  9.1  Finding series that represent functions
               HW p.482-483/54-61, 63-65, 72;  read p.484-488; do Explorations 1 and 2

3/05  9.2  Taylor and Maclaurin series
               HW p.492-493/1, 3, 5-18, 20-24, 26, 27, 32, 33, 36, 43
3/07  HH   10.3  Finding and using Taylor series  (Half Day - C B H F)
               HW handout/1-22
3/08  Snow Delay - no class, the whole schedule pushes one day

3/11  9.2  More with Taylor series
               HW p.492-494/25, 28, 30, 31, 34-36, 44  and p.500/1-10
3/12  HH 10.4 The Error in Taylor Polynomial Approximations/ 1- 14 except 3
3/14  Extra Problems  HW finish handout
3/15  Review

3/18  Series Approximation Test

Ch 10: Polar and Parametric Calculus

Chapter 10 is calculus with parametric, vector and polar curves.  Here is the proposed syllabus for the rest of the chapter.  Snow days (and any discretionary decisions on my part) may change things.

2/05  10.1  Parametric Review
                 HW p.535-537/1-15 odd, 18-33 by 3's, 35, 36, 39-44, 57, 59
2/07  10.2  Vector Calculus
                 HW p.545/3-24 by 3's, 25, 26, 27-35 odd
2/08  10.2  Vector-Valued Functions SNOW DAY (but I already taught you what you need to know...)
                 HW p.546-547/37-49 odd, 57-60

2/11  10.3  Polar Review
                 HW p.557-558/1-37 odd
2/12  10.3  Derivatives of Polar Curves
                 HW handout problems 54-66, 68, 75, 76, 81, 82 plus text p.558/39-42, 71 if you need more practice 
2/14  10.3  Polar Area
                 HW p.558/43-60
2/15  10.3  Polar Curve Length and Surface Area

2/16-24  February Break

2/25  Recap and Review of Parametric and Polar Caluclus
                 HW Sheet of problems from the Calculus book by Larson
2/26  AP and Extra Problems (answer key to Extension problems)
2/28  Ch 10 Test  
 

A couple of notes...

I want to remind you that, in addition to all of the geometry applications of integration, the chapter started with the fact that integration is net change.  Don't forget to study that.

Secondly, here is the answer key to the review/extension sheet of problems.  You can email me if you have any questions.