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Section 7.3: Separable Equations
Practice HW from Stewart Textbook (not to hand in)
p. 519 # 1-21 odd
In Section 7.2, we looked at graphical and numerical techniques for examining the
solutions of differential equations. For differential equations in sp
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Section 9.4: The Cross Product
Practice HW from Stewart Textbook (not to hand in)
p. 664 # 1, 7-17
Cross Product of Two Vectors
The cross product of two vectors produces a vector (unlike the dot product which
produces s scalar) that has important proper
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Section 9.2: Vectors
Practice HW from Stewart Textbook (not to hand in)
p. 649 # 7-20
Vectors in 2D and 3D Space
Scalars are real numbers used to denote the amount (magnitude) of a quantity. Examples
include temperature, time, and area.
Vectors are used
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Section 9.3: The Dot Product
Practice HW from Stewart Textbook (not to hand in)
p. 655 # 3-8, 11, 13-15, 17, 23-26
Dot Product of Two Vectors
The dot product of two vectors gives a scalar that is computed in the following manner.
In 2D, if a = < a1 , a
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Section 9.1: Three Dimensional Coordinate Systems
Practice HW from Stewart Textbook (not to hand in)
p. 641 # 1, 2, 3, 7, 10, 11, 13, 14, 15b, 16
3-D Coordinate Axes
In this chapter, we want to consider the 3 dimensional coordinate axes.
z
y
x
Points ar
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Section 8.6/8.7: Taylor and Maclaurin Series
Practice HW from Stewart Textbook (not to hand in)
p. 604 # 3-15 odd, 21-27 odd
p. 615 # 5-25 odd, 31-37 odd
Taylor Series
In this section, we discuss how to use a power series to represent a function.
Defini
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Section 8.9: Applications of Taylor Polynomials
Practice HW from Stewart Textbook (not to hand in)
p. 628 # 1-21 odd
Taylor Polynomials
In this section, we use Taylor polynomials to approximate a given function f ( x) near a
point x = a.
Definition: The
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Section 8.5: Power Series
Practice HW from Stewart Textbook (not to hand in)
p. 598 # 3-17 odd
Power Series
Definition: A power series is an infinite series of the form
cn x n = c0 + c1 x + c2 x 2 + c3 x 3 + + cn x n +
n =0
or more generally, a power
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Section 8.2: Series
Practice HW from Stewart Textbook (not to hand in)
p. 575 # 9-15 odd, 19, 21, 23, 25, 31, 33
Infinite Series
Given an infinite sequence cfw_a n , then
a n = a1 + a 2 + a3 + + an +
n =1
is called an infinite series.
Note: a n =
123
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Section 8.3: The Integral and Comparison Tests; Estimating Sums
Practice HW from Stewart Textbook (not to hand in)
p. 585 # 3, 6-12, 13-25 odd
In this section, we want to determine other methods for determining whether a series
converges or diverges.
Th
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Section 8.4: Other Convergence Tests
Practice HW from Stewart Textbook (not to hand in)
p. 592 # 3-7, 12-17, 19-25 odd, 33
Alternating Series
An alternating series is a series whose terms alternate (change) in sign (from + to -)
Examples:
n =1
(1) n 1 n
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Section 7.5: The Logistic Equation
Practice HW from Stewart Textbook (not to hand in)
p. 542 # 1-13 odd
The basic exponential growth model we studied in Section 7.4 is good for modeling
populations that have unlimited resources over relatively short spa
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Section 7.4: Exponential Growth and Decay
Practice HW from Stewart Textbook (not to hand in)
p. 532 # 1-17 odd
In the next two sections, we examine how population growth can be modeled using
differential equations. We start with the basic exponential gr
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Section 8.1: Sequences
Practice HW from Stewart Textbook (not to hand in)
p. 565 # 3-33 odd
Sequences
Sequences are collection of numbers or objects that is ordered by the positive integers.
Notation: a1 , a 2 , a3 , a 4 , , a n (known as the terms of t
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Section 7.2: Direction Fields and Eulers Methods
Practice HW from Stewart Textbook (not to hand in)
p. 511 # 1-13, 19-23 odd
For a given differential equation, we want to look at ways to find its solution. In this
chapter, we will examine 3 techniques f
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Section 7.1: Modeling with Differential Equations
Practice HW from Stewart Textbook (not to hand in)
p. 503 # 1-7 odd
Differential Equations
Differential Equations are equations that contain an unknown function and one or more
of its derivatives. Many m
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Section 9.6: Functions and Surfaces
Practice HW from Stewart Textbook (not to hand in)
p. 683 # 9-13, 19, 20, 23, 24, 25
Handout Sheet 1-6, 7-27 odd
Functions of More Than One Variable
So far most of our experience has been working with functions of one