| January 12 |
First Day of Class Policies |
- Class policies for the semester
- Tentative day-by-day outline of the course
|
| January 12 |
Influences on Teenage Drug Use |
- Identifying variables in a relationship
- Definition of a function
- Vertical line test for a function represented by a graph
|
| January 14 |
Working with Function Notation |
- Understanding graphical, numerical and symbolic representations of a function
- Evaluating symbolic ststements expressed in function notation using functions defined by graphs and tables
|
| January 12 |
Finding a Polynomial Formula using Roots and Multiplicities |
- Locating the roots of a polynomial function defined by a graph
- Determining the possible multiplicty of each root
- Evaluating the constant of proportionality
- Writing down a polynomial formula compatible with a graph
|
| February 6 |
Finding derivatives using the Product and Quotient rules |
- Reading the formula of a function to determine when the product or quotient rules can be applied
- Representing functions as products of simpler functions (whose derivatives we know or can work out)
- Representing functions as quotients of simpler functions (whose derivatives we know or can work out)
- Finding formulas for derivatives of functions
|
| February 6 |
Finding derivatives using the Chain rule |
- Reading the formula of a function to determine when the Chain rule can be applied
- Representing functions as compositions of simpler functions (whose derivatives we know or can work out)
- Finding formulas for derivatives of functions
|
| February 11 |
Problems for in-class exam review |
- The exam covers Sections 1.1 to 2.5 (inclusive)
|
| February 11 |
Solutions to in-class review problems |
- The exam covers Sections 1.1 to 2.5 (inclusive)
|
| February 16 |
Practice at implicit differentiation |
- Working through the steps that we identified in class to calculate the derivative even when y cannot be isolated from x.
|
| February 18 |
Experimental verification of the Chain rule |
- Collecting data on the rate of change of two quantities
- Creating a theoretical relationship between the two rates of change (using the Chain rule)
- Comparing theory and experiment to test the Chain rule experimentlly
|
| February 18 |
The Gulf of Sidra Incident |
- Using the Theorem of Pythagoras to create a relationship between to quantities
- Relating two rates of change using the Chain rule
- Using the results to correct the relative speed reported by a radar
|
| February 18 |
Solutions for the Gulf of Sidra |
|
| February 20 |
The Long Shadow of Jack the Ripper |
- Using the Principle of Similar Triangles to create a relationship between to quantities
- Relating two rates of change using the Chain rule
- Using the results to correct the relative speed reported by a radar
|
| February 20 |
Solutions for Jack the Ripper |
|
| February 23 |
Age of a giant shark tooth |
- Testing a table of values for perfect exponentiality
- Finding a formula for an exponential function
- Setting up and solving equations involving exponential functions
|
| February 23 |
Solutions for the giant shark tooth |
|
| February 25 |
Age of the desert mummies of Xinjiang province |
- Testing a table of values for perfect exponentiality
- Finding a formula for an exponential function
- Setting up and solving equations involving exponential functions
|
| February 25 |
Solutions for the desert mummies |
|
| February 25 (Not distributed in class) |
Solving equations using logarithms |
- Algebraic properties of the common logarithm function
- Solving equations that involve common logarithms
|
| February 25 (Not distributed in class) |
The concept of the inverse of a function |
- Reversing the actions of a function
- Testing a function to determine when the inverse is also a function
- Finding a formula for the inverse
- Sketching the graph of the inverse
|
| February 25 (Not distributed in class) |
Logarithms as inverses of exponential functions |
- Setting up exponential equations
- Solving exponential equations using logarithms
- Understanding why the common logarithm is the inverse of the exponential function y = 10x
- Properties of the logarithm that can be inferred because it is an inverse
|
| March 2 |
Solving equations using logarithms |
- Recognizing when and when not to use logarithms to solve an equation
- Using the properties of logarithms to solve equations that involve exponential functions
|
| March 2 |
Solutions for the logarithms handout |
|
| March 18 |
In-class review problems for Exam 2 |
- Everything from implicit differentiation to L'Hopital's rule (inclusive of both)
|
| March 18 |
Solutions for in-class review problems |
|
| April 8 |
Calculating the absolute oral bioavailability of Viagra |
- Setting up and evaluating a left-hand Riemann sum on a calculator
- Setting up and evaluating a right-hand Riemann sum on a calculator
|
| April 8 |
Solutions for Riemann sums handout |
|
| April 22 |
In-class review problems for Exam 3 |
- Everything from maximum and minimum values to u-substitution (inclusive of both)
|
| April 22 |
Solutions for in-class review problems |
|
| April 27 |
The technique of u-substitution |
- Identifying the inside function u
- Calculating the derivative du/dx and making dx the subject
- Replacing the inside function (by u) and dx in the original integral
- Calculating the anitderivative with respect to du
- Converting the antiderivative formula so that it is expressed in terms of x
|
| May 1 |
In-class review for the final exam |
- The final exam is cumulative and may include any topic covered during the semester.
|
| May 1 |
Solutions for final exam review problems |
|
