Work on WebWorks 2.3-2.4! |
Moshe Cohen
B.S. in Mathematics, Binghamton University (SUNY) Phone: 225.578.4965 Fax: 225.578.4276 Email: moshe@math.lsu.edu |
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Math 1550: (Analytic Geometry &) Calculus I, Spring 2008
Section 1: Mondays-Fridays 7:30am-8:30am, Room 201 Tureaud Hall
Instructor: Moshe Cohen, moshe@math.lsu.edu
Textbook: Calculus, Early Transcendentals, 1st edition by Rogawski
Course Website: http://math.lsu.edu/~moshe/08s1550.html
Office: Room 109 Lockett Hall, (225)578-4965
Office Hours after class daily and by appointment.
TABLE OF CONTENTS
- Join a Study Group
- Frequently Asked Questions
- Course Description
- Log on to WebWorks here: https://webwork.math.lsu.edu/webwork2/Math-1550-01-Spring/
Frequently Asked Questions
Question on Rogawski section 2.5 #15:
The limit was of a rational function whose numerator (y-2)^3 and denominator (y^3-5y+2) were both polynomials (and thus continuous), and so this function should be continuous except where the denominator is 0. That should give us the idea to try Substitution (plugging in the number). When we do, we get "0/0", which means we have a little work to do.
One technique we might think about using is factoring. This is easy to do in the numerator, since it's already factored. It is quite difficult to factor the denominator, but we have the added knowledge that plugging in 2 makes it 0. Thus (y-2) is a root of (y^3-5y+2). To find the other factor, we have some options. You can:
-use long division of polynomials;
-use synthetic division; or
-use my method.
You should have already seen the first two methods. See Chapter 1 of the textbook or look online for them if you don't remember. My method is sort of intuitive.
(y-2) has degree 1, and (y^3-5y+2) has degree 3, so the other factor has degree 2: in general, it must look something like (ay^2+by+c) for some numbers a,b, and c. Let's figure out what they are by multiplying the two factors and checking it with the denominator.
(y-2)(ay^2+by+c)= ay^3-2ay^2+by^2-2by+cy-2c, and this should be equal to (y^3-5y+2).
ay^3=y^3 when a=1.
-2y^2+by^2 = 0y^2 when b=-2.
-4y+cy = -5y when c=-1.
Then +2 = +2, and so (ay^2+by+c)=(y^2-2y-1).
Then we can cancel out a (y-2) from both the numerator and the denominator, leaving other factors left. Finally, try using Substitution again because your new rational function should be continuous.
Question on Webworks assignment 2.3-2.4 questions 12,15:
This looks a lot like the problem that I gave in class on Wednesday January 23rd. Here "c" is some constant, and we want to figure out which constant it should be in order to have continuity.
The piecewise function has two pieces, each of which looks continuous to me. If you glue together two continuous functions, you get a continuous function as long as you glue them together correctly. Thus the only point we should check for continuity is where the two domains come together.
Remember the quiz? What are the three things you need to check for continuity at a point?
Question on Webworks assignment 2.1-2.2 question 2: It deals with the instantaneous ROC. I'm not quite sure which formula I need to use. I understand how to do the average velocity, but not the instantaneous one.
Response on Webworks assignment 2.1-2.2 question 2 deals with instantaneous rate of change (ROC), but in class for section 2.1 we only talked about computing the average rate of change (ROC). The average ROC is given by the "Difference Quotient" as determined by a specified interval. To ESTIMATE the instantaneous ROC, you will need to take several intervals that approach the x value you are looking for, compute their average ROC, and then "guess" the values that these averages approach.
For example, if you want the instantaneous ROC at x=0, then you could choose intervals like [0,.1], [0,.01], [0,.001], and [0,.0001] on the right while choosing [-.1,0], [-.01,0], [-.001,0], and [.0001,0] on the left. Then if the average ROCs were 163.51, 163.501, 163.5001, 163.50001 on one side and 163.49, 163.499, 163.4999, and 163.49999 on the other side, you could ESTIMATE that the instantaneous ROC to be 163.5 (with perhaps 4-5 decimal places, as is requested by WebWorks).
Course Description
This information is meant to help you get an idea for the way the course will be run.
I reserve the right to change minor details as the class progresses.
I hope to use this page to post Frequently Asked Questions and other suggestions throughout the course, so be sure to check back here.
For a printable version of the syllabus, see http://www.math.lsu.edu/~moshe/calculus.html.
See the department's list of courses for a detailed syllabus and textbook information.
We will cover roughly three or four sections a week, in case you want to read ahead.
I would like to impress upon you the importance of developing your own routine for this course within the first week of classes. As my high school physics teacher used to warn me: "When you get to college, for every one hour you spend IN class, you will have to spend three hours OUTSIDE of class." Be sure to find room in your schedule NOW for these hours. As my Calculus professor in college wrote in his syllabus: "The ONLY way to learn math is to DO math." Be sure to spend these allotted hours working problems and using the insights hidden in each section of the textbook.
Final Grade:
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Grading Scale:
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WebWork: Go to https://webwork.math.lsu.edu/webwork2/Math-1550-01-Spring/ and bookmark this site, as you will be accessing it frequently. (You can also go to the Math Department home page http//www.math.lsu.edu, click Departmental Login, click WebWork, and then click Math-1550-01-Spring.) Your Username is your PAWS ID and your Password is your LSU ID number (beginning with 89). These 20 homeworks will have due dates posted and will be graded online. |
Odd-Numbered Problems in the Text: These will be assigned regularly with each section, and students should check their answers in the back of the book. It is possible that you will see problems like these in other graded aspects of the course, although this work itself will not be graded.
Make-Up Policy: No execptions will be made for quizzes and homeworks. Students with conflicts for exams should see me immediately. Special consideration may be taken for students with extenuating circumstances, but nothing is guaranteed.
Calculator Policy: No graphing and/or programmable calculators are permitted. Scientific only.
Electronics Policy: Don't bring your laptops to class, unless you have a tablet and will be "hand writing" your notes. Leave your MP3 players tucked away in your bags; I don't want to see headphones in your ears, either. Your phone shouldn't disturb class.
Drop Dates: January 22nd is the final date for dropping courses without receiving a grade of "W". April 7th is the final date for resigning from the University and/or dropping courses. If you are concerned about failing this class, please see me as soon as possible to discuss ways you study more effectively.
I very much want to see you all succeed: in my class, here at LSU, and in life. Please do not hesitate to see me if you have any concerns that you'd like to discuss.