Assignment 2: More about Functions

Week 2

Reminder:

By 4:00 pm on Tuesday, [date]: Write and submit your personal essay.

If you are taking more than one course from me this semester, you may write one essay for all the courses.  Just be sure to answer all of the questions as the questions for each course are slightly different.

·        Write a personal essay in which you answer two questions:

1.      What is a function?

The concept of function is foundational in the study of mathematics, and is also used extensively in computer science.  Being able to see functions in a problem scenario is a useful problem-solving strategy in all fields.  What is your current understanding of function as a mathematical concept?

2.      What events in your mathematical life have prepared you for this course?

What background or experiences do you have in algebra and trigonometry?  Discuss three to five significant events in your mathematical life that have helped to prepare you to take Calculus. (You don’t need to tell me about every teacher or every course you have ever taken, just those experiences that have helped to prepare you for Calculus.) 

o       Write your essay and save it as a Word document. 

o       This essay will probably just be one or two single-spaced pages long.

o       Upload this document to your folder for this course in Educator* by 4:00 pm on Tuesday, [date]. Part of the point of this assignment is to be sure that everyone in the class can upload work to Educator*, so it is not acceptable to hand in a hardcopy on paper. 

 

Continue to sit with different people in class next week so that you can get better acquainted with your classmates.  On Friday, [day 6], we will choose permanent groups for the rest of the semester.

 

By Monday, [day 4]:

·        There are WeBWorK problem sets for each of the sections of the text that we have discussed so far.  

Attempt at least one of these sets of exercises that are available in WeBWorK. 

I want to see that everyone is able to login to WeBWorK, and is able to submit responses to the Hwk sets that are posted there.  Remember that for you to get credit for these Hwk sets, you have to be the one who is logged into WeBWorK.  You are encouraged to work together on these problems.  However, if you work together, you will each have to login and submit answers to the problems that are posted for you.

 

·        Preview Section 1.4: Functions as Objects. 

We will discuss this section during class on Monday.  You will have an opportunity to work in small groups on the Activities and Checkpoints in this section. 

 

By Wednesday, [day 5]:

·        Review Section 1.4. 

·        Complete the WeBWorK exercises for Section 1.4 (Hwk 1.4) before coming to class on Wednesday.  Remember that for you to get credit for these Hwk sets, you have to be the one who is logged into WeBWorK.  

 

·        Preview Section 1.5: Algebra of Functions. 

We will discuss this section during class on Wednesday.  You will have an opportunity to work in small groups on the Activities and Checkpoints in this section. 

 

By Friday, [day 6]:

·        We will form permanent groups in class on Friday. 

You have had opportunities to work with each other in different small groups, and to get to know many of your classmates.  Perhaps you have begun to talk with each other about who you would like to work with during classes throughout the rest of the semester.  If there are particular persons you would like to work with, consider inviting them to be in your group.

(In my classroom computer lab at this time, there are five workstations with space for 2 – 3 students at each workstation.  Depending on the classroom situation, I find that students work well in groups with as few as 2 students and as many as 5 students.  I usually let the students choose their own groups, and encourage them to make their groups as diverse as possible.  In a class like Calculus I where most of the students don’t really know each other yet, I am more directive in helping them form groups.  In other classes, the students may already know each other and know who they want to be in their group.  I often let them choose whether to work with different persons outside of the class on homework or projects.)

 

·        Review Section 1.5. 

·        I have set up three WeBWorK assignments for Section 1.5.  Do at least one of these by Wednesday [day 7]. 

 

 

Chapter 2: Models of Growth: Rates of Change

We will begin Chapter 2 in class on Friday.  One of the computational strategies that is fundamental in the study of Calculus is differentiation, or calculating the derivative.  The derivative gives us a measure of the rate of change.

 

·        Preview Section 2.1: Rates of Change. 

You have already studied the idea of slope in your algebra or precalculus course.  Slope is usually calculated as “rise over run.”  In calculus, we extend the concept of slope to the difference quotient.  The derivative, then, will be defined in Section 1.2 as the limit of the difference quotient.

 

·        Check Educator* for Assignment 3, which will be posted by Friday, [day 6]. 

*Educator is the course management system in use at Cardinal Stritch University.