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 Mathematics Department |  Ohio University |
Class meets Mon, Tues, Thurs, Fri 8:10am-9:00am in Morton 318.
My office hours are Mon, Tues, Wed, Thurs 4:00pm-5:00pm in Morton 418.
Students from all sections of Math 163A, not just section 01, are welcome to come to my office hours.
The information on this page mirrors the information posted on the course's "Blackboard" site.
On Tuesday, Jan 18, we did a set of graphing drills involving limits and sign charts.
On Monday, Jan 24, we discussed techniques for finding derivatives graphically. We did a graphing drill involving sketching a derivative. More such drills are posted in the "supplemental materials" section.
On Tuesday, Jan 25, we began with the following group work involving the graphical approach to finding the derivative of f(x) = x2 - 2x - 3. Immediately following that group work, we found the same derivative using calculus.
On Friday, Feb 7, we wrapped up our discussion of chapters 3 & 4 of the text with a group work drill involving recognizing expressions that represent slopes.
On Tuesday, Feb 15, we did a group work drill using the ten-step method to graph a polynomial.
On Tuesday, March 8, we did a group work exercise using the "D-test" to find saddle points and relative extrema in the graph of a function of two variables. We used a worksheet with a step-by-step guide to the method. That worksheet has been reworked and is on the list of Classroom Math Handouts, below.
We began the course review with Thursday, March 10 group work exercises discussing the solution to two homework problems turned in by an imaginary student. The student got the right answers, but left out most of the important symbols that would help the solutions make sense. The group work assignment was to to fill in the missing symbols and to state the problems.
We continued the course review with Friday, March 11 group work exercises involving the interpretation of graphs. In the first, a graph of f ' was given and questions were asked about f . In the second, a graph of Marginal Profit was given and a question was asked about Profit.
On the first day of class, we discussed the shift in attitude about functions that we would see in calculus, 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", which was recycled from my fall 2004 Math 115 Precalculus course.
The textbook's approach to graphing rational functions is 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, which was recycled from my fall 2004 Math 115 course.
The seven-step method for graphing dates from early in the quarter, before we learned about derivatives. Later in the quarter, we re-visited graphing, but this time with the derivative available as a tool. The ten-step method for graphing with calculus was an extension of the seven-step method that included calculus techniques.
The table of equivalent statements was a translation aid that we used when discussing functions and their derivatives.
The Worksheet for the "D-test" gave a step-by step approach to using the "D-test" for finding saddle points and relative extrema in the graph of a function of two variables. The Worksheet for the method of Lagrange Multipliers gave a step-by step approach to using the method of Lagrange Multipliers for finding relative extrema in the output of a function of two variables subject to an additional constraint.
Many of graphs that we dealt with in 163A 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. Some students needed more review than our textbook or our class time could provide. (For example, most could not rememember or could not explain why the graph of f(2x) was shrunk and not stretched. This transformation was not even mentioned in the textook.) The document entitled "Transformation of Graphs" was meant to provide a thorough review. Many worked examples are provided, and a list of exercises was also suggested, all drawn from the homework list for Math 163A. The document was recycled from my fall 2004 Math 115 Precalculus course
On Monday, Jan 24, we discussed techniques for finding derivatives graphically. We did a group-work exercise involving sketching a derivative. Some similar drills involving graphing derivatives are posted here.
''Sign chart'' was the name we gave to a tool for determining when a function is positive, negative, or zero. It used concepts from algebra and precalculus. Students who took those courses only in high school might not have learned about sign charts. Students who took those courses at the college level would have encountered the sign chart there, although it may have had a different name or no name at all. Furthermore, in many books, the approach taken to sign charts involves plugging "sample numbers" into the function and seeing whether the result is positive or negative. We discussed in class why this approach was both too hard and not hard enough. The method was too hard because one was often called upon to plug a fraction into a high degree polynomial. Computing the function value in such a case was a nuisance, especially without a calculator. The method was not hard enough because it did not make one think about why the function had the sign that it did. The document entitled "Roots, Linear Factors, and Sign Charts" was meant to be complete enough to give a student who had never seen sign charts an understanding sufficient for the needs of Math 163A. The content of the document was very similar to what I did in class on Tuesday, February 8 (and on another day earlier in the quarter, when we were discussing rational functions). The approach taken did not use sample numbers, using instead only the symbols +, -, and 0. The handout ended with a list of six exercises, a list that I handed out in class on Thursday, February 10. Four of those exercises are directly related to problems on Homework 7, due Monday Feb 14.
Midterm 1 was given in class on Thursday, January 20.
Midterm 2 was given in class on Monday, February 7.
Midterm 3 was given in class on Friday, February 25.
Here is the final exam information that I put on the board on the last day of class, Friday March 11. It includes the list of 10 topics that would be included on the final exam, and the list of supplemental material that I would make available on the exam.
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