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Section 02 meets Mon, Tues, Thurs, Fri 8:10am-9:00am in Morton 226.
My office hours are 11:10am-noon Mon, Tues, Thurs, Fri in Morton 538.
Students from all sections of Math 163A, not just section 04, are welcome to come to my office hours.
The information on this page mirrors the information posted on the course's "Blackboard" site.
Course Information Sheet, including general information, syllabus, and homework list (link)
In the first week 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 "Handout 01: Functions in Precalculus and Beyond", which was recycled from my fall 2004 Math 115 Precalculus course.
Handout 01: Functions in Precalculus and Beyond (link)
In the second week of class, we discussed transformations of graphs by shifting and stretching, both horizontal and vertical. On Tuesday, September 12, I distributed the small "Handout 02: Transformations of Graphs".
Handout 02: Transformations of Graphs (link)
''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. In class on Thursday September 14, we discussed why this approach is both too hard and not hard enough. The method is too hard because one is often called upon to plug a fraction into a high degree polynomial. Computing the function value in such a case is a nuisance, especially without a calculator. The method is not hard enough because it does not make one think about why the function had the sign that it did. The document entitled "Handout 03: Roots, Linear Factors, and Sign Charts" is 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 approach taken is to not use sample numbers, using instead only the symbols +, -, and 0. The handout ends with a list of six exercises. Two of these problems are on Homework #2. The others will show up on later homework sets.
Handout 03: Roots, Linear Factors, and Sign Charts (link)
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. On Monday, September 18, we discussed a six-step method for graphing rational functions. I distributed "Handout 04: Six Step Method for Graphing Rational Functions without Calculus".
Handout 04: Six Step Method for Graphing Rational Functions without Calculus (link)
We discussed the "end behavior" of polynomials graphs on either Tues Sept 12 or Thurs Sept 14. This small "Handout 05: End behavior of polynomial graphs" was posted on the course Blackboard site, but I forgot to distribute it in class.
Handout 05: End behavior of polynomial graphs (link)
We used a small "Table of Equivalent Statements" to help organize our thoughts when discussing properties of a function f, its derivative f ', or its second derivative f ''. This table is certainly useful when graphing functions. But in fact, the table will pop up in discussions of almost every type of problem during the rest of the course..
Handout 06: Table of Equivalent Statements (link)
In Section 5.4, we revisited the topic of graphing rational functions, this time with the additional tools of calculus available. The Six Step Method for Graphing Rational Functions grew into the 10-Step Method. The additional four steps involved analysis of the first and second derivative. In Handout 07, the 10-Step Method is presented. In Handout 08, we see a simple example of its use.
Handout 07: 10-Step Method for Graphing Rational Functions with Calculus (link)
Handout 08: Graphing a Polynomial with the 10-Step Method (link)
In Section 9.3 of the textbook, we learned one method for finding relative maxs, mins, and saddle points in a function of two variables. We called the method the "D-test". To use the method, we followed the step in the handout below.
Handout 09: Worksheet for the "D-Test" (link)
On Friday, September 29, we did our first group work exercise. In it, the students are given a ruler and the graph of a function. They used the ruler to draw tangent lines on the graph and to make measurements for computing the slopes of those tangent lines. With the information about the slopes of the tangent lines, they sketched a graph of the derivative. That exercise is posted here, along with four more practice exercises.
Group Work 01: Finding Derivatives Graphically Using the Ruler Method (link)
On Friday, October 6, we did our second group work exercise. Entitled "Recognizing Representations of Slopes", it consisted of drills that test the reader's recognition of mathematical expressions that represent the slopes of secant lines and tangent lines for a given graph.
Group Work 02: Recognizing Representations of Slopes (link)
On Tuesday, October 17, we did our third group work exercise. Entitled "Identifying three kinds of graph behavior", it presented the graph of a function f and asked the students to identify positive/negative behavior, increasing/decreasing behavior, and concavity behavior in the graph.
Group Work 03: Identifying three kinds of graph behavior (link)
Also on Tuesday, October 17, we did our fourth group work exercise. Entitled "Using a graph of f ' to answer questions about f," it presented the same curve that was used in group work 03, but this time the curve was playing the role of the derivative, f '. Using this graph of f ', the students had to answer questions about f.
Group Work 04: Using a graph of f ' to answer questions about f (link)
On Friday, October 20, we discussed the "10-Step Method for Graphing Rational Functions With Calculus". In this fifth group work exercise, done on that day, the students work on an example very similar to the one presented in Handout 08, above.
Group Work 05: Graphing a Polynomial With the 10-Step Method (link)
On Monday, October 23, we started discussing absolute extrema, and did our sixth group work exercise. In it, the students discover that if a function's domain is not a closed interval, the function may or may not have relative and absolute extrema.
Group Work 06: Relative and Absolute Extrema (link)
Group Work 06: Relative and Absolute Extrema SOLUTIONS (link)
On Tuesday, November 7, we started discussing the use of the "D-Test" to find extrema and saddle points in functions of two variables. On Thursday, November 9, we did a group work in which we used the "D-Test" to match functions with graphs.
Group Work 07: Using the "D-Test" to Match Functions with Graphs. (link)
Midterm Exam #1 was given in class on Friday, September 22, 2006. It covered through section 3.2 of the textbook. ("Continuity").
Midterm #2 was given in class on Tuesday, October 10,2006. It covered through section 4.3 of the textbook. ("The Chain Rule").
Midterm #3 was given in class on Tuesday, October 31,2006. It covered through section 6.2 of the textbook. ("Applications of Extrema").
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