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The information on this page was formerly posted on the course's "Blackboard" site.
On the first day of class, we discussed the shift in attitude about functions that we would see in precalculus, a shift from thinking of them as equations to thinking of them as "mathematical machines", with input and output. I distributed the one-page handout entitled "Functions in Precalculus and Beyond".
The textbook's approach to graphing rational functions was rather ad-hoc. In class, I stressed the importance of establishing a plan and and sticking to it, both to keep one's own thoughts organized when solving a problem, and to help give a clear structure to the written solution. We always used a seven-step method for graphing rational functions.
When discussing exponential and logarithmic functions in class, I often wrote on overhead transparencies, illustrating the inverse function relationship by flipping transparencies. The set of colored overhead transparencies of exponential functions that I used for my basic graphs was posted on blackboard.
College courses don't devote much time to trignometry, one reason being that students have all learned some trig in high school. But college precalc and calculus students are perennially terrified of the subject, and don't understand why the trig they learned in high school is somehow no longer valid, or at least no longer sufficient. I think one source of the confusion is the fact that three families of trig functions are used, but all are given the same name. I discussed the three families class and in this handout on trig functions. We used different names for the three families, to help keep them distinct. ''SOHCAHTOAH trig functions'' was our name for the versions of the functions that involved ratios of lengths of sides in right triangles; ''unit circle trig functions'' was our name for the more general versions that invoke the unit circle; ''capital trig functions'' was our name for those with domain restricted in order that they be one-to-one. It is this third family of functions that is used for the ''inverse trig functions''. The handout presents definitions for all three families of functions, along with a table summarizing their domain and range properties.
As with the exponential and logarithmic functions, I also wrote on overhead transparencies when discussing inverse trig functions in class, illustrating the inverse function relationship by flipping transparencies. The set of colored overhead transparencies of trig functions that I used for my basic graphs was posted on blackboard.
In class, I often used this overhead transparency of the unit circle.
On Tuesday, October 12, we did a group work drill involving the unit circle.
Many of graphs that we dealt with in 115 were simple transformations of basic graphs. The techniques of shifting, stretching, and flipping graphs - and the corresponding changes in the functions that generate the graphs - are taught in precalculus and reviewed in calculus. Many students needed more discussion than the textbook provided. The document entitled "Transformation of Graphs" was meant to provide a thorough review. Many worked examples are provided, and a list of exercises is also suggested, all drawn from the homework list for Math 115.
Quiz 1 was given in class on Friday, September 10.
Quiz 2 was given in class on Friday, September 17.
Quiz 3 was given in class on Wednesday, September 22.
Quiz 4 was given in class on Tuesday, September 28.
Quiz 5 was given in class on Friday, October 1.
Midterm 1 was given in class on Friday, October 8.
Midterm 1 solutions were posted on blackboard.
Quiz 6 part 1 and part 2 was given in class on Friday, October 15.
Quiz 7 was given in class on Thursday, October 21.
Quiz 8 was given in class on Wednesday, October 27.
Quiz 9 was given in class on Friday, October 29.
Quiz 10 was given in class on Thursday, November 4.
Midterm 2 was given in class on Friday, November 12.
Midterm 2 solutions were posted on blackboard.
A cumulative final exam was given on Monday, November 22.
| Ohio University Links | |
| Mathematics Department | Ohio University |