Date

Topics

Assignment

Thu, Apr 29
B4  24 days  ends June 2

Review 


Review 


Review 
Review Assignment:
 Scan each section in Ch 12. In particular, refresh your memory on the material in the colored boxes, and read through the example problems. Then work the exercises below:
 121 (p. 423) Written Exercises #1, 3
 122 (p. 429) WE #9, 11
 123 (p.435) WE #1, 3, 5
 124 (p. 444) WE #1, 3, 5
 125 (p. 450) WE #7, 9
 126 (p. 455) WE #1, 9


127 Determinants
 What is a determinant?
 rows and columns
 size of a determinant
 Evaluating a 2x2 determinant
 Evaluating larger determinants
 minors
 the minor of an element is the determinant formed after you cross off the row and column containing that element
 sign of a minor
 alternates, starting with "+"
 evaluating a determinant using minors
 You can add or subtract any multiple of any row/column to any other row/column in a determinant without changing the determinant's value

 Read:
 127 and study the examples
 Work:
 127 Written Exercises #113

Wed, May 5 
128 Applications of Determinants
 Cramer's Rule
 Solving 2 equations with 2 unknowns. If
ax + by = c
dx + ey = f, then
 Solving 3 equations with 3 unknowns
 Geometry
 Area of parallelogram determined by A = (x_{a}, y_{a}) and B = (x_{b}, y_{b}) is:
Area = absolute value of
 Area of parallelepiped determined by A = (x_{a}, y_{a}, z_{a}), B = (x_{b}, y_{b}, z_{b}) and C = (x_{c}, y_{c}, z_{c})is:
Area = absolute value of

 Read:
 128 and study the examples
 Work:
 128 Written Exercises #117odd, 21


129 Determinants and Vectors in Three Dimensions
 Unit Vectors
 a unit vector is a vector whose length is 1
 Special unit vectors
 i is a unit vector in the +x direction
 j is a unit vector in the +y direction
 k is a unit vector in the +z direction
 Unit vector notation
 Cross Product
 The cross product of two vectors A x B is a vector which is perpendicular to both A and B.
 If A = (x_{a}, y_{a}, z_{a}) and B = (x_{b}, y_{b}, z_{b}) then
 Geometric cross product
 If is the angle between vectors A and B, then
A x B = ABsin
 The direction of A x B is given by the right hand rule:
"Point the fingers of your right hand in the direction of A, then curl them toward the direction of B. Your thumb points in the direction of A x B."
 Properties of the Cross Product
 A x B is perpendicular to both A and B .
 A x B = (B x A) . This means that the vectors A x B and B x A are opposite in direction  The cross product is NOT a commutative operation!
 A x (B + C) = (A x B) + (A x C). The cross product is distributive across (vector) addition.
 A x B is the area of the parallelogram formed by vectors A and B.
 A x B = 0 means that A and B are parallel (and vice versa).
 Cross product and dot product on the TI89

 Read:
 129 and study the examples
 Work:
 129 Written Exercises (p. 467) #19, 1115odd


129 Determinants and Vectors in Three Dimensions 
 Finish the 129 assignment


Cellular Automata  1 
Assignment 

Cellular Automata  2 


Cellular Automata  3 


Cellular Automata  4 

Fri, May 14
(Mr. S absent)

Review 
 Read:
 Chapter Summary on P. 468469
 Answer:
 Chapter Test (p. 469) #113
 [Hint for #10: The center of the sphere is the point (0, 1, 3), so a vector normal (perpendicular) to the plane goes through the points (0, 1, 3) and (2, 3, 2).]


Reward Day 


Review 


Test  Ch 12 & Cellular Automata



131 Arithmetic and Geometric Sequences
 Sequence
 function whose domain is usually the positive integers (natural numbers)
 first term, t_{1}, second term t_{2}, n^{th} term t_{n}
 can be specified by a formula:
t_{n} = n^{2}  1
 Arithmetic Sequences
 common difference, d = difference between any two adjacent terms
 the n^{th} term:
 Example:
 1, 4, 7, 10, 13, ... is an arithmetic sequence with common difference, d = 3.
 t_{1} = 1, t_{2} = 4, etc.
 the seventh term, t_{7} = 1 + 3(71) = 1 + 18 = 19
 Geometric Sequences
 common ratio, r = quotient of any two adjacent terms
 the n^{th} term:
 Example:
 1, 4, 16, 64, 256... is a geometric sequence with common ratio, r = 4.
 the seventh term, t_{7} = (1)(4^{71}) = 4^{6} = 4096

 Read:
 131 and study the examples
 Work:
 131 Written Exercises (p. 476) #141odd


132 Recursive Definitions
 The formulas we used in 131 are called explicit definitions
 An explicit definition lets you calculate the value of any term
 A recursive definition has two parts:
 initial condition tells where the sequence starts
 recursion formula tells how to get the next term from the current term
 Finding:
 an explicit definition from a recursive definition
 Example: What is an explicit definition for the sequence t1 = 1, tn = tn1 + 4?
 Generate some terms: 1, 5, 9, 13, 17, ...
 Recognize: This is an arithmetic sequence with t_{1} = 1 and d = 4.
 Since t_{n} = t_{1} + d(n  1) for an arithmetic sequence, t_{n} = 1 + 4(n  1), which simplifies to t_{n} = 4n  3.
 a recursive definition from an explicit definition
 a recursive definition from a description
 Some recursive functions

 Read:
 132 and study the examples
 Work:
 132 Written Exercises (p. 481) #15odd, 1119odd, 2125


133 Sums of Arithmetic and Geometric Series
 Arithmetic Series
 The sum equals n times the "average term"
 Geometric Series
 S_{n} = nt_{1} (if r = 1)
 Calculating sums of series using a spreadsheet

 Read:
 133 and study the examples
 Work:
 133 Written Exercises (p. 489) #19odd, 1723odd, 29, 31


134 Limits of Infinite Sequences
 In mathematics, "limit" does not mean "limitation" or "handicap"  it means "a number that the terms of the sequence get closer and closer to, or homes in on"  it is a "target."
 means "As the number of terms gets larger and larger, the value of the terms of sequence S get closer and closer to (or homes in on) L"
 limits that "do not exist"

 Read:
 134 and study the examples
 Work:
 134 Written Exercises (p. 496) #16, 9 (ans: 0), 10, 13, 15, 19, 20, 26


Quiz  Chapter 13 

Thu, May 27
(Last day for seniors with privileges)


 Seniors
 turn in books
 last day to turn in assignments

Fri, May 28
(Senior grades due 8 A.M.)

No Seniors (who still have senior privileges) 
Goodbye Seniors and Best Wishes


Memorial Day  No School 




Wed, June 2
End of B4  23 days 

Have a GREAT summer break! 