Tuesday, March 25, 2014

Vectors and Parametrics

Here is the syllabus for the topics. In Demana it is the beginning of Chapter 6.  In Brown it is Chapter 12.  The skills you should know for manipulating and using vectors are listed here.  Make sure you know how to do all of them before the test!

3/26      Intro to Vectors
             Demana p.464-465/3-27 by 3's and 29-39 odd and Brown p.423, 425/5-7, 17-20
3/28      Angles between vectors, The Dot Product (End of Term 3)
             Brown p.444-445/1-19 odd, 23, 28, 29 and p.429-431/11,12,15,18, 31, 32

3/31      Vector Proofs (D: 6.1 and B: 12.1, 12.2)  (some example solutions)
             finish worksheet plus Brown p.425-426/21-23 and p.429-431/27-29,33,34, 37, 38
4/01      Equations of Lines, Vectors in 3D
             finish worksheet plus B p.436-437/17 and D p.466/63,64
             If you still feel that you need extra practice to feel comfortable with the material,
             section 12.5 in the Brown book is the place to go (clear explanations, good
             diagrams, comprehensive problems).
4/02      Parametric Equations
             HW B p.437-439/24-29, 39, 40 and p.451/27, 28
4/04      More Parametric Equations
             HW Worksheet

4/07   More 3D: Equations of Planes, vectors perpendicular to planes (B: 12.5)
             Worksheet problems 1-10 plus B p.452/43-45 and p.455/15,28-31,33
             We talked about equations of planes & vectors perpendicular to the planes. Read the
             corresponding explanations in the book. They are very clear, have lots of examples and
             better pictures than anything I can draw. (This reading should be considered
             part of the homework!)
4/08   Spheres, vectors & planes, Angles between planes (B: 12.5, 12.6)
             B p.450-452/11,13,17,31-36,41,42 and p.456-458/21,25,27,34,35,37-39
4/09   The Cross Product
             Vector Cross Product worksheet B p.466/2,3 p.467/9,13,15bd
4/11   Projections, Distance from a point to a plane
             Do p.457-458/37-39 if skipped before and "Points, Lines and Planes in 3D" problems 11-14

4/14   Start Review Problems (this is the first night of Passover)  (answer key)
4/15   Finish Extension Problems  (download a practice test, download solutions)
4/16  Vector Unit Test  (tell me early if this date is a problem because of Passover)
  • For projection practice, do Demana p.473/25-28 and 58a.
  • Other than that, go back and make sure you have done and understood all of the previous homework in light of the objective skills of the unit. 
4/18-4/27   April Vacation

Friday, March 7, 2014

Polar Coordinates

This is a quick but interesting unit on another way of describing the location of points in space.  It is a somewhat surprising application of trig that can also be used to work with complex numbers.  The schedule is plagued by holidays and MCAS but we will work around it as best we can. Polar coordinates are covered in the Demana book in sections 6.4-6.6 and in the Brown book in Chapter 11.  I am using Day1 notation rather than dates because the E-Block and G-Block sections will be off (due to the half day and MCAS).

Day 1    Intro to Polar  CW Brown p.400-402/1-11 odd  (this is 3/07, before the Trig Identities Test)
            HW Demana p.492-493/5,6,23-30,52-54,61,63
Day 2    Converting equations and graphs (polar <=> rectangular)
            HW D p.500-502/5,7-13,17,21,23,45,49,53,55
Day 3    Cylindrical & Spherical Coordinates (helpful website)
            HW Worksheet and Answer Key (check your graphs on your calculator)
Day 3a  More practice with Cylindrical & Spherical Coordinates (only E-Block)
            HW Worksheet (answer key)

Day 4    cis, Products of Complex Numbers
            HW B p.406-407/11, 12, 15-17, 23, 24, 29, 30, 32 and D p.512/63 (derive Quotient Rule)
Day 5    Powers and Roots of Complex Numbers (De Moivre's Theorem)
B p.410-411/4,5,9-14 and p.413/5,6,8,11-13
Day 6    Extra Practice 
            HW finish worksheet (answer key)

3/24     Review (answer key)
3/25     Polar Test (Practice Test, Answer Key)

Important Dates
3/13  Professional Development Half-Day C B H F
3/18  MCAS Day 1 (Hr G H A)
3/19  MCAS Day 2 (E F H D)
3/21  MCAS Day 3 (D E F B C)
3/28  End of Term 3