| Wed 12/12 |
Assessing the Impact of the
1998 ICCAT and NRC Initiatives to Reform the Atlantic
Bluefin Tuna Fishery using a Slope FIeld |
- To realize that a function can be defined by
its rate of change and one "initial value" of the
function
- To use data collected from the Atlantic
bluefin tuna fishery to create an equation for the
net rate of change of the Atlantic bluefin tuna
population
- To use the equation for the net rate of change to
draw a slope field
- To use an initial value and the slope field
to draw a graph showing the size of the Atlantic
bluefin tuna population versus time
- To use the information calculated to assess the
1998 ICCAT and NRC reforms of the bluefin tuna fishing
industry
|
| Mon 12/10 |
Assessing the Impact of the
1998 ICCAT and NRC Initiatives to Reform the Atlantic
Bluefin Tuna Fishery |
- To realize that a function can be defined by
its rate of change and one "initial value" of the
function
- To use data collected from the Atlantic
bluefin tuna fishery to create an equation for the
net rate of change of the Atlantic bluefin tuna
population
- To use an initial value, an equation for the
rate of change of a function and a given "step-
size" to approximate the size of the bluefin tuna
population as time goes by
- To use the information calculated to assess the
1998 ICCAT and NRC reforms of the bluefin tuna fishing
industry
|
| Fri 12/7 |
Implicit Differentiation |
- To recognize when it is appropriate to use
the technqiue of Implicit Differentiation to for
calculate the derivative of a function
- To practice using the technique of Implicit
Differentiation
|
| Wed 12/5 |
The Gulf of Sidra Incident |
- To use functions and derivatives to represent
the important aspects of a situation that is
described in words and pictures
- To translate a question phrased in plain English
into an appropriate symbolic representation
- To identify the quantities that will enable solution
of the question and represent these quantities using
functions
- To relate the values of derivatives of two functions
using a geometrical relationship (Pythagorean Theorem)
that relates the functions that are involved
|
| Mon 12/3 |
Calculating Derivatives Using
the Chain Rule |
- To recognize when it is appropriate to use
the chain rule to calculate the derivative of a
function
- To practice using the chain rule for
calculating the derivative of a composite function
when the function is defined by an equation
- To use the chain rule in
combination with the other rules that you know for
calculating derivatives
|
| Fri 11/30 |
Assessing the Impact of
the 1972 Marine Mammals Protection Act on the Killing
of Dolphins by Tuna Fishermen |
- To realize that you can differentiate the
derivative of a function. The result is called
the second derivative.
- To learn that when the second derivative of
a function is negative, the function is concave
down
- To learn that when the second derivative of
a function is positive, the function is concave
up
- To use the second derivative of a function to
determine when the Marine Mammals Protection Act
of 1972 appeared to be reducing the rate at which
dolphins were killed by tuna fishermen.
|
| Mon 11/19 |
The Global Minimum Water
Company's Pledge to its Customers |
- To translate a verbal and pictorial
description of a situation into a collection of
functions defined by equations
- To recall and use formulas for volume and
area from geometry to describe the volume and surface
area of a three dimensional object
- To translate a verbal description into a
situation into a calculus problem involving derivatives and
critical points
- To recognize that you can only do calculus
when the function you are working with is
expressed using only one independent variable and
to use the equations you have found to re-express
a function with two independent variables in
terms of only one independent variable
- To use calculus to find the derivative of a
function
- To use the derivative of a function to locate
the maximum and minimum values of a function
- To use the derivative of a function to
classify the critical points as (local) maximums, (local)
minimums or neither
|
| Fri 11/16 |
Derivatives of Exponential
Functions |
- To recognize when it is appropriate to use
the rule for calculating the derivative of an
exponential function
- To practice using the rule for
calculating the derivative of an exponential function
when the function is defined by an equation
- To use the rule for differentiating an exponential
function in
combination with the other rules that you know for
calculating derivatives
|
| Friday 11/9 |
A Straight-forward Optimization
Problem |
- To model a straight-forward situation using a
polynomial function
- To practice using the derivative rules you
have been learning to find the derivatives of
functions
- To use the first derivative to locate the
points where a function has maximum or minimum
value
|
| Fri 11/9 |
Calculating Derivatives |
- To recognize when it is appropriate to use
various rules for calculating derivatives
- To practice using rules for calculating
derivatives when functions defined by equations
- To use the derivative rules you have been
learning together in combinations
|
| Wed 11/7 |
The Product and Quotient
Rules |
- To recognize when it is appropriate to use
the product and quotient rules for calculating
derivatives
- To practice using the product and quotient
rules for functions defined by equations
- To use the product and quotient rules in
combination with the other rules that you know for
calculating derivatives
|
| Mon 11/5 |
The Fastest Man in the
World |
- To express familiar quantities such as
position, speed, distance covered and velocity in terms of
functions and derivatives
- To create a function (defined by an equation) to
represent the distance covered by an athlete during a
race
- To use the rules for calculating derivatives:
- The Sum and Difference Rules
- The Constant Multiple Rule
- The Power Rule
- The Derivative of a Constant Rule
to calculate the derivative of a polynomial
function
|
| Wed 11/2 |
Pricing a Consumer Good |
- To use the limit definition of the derivative
to calculate an equation for the derivative of a
polynomial function
- To interpret the value of the derivative in a
practical setting
- To find a way of explaining what the
numerical value of a derivative means in a way
that would be comprehensible to someone who was
not familiar with calculus
- To relate the material from this class to the
material from another class (Economics)
- To express the economic quantities of
marginal revenue and marginal cost in terms of
functions and derivatives
- To use the condition for profit maximization
from economics (marginal revenue = marginal cost)
to price a consumer good
|
| Mon 10/29 |
The Legendary Darwin
Stubbie |
- To distinguish between average rate of change
over an interval and instantaneous rate of change
at a point of time
- To calculate the average rate of change of a
quantity over an interval of time
- To use a graph of a function and a tangent
line to find the instantaneous rate of change of
a function at a point
- To use a table to calculate the limit of the
slopes of secant lines as the interval becomes
shorter and shorter
- To use a table of secant line slopes to
estimate the instantaneous rate of change of a
function at a point
- To learn about the serious (and usually adverse)
effects of alcohol abuse
|
| Mon 10/22 |
Analyzing President Bush's
New Tax Plan |
- Find linear functions relating Federal tax
to taxable income
- Use a collection of linear functions to
describe a complicated function that is defined
in pieces
- Decide what could possibly be meant by a
"percentage tax cut"
- Create rational functions relating taxable
income to "percentage tax cut"
- Use a collection of rational functions to
describe a complicated function that is defined
in pieces
- Use numerical and graphical evidence to evaluate
President Bush's claims on who will benefit most
from his new tax schedule
|
| Fri 10/19 |
Enhancing Agricultural
Production in Tanzania |
- Use a graphing calculator to represent data
and to find a symbolic description of the
relationships in the data
- Create an equation for a quadratic function
- Use a graphing calculator to locate the
coordinates of the maximum (or minimum) point on the
graph of a quadratic function
- Learn to use the technique of Completing the
Square to convert the symbolic representation for a
quadratic function from standard to vertex form
- Relate the algebraic structure of the equation for
a quadratic function in vertex form to the coordinates
for the maximum (or minimum) point on the graph of the
function
|
| Mon 10/15 |
Finding equations for
polynomial and rational functions |
- Locate the zeros (x-intercepts) of
polynomial functions
- Determine the multiplicities of the zeros of
polynomial functions
- Use information about the zeros and their
multiplicities to find an equation for a
polynomial function that is defined by a graph
- Locate the horizontal and vertical asymptotes
of a rational function that is defined by a graph
- Use the graph of a rational function to determine
a possible equation for the rational function
|
| Fri 10/12 |
Acid-Base Titration |
- Find the inverse of a function that is
defined by a table of values
- Find the inverse of a function that is
defined by a graph
- Examine the geometrical relationship between the
graph of a function and the graph of the inverse
- Find an equation for the inverse of a
function
|
| Wed 10/10 |
Administering
Morphine for the Relief of Pain |
- Find equations for exponential functions
- Translate written descriptions of situations
into equations and graphs
- Create new functions from old using the
following kinds of transformations:
- Vertical translations
- Horizontal translations
- Vertical stretches
- Horizontal stretches
|
| Fri 10/5 |
Methods for Valuing Stocks |
- Create new functions from old using the
operations of addition, subtraction,
multiplication and division
- Create new functions from existing functions
that are represented as graphs, tables of values
or equations (or combinations of all three
- Recognize that when constructing a new
function from existing functions, the domain of
the new function is the intersection of the
domains of the building blocks
- Learn about some indices (the PE ratio and
the PS ratio) that can be used to value stocks
- Learn something about how to use the financial
information that companies disclose to evaluate their
potential as an investment
|
| Wed 10/3 |
Determining the
Advertising Budget for a Small Business |
- Translate information presented in graphical
form to numerical and symbolic forms of representation
- Use function notation to name functions and
denote their outputs
- Use your intuitive ideas about the situation
that a function represents to interpret complicated
expressions involving function notation
- Use functions and function notation to help you
combine information in a way that helps to make
financial decisions affecting a business
|
| Mon 10/1 |
Governor Pataki Cracks Down
on Violent Crime |
- Use a graph showing the rate of change
of a function to develop information about the
appearance of the graph of the actual function
- Sketch the graph of a function that is not
defined by values or a graph or an equation, but
by a rate of change
- Use specific values of the rate of
change of a function to approximate the values
of the actual function itself
|
| Fri 9/28 |
Orbital Period of the
Planets |
- Use your graphing calculator to plot
data and fit equations to the data
- Use your graphing calculator as a
visualization tool to find patterns in numerical data
- Compare the predictions of an equation fitted to a
data set with measured values
- Realize that exponential functions are not
the only functions that can have increasing, concave
up graphs
- Use your calculator to fit a power function to a
set of data
- Use the equation of a power function to make
predictions
|
| Wed 9/26 |
The Story of
Zarathustra and King Vishtaspa |
- Translate a written decription of a situation
into numbers (and possibly an equation)
- Numerically analyze an example of exponential
growth
- Gain an appreciation of how quickly an
exponential function can grow
|
| Wed 9/26 |
The Desert Mummies of
Xinjiang Province |
- Create an equation for an exponential
function based on a written description of
a relationship
- Use the equation of an exponential function
with the TRACE function of a graphing calculator
to date ancient remains based on carbon-14
abundance
- Interpret the predictions of an exponential
function in historical and political contexts
|
| Mon 9/24 |
Hippocampal Development
of London Taxi Drivers |
- Use linear functions to describe trends in
data
- Sketch the graph of a linear function
- Calculate the equation of a linear function
- Use the equation for a linear function to
make predictions
- To determine the mathematical domain and the
problem domain for a linear function
|
| Fri 9/21 |
War on Drugs |
- Detect intervals where a function is
increasing or decreasing
- Calculate the average rate of change of a
function over an interval
- Relate the sign and magnitude of the rate of
change to the appearance of the graph of a
function
- Detect intervals on which a function is
concave up or concave down
- Relate the behavior of the rate of change to
the concavity of the graph of a function
|
| Wed 9/19 |
Woody Allen |
- Use clues from context to decide which
quantity is the independent variable and which
quantity is the dependent variable
- Represent numerical and verbal information
graphically
- Use graphs to distinguish between functions
and relationships that are not functions
- Decide what features of a mathematical
relationship are most useful for making
predictions
|
| Mon 9/17 |
Bigfoot |
- Understand which of the variables in a
relationship is the independent and which is the
dependent variable
- Learn how the choice of independent and dependent
variables affects the appearance of a graph
- Locate the numerical coordinates of data points on
a graph
- Identify when a relationship can be used to make
unambiguous predictions, and when it can't
|