Be sure to check back, because this may change during the semester.
All numbers indicate sections from
Calculus by Taalman and Kohn.
For Friday January 27 (Due 1/26 @ 8:00 pm)
Section 5.1 Integration by Substitution
To read
 Topics:
 The Art of Integration
 Undoing the Chain Rule
 Choosing a Useful Substitution
 Finding Definite Integrals by Using Substitution
 Examples: 1  6
Reading Questions
 Substitution attempts to undo one of the techniques of differentiation. Which one is it?
 Use usubstitution to find an antiderivative of f(x) = 3x^{2} cos(x^{3})
 Explain why ∫ cos(x) sin(x)^{2} dx and ∫ ln(x)^{2} / x dx are essentially the same integral after performing a substitution.
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For Monday January 30 (Due 1/29 @ 8:00 pm)
Section 2.6 Inverse Trigonometric Functions
To read
 Topics:
 Derivatives of Inverse Trigonometric Functions
 Example: 3
Reading Questions
 Why do you think we are studying the inverse trig functions now?
 Find an antiderivative of f(x) = x^{2} / ( 1 + x^{6} )
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For Wednesday February 1 (Due 1/31 @ 8:00 pm)
Section 5.2 Integration by Parts
To read
 Topics:
 Undoing the Product Rule
 Strategies for Applying Integration by Parts
 Finding Definite Integrals by Using Integration by Parts
 Examples: 1  4
Reading Questions
 Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
 Use integration by parts to find an antiderivative of f(x) = 2x e^{4x}
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For Friday February 3 (Due 2/2 @ 8:00 pm)
Section 5.2 Integration by Parts
To read
Reading Questions
Would you use usubstitution or integration by parts to find each antiderivative? Find the antiderivative and explain why the other method would not work.
 ∫ cos(x) sin(x) dx
 ∫ e^{x} cos(x) dx
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For Monday February 6 (Due 2/5 @ 8:00 pm)
Section 5.6 Improper Integrals
To read
 Topics:
 Integrating over an Unbounded Interval
 Integrating Unbounded Functions
 Improper Integrals of Power Functions
 Examples: 1, 2, 3
Reading Questions
 Explain why ∫_{1}^{∞} 1/x^{2} dx is improper.
 Explain why ∫_{0}^{1} 1/x^{2} dx is improper.
 Explain why ∫_{1}^{1} 1/x^{2} dx is improper.
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For Wednesday February 8 (Due 2/7 @ 8:00 pm)
Section 5.6 Improper Integrals
To read
 Topics:
 Determining Convergence or Divergence with Comparisons
 Examples: 4
Reading Questions
Suppose f and g are continuous and 0 ≤ f(x) ≤ g(x) for x>0.
 If the improper integral ∫_{1}^{∞} g(x) dx
converges, what can you conclude
about the improper integral ∫_{1}^{∞} f(x) dx ?
 If the improper integral ∫_{1}^{∞} f(x) dx
diverges, what can you conclude
about the improper integral ∫_{1}^{∞} g(x) dx ?
 If the improper integral ∫_{1}^{∞} f(x) dx
converges, what can you conclude
about the improper integral ∫_{1}^{∞} g(x) dx ?
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For Friday February 10 (Due 2/9 @ 8:00 pm)
Section 5.7 Numeric Integration
To read
 Topics:
 Approximations and Error
 Error in Left and Right Sums
 Example: 1
Reading Questions
 Why would we want to approximate a definite integral?
 When approximating an integral, which would you expect to be more
accurate, LEFT(5) or LEFT(20)? Why?
 If a function f(x) is decreasing on an interval, will LEFT(n) underestimate or overestimate the integral? Why?
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For Monday February 13 (Due 2/12 @ 8:00 pm)
Section 5.7 Numeric Integration
To read
 Topics:
 Error in Trapezoid and Midpoint Sums
 Example: 2
Reading Questions
 If a function f(x) is concave down on an interval, will TRAP(n)
overestimate or underestimate the integral?
 Consider the integral ∫_{2}^{1} x^{3} dx.
Is 4 a valid value for M in Theorem 5.27? Why or why not?
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For Wednesday February 15 (Due 2/14 @ 8:00 pm)
Section 6.1 Volumes by Slicing
To read
 Topics:
 Approximating Volume by Slicing
 Volume as a Definite Integral of CrossSectional Area
 Volumes by Disks and Washers
 Examples: 1, 2, 3
 Another optional resource are the videos at Kahn Academy on Solids of Revolution. The first two, "Disk method around xaxis" and "Generalizing disc method around xaxis", are relevant for today.
Reading Questions
 Let R be the rectangle formed by the xaxis, the yaxis, and the lines y=1 and x=3. Describe the shape of the solid formed when R is rotated about the xaxis.
 Let T be the triangle formed by the lines y=2x, x=3 and the xaxis. Describe the shape of the solid formed when T is rotated about the xaxis.
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For Friday February 17 (Due 2/16 @ 8:00 pm)
Section 6.1 Volumes by Slicing
To read
 Reread the topics from Wednesday
 Example: 5
Reading Questions
 Let R be the rectangle formed by the xaxis, the yaxis, and the lines y=1 and x=3. Describe the shape of the solid formed when R is rotated about the line y=5.
 Let T be the triangle formed by the lines y=2x, y=6 and the yaxis. Describe the shape of the solid formed when T is rotated about the xaxis.
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For Monday February 20 (Due 2/19 @ 8:00 pm)
Section 3.6 l'Hopital's Rule
To read
 Topics:
 Geometrical Motivation for l'Hopital's Rule
 l'Hopital's Rule for the Indeterminate Forms 0/0 and ∞/∞
 Using Logarithms for the Indeterminate Forms 0^{0}, 1^{∞}, and ∞^{0}
 Examples: 1, 2, 3
Reading Questions
 Does l'Hopital's Rule apply to lim_{(x > ∞)} x^{2} / e^{x} ?
Why or why not?
 Does l'Hopital's Rule apply to lim_{(x > ∞)} x^{2} / sin(x) ?
Why or why not?
 For each limit in #1 and #2 where l'Hopital's applies, use it to
find the limit.
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For Wednesday February 22 (Due 2/21 @ 8:00 pm)
Section 7.1 Sequences Section 7.2 Limits of Sequences
To read
 Topics in 7.1:
 Sequences of Numbers
 Recursively Defined Sequences
 Geometric and Arithmetic Sequences
 Monotonic Sequences
 Bounded Sequences
 Examples in 7.1: 1, 2, 3, 5
 Topics in 7.2:
 Convergence or Divergence of a Sequence
 Theorems About Convergent Sequences
 Convergence and Divergence of Basic Sequences
 Bounded Monotonic Sequences
 Examples in 7.2: 1, 2, 3
Reading Questions
 Does the following sequence converge or diverge? Be sure to explain your answer.
1, 3, 5, 7, 9, 11, 13, . . .
 Find a symbolic expression for the general term a_{k} of the sequence
1, 2, 4, 8, 16, 32, . . .
 Is the following sequence bounded? Is it monotone? Explain.
1, 1/2, 1/4, 1/8, 1/16, 1/32, . . .
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For Friday February 24 (Due 2/23 @ 8:00 pm)
Section 7.3 Series
To read
 Topics:
 Adding Up Sequences to Get Series
 Convergence and Divergence of Series
 The Algebra of Series
 Geometric Series
 Examples: 1, 3, 4
Reading Questions
 There are two sequences associated with every series. What are they?
 Does the geometric series Σ (1/4)^{k} converge or diverge? Why?
 Does the geometric series Σ (π/e)^{k} converge or diverge? Why?
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For Monday February 27
Q&A for Exam 1. No Reading Assignment.
For Wednesday March 1 (Due 2/28 @ 8:00 pm)
Section 7.4 Introduction to Convergence Tests
To read
 Topics:
 An Overview of Convergence Tests for Series
 The Divergence Test
 The Integral Test
 Convergence and Divergence of pSeries and the Harmonic Series
 Approximating a Convergent Series
 Examples: 1, 2, 3
Reading Questions
 What does the Divergence Theorem tell you about the series
Σ 2^{k} ?
 What does the Divergence Theorem tell you about the series
Σ 1/k ?
 What does the Integral Test tell you about the series
Σ 1/k^{2} ?
 What does the Integral Test tell you about the series
Σ 1/k ?
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For Friday March 3 (Due 3/2 @ 8:00 pm)
Section 7.7 Alternating Series
To read
 Topics:
 Alternating Series
 Absolute and Conditional Convergence
 The Curious Behavior of a Conditionally Convergent Series
 Examples: 1, 2
Reading Questions
Consider the series Σ (1)^{(k+1)} / k^{2}
 Why does this series converge?
 How closely does S_{50} approximate the value of the series? Why?
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For Monday March 6
Reread Section 7.7 Alternating Series
No Reading Questions for today.
For Wednesday March 8 (Due 3/7 @ 8:00 pm)
Section 8.1 Power Series
To read
 Topics:
 Power Series
 The Interval of Convergence of a Power Series
 Power Series in x  x_{0}
 Examples: We'll go over a few different ones in class
Reading Questions
 How do power series differ from the series we have looked at up to this point?
 What is the interval of convergence of a power series? Explain in your own words.
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For Friday March 10 (Due 3/9 @ 8:00 pm)
Section 8.2 Maclaurin Series and Taylor Series
To read
 Topics:
 Maclaurin Polynomials and Taylor Polynomials
 Taylor Series and Maclaurin Series
 Examples: 1, 2, 3
Reading Questions
 What is the basic idea of constructing the nth degree Taylor polynomial for a function f(x)? Do not give the formula, but explain in your own words in a few sentences.
 What is the difference between a Taylor series and a Maclaurin series?
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March 13  17
Spring Break. Surprisingly, no Reading Assignments.
For Monday March 20
Reread Section 8.2 Maclaurin Series and Taylor Series
No Reading Questions for today.
For Wednesday March 22
Flex Day. No Reading Assignment.
For Friday March 24 (Due 3/23 @ 8:00 pm)
Section 12.1 Functions of Two and Three Variables
To read
 Topics:
 Functions of Two Variables
 Graphing a Function of Two Variables
 Functions of Three Variables
 Level Curves and Level Surfaces
 Examples: 1, 4
Reading Questions
 Is the graph of the hyperboloid of one sheet x^{2} + y^{2}  z^{2} = 1 the graph of a function of two variables? (See page 785 for a sketch of this surface.) Explain.
 Is the graph of the elliptic paraboloid z = x^{2} + y^{2} the graph of a function of two variables? (See page 785 for a sketch of this surface.) Explain.
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For Monday March 27
Q&A for Exam 2. No Reading Assignment.
For Wednesday March 29
Reread Section 12.1 Functions of Two and Three Variables
No Reading Questions for today.
For Friday March 31 (Due 3/30 @ 8:00 pm)
Section 12.3 Partial Derivatives
To read
 Topics:
 Partial Derivatives of Functions of Two and Three Variables
 Higher Order Partial Derivatives
 Finding a Function When the Partial Derivatives Are Given
 Examples: 1, 2, 4, 5
Reading Questions
 For a function f(x,y), what information does f_{x}(1,0) give?
 How many secondorder partial derivatives does g(x,y,z) have? Why?
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For Monday April 3
Reread Section 12.3 Partial Derivatives
No Reading Questions for today.
For Wednesday April 5 (Due 4/4 @ 8:00 pm)
Section 12.6 Extreme Values
To read
 Topics:
 You'll need to understand Definition 12.35 The Gradient on pg 957
 The Gradient at a Local Extremum
 Examples: 1 and 3. We'll talk about classifying extrema by methods other than the SecondDerivative Test.
Reading Questions
 If f(x,y)= x^{2}y + 3 x y, give an expression for ∇ f(x,y).
 If the partials f_{x} and f_{y} exist everywhere, at what points (x_{0}, y_{0}) can f(x,y) have a local max or a local min?
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For Friday April 7
Reread Section 12.6 Extreme Values
No Reading Questions for today.
For Monday April 10 (Due 4/9 @ 8:00 pm)
Section 13.1 Double Integrals over Rectangular
To read
 Topics:
 Volumes
 Double and Triple Summations
 Iterated Integrals and Fubini's Theorem (pay special attention here)
 Examples: 1 and 2
Reading Questions
 If f(x,y) is a function of two variables and R is a rectangle in the xyplane, what does ∫ ∫_{R}
f(x,y) dA measure?
 Explain the idea of Fubini's Theorem in a couple of sentences in your own words.
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For Wednesday April 12 (Due 4/11 @ 8:00 pm)
Section 13.2 Double Integrals over General Regions
To read
 Topics:
 General Regions in the Plane
 Double Integrals over General Regions
 Algebraic Properties of Double Integrals
 Examples: 1, 2, 3
Reading Questions
Let Ω be the region in the xyplane bounded by the parabola y=x^{2} and the horizontal line y=9.
 Give values for a, b, g1(x), and g2(x) so that
∫ ∫_{Ω}
f(x,y) dA = ∫_{a}^{b}
∫_{g1(x)}^{g2(x)} f(x,y) dy dx.
 Give values for c, d, h1(y), and h2(y) so that
∫ ∫_{Ω}
f(x,y) dA = ∫_{c}^{d}
∫_{h1(y)}^{h2(y)} f(x,y) dx dy.
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For Friday April 14 (Due 4/13 @ 8:00 pm)
Section 13.2 Double Integrals over General Regions
Examples: Make sure to understand Example 4
Reading Questions
Consider the integral
∫_{0}^{1}
∫_{y}^{1}
e^{x2} dx dy.
 Explain why you would want to reverse the order of integration for this integral.
 Evaluate the integral by reversing the order of integration.
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For Monday April 17
Flex Day. No Reading Assignment.
For Wednesday April 19 (Due 4/18 @ 8:00 pm)
Section 9.2 Polar Coordinates
To read
 Topics:
 Plotting Points in Polar Coordinates
 Converting Between Polar and Rectangular Coordinates
 The Graphs of Some Simple Polar Coordinate Equations
 Examples: 1, 2, 3, 4
Reading Questions
 What do the coordinates (r, θ) in polar coordinates measure?
 Why do you think we are studying polar coordinates now?
 Is the graph of the polar function r = 4 cos(θ) is the graph of a
function y=f(x)? Explain.
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For Friday April 21 (Due 4/20 @ 8:00 pm)
Section 9.3 Graphing Polar Equations
To read
 Topics:
 Using the θr  plane to Get Information About a Polar Graph
 Symmetry in Polar Graphs
 Examples: 1  6
Reading Questions
Describe the shape of the graph of the following polar equations.
 r = 2θ, θ≥ 0
 r = 2 sin(θ)
 r = sin(2θ)
 r = sin(3θ)
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For Monday April 24
Q&A for Exam 3. No Reading Assignment.
For Wednesday April 26 (Due 4/25 @ 8:00 pm)
Section 13.3 Double Integrals Using Polar Coordinates
To read
 Topics:
 Polar Coordinates and Double Integrals
 Double Integrals in Polar Coordinates over General Regions
 Examples: 1, 4, 5
Reading Questions
 Describe the shape of a polar "rectangle."
 Why would you ever want to use polar coordinates to evaluate a
double integral?
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For Friday April 28
Reread Section13.3 Double Integrals Using Polar Coordinates
No Reading Questions for today.
For Monday May 1
Flex Day. No Reading Assignment.
For Wednesday May 3
The BIG Picture. No Reading Assignment.
For Friday May 5
The BIG Picture. No Reading Assignment.

