Math 211: Calculus (R. Jones)

Spring 2008

Lecturer: Dr. Raphael ("Rafe") Jones
Email: jones@math.wisc.edu
Phone: 263-5640
Office: 317 Van Vleck Hall
Office Hours:

Tuesday Wednesday Friday Monday, 5/12	3:00-4:00 10:00-11:00 11:00-12:00 10:30-12:00

Or by appointment.

Math 320 lecture meeting Times: MWF 2:25–3:15PM (Van Vleck B102)

Jump to: EXAM INFORMATION Important Announcements Textbook Discussion Sections and TA Office Hours Getting Help Classlist

Important Announcements (updated May 12)

Solutions to the final quiz can be found here.

The diagram I drew on the board last Friday connecting the various ideas and techniques we've seen in the course can be found here.

For practice exams for the final, one that I recommend is this one (note that you should skip number 4, which we did not cover). It is a bit shorter than ours will be. Another way of practicing for the final is to re-take the midterms from our class, only looking at the solutions after you've finished retaking them. For a blank copy of exam 1, click here. For a blank copy of exam 2, click here.

Notes on the final: It will be cumulative, with 25-30% of the questions drawn from material covered since the second midterm (6.2, 6.3, 7.1, 7.2, 7.3).

You will be allowed to have a sheet of notes on the exam: one side of one sheet of paper, handwritten. No magnifying devices allowed. You may put on the sheet anything you like; I would suggest not just writing formulas, but also perhaps examples you think would be helpful, or that illustrate key techniques like u-substituion.

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Solutions to the second exam are here.

There will be a review session on Friday from 2:25-5:30 in Van Vleck B102.

There will be a review session on Saturday from 1:00-3:00 pm in Ingraham 22.

There will be no class on Monday, April 21, the day of the second midterm. Instead I will have an office hour from 2:00 to 3:30.

Comments on the second midterm: It will cover sections 4.3 to 5.6, inclusive. It will be similar in length to the first midterm.

As for the first midterm, doing problems is the best way to review. The review problems for Chapter 4 (p. 311-313) and for Chapter 5 (p. 400-402) are good sources for problems. Also, the review problem sheet that was emailed to you on Monday, 4/14 is a good source.

Practice exams are also a good idea. The one I'd recommend is here. It is a bit longer than ours will be. There are many other practice exams available here.

Solutions to the practice exam recommended above:

• 1. P(x)= -0.25x^2 + 1000x - 9900. Integrate and then use P(20) = 10000 to solve for C.
• 2 a. -t^2e^(-t) - 2te^(-t) - 2e^(-t) + C     b. (SquareRoot(x^2 + 3)) + C     c. -ln(t+1) + ln(t)     d. -(1 + SquareRoot(x))^2 + 6(1 + SquareRoot(x)) - 4ln(1 + SquareRoot(x))
• 3. NOTE: neither of these problems will be on our exam. Part a is from section 3.8, covered on the last exam. Part b is a related rates problem, which we did not cover at all. The answers are: a. dy/dx = 12x^2y / (2y + 1).     b. (3/2)SquareRoot(5)
• 4. x = 64, y = 160
• 5. a. 20 + ln(21)     b. 7/24     c. (1/2)(e^4 - e^-2)
• 6. Critical points at -2,0,2. Local mins at -2, 2, local max at 0. Inflection points at plus/minus 2/SquareRoot(3). No asymptotes. As x goes to -infinity graph goes to infinity. As x goes to infinity graph also goes to infinity. Graph looks like a curvy W.
• 7. First draw the graph. To do geometric method, take the difference of the areas of two triangles. Either way, answer is 8.
• 8. 7/4. Integrate and use f(0) = 4 to find f exactly. Then find the global min of this function.

Outline of what we've covered since the first exam:

• Curve sketching -- finding asymptotes, intervals where function is increasing/decreasing, intervals where function is concave up/down, critical points, inflection points, local max/mins. Then using all this to sketch a reasonable picture of the graph of a function. (Section 4.3)
• Finding the global max and min of a function on an interval. The case of an interval with both its endpoints, such as [1,5], is a bit different from the case where the interval is missing one or more endpoints, such as (1,5] or (1, infinity). Loosely, the global max and min will occur either at critical points or at endpoints of the interval. (Section 4.4)
• Word problems involving optimization. Translate a word problem into a problem about finding the global max or min of a specific function. Then apply what we did in 4.4. (Section 4.5)
• Indefinite integrals. This is another name for the collection of all antiderivatives of a function. We saw how to find the indefinite integral for polynomials and exponential functions (Section 5.1) and how to use u-substitution (Section 5.2), integration by parts, and partial fractions (Section 5.3) to integrate more complicated functions.
• We also saw the Fundamental Theorem of Calculus, which says that to find the area under a curve (called the definite integral) on an interval, you need to find the indefinite integral and evaluate it at the endpoints of the interval. We did many examples of such computations. (Sections 5.4, 5.5)
• We then saw applications of definite integrals to marginal cost and revenue problems, finding the area between two curves, and computing the average value of a function on an interval (Sections 5.5, 5.6).

The first midterm will be a 90-minute exam, and will have about 7 problems.

To review for the first midterm, do problems! The exam questions will be similar to HW problems. There are good collections in the Review Problems sections of the chapters we've covered (1, 2, 3, first part of 4).

After you've done some review problems, another good way to review is to take one or more of the practice exams posted here. Two in particular you might try are Bolotin's Fall 2004 exam (it is a bit shorter than our exam will be) and Certain's Fall 2001 exam (a bit longer than our exam will be). I'd recommend treating them like you would an exam, especially if you are worried about time pressure: print them out, set aside 90 minutes in a quiet place, and see how many you can do. If you run into trouble, come talk to me or your TA. For solutions to Bolotin's Fall 2004 exam, click here.

Solutions to the first exam are here.

Welcome to the class!

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Textbook
	Himonas and Howard, Calculus: Ideas and Applications, 2nd ed., Prentice Hall.
This book is available for purchase at the University Bookstore and at the Underground Textbook Exchange, but you can compare new and used prices at several different online booksellers at CampusBooks4Less.com. Warning: If you choose to purchase the (optional) Student Solutions Manual, you may develop a syndrome known as over-reliance, which puts you at a high risk for over-confidence and, if left untreated, could result in severe exam underperformance. Use sparingly.

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TA Office hours:

Achilles Beros: Wednesday 2:25-3:30, Thursday 2:25-3:30, and by appointment

Nicos Georgios: Monday 1:20 - 2:20, Thursday 1:00- 2:15, and by appointment

Rohini Kumar: Tuesday 1:30-2:30, 1:00-2:00 Wednesday, and by appointment

Christine Lien: Tuesday 10:00-11:00, Thursday 10:00-11:00, and by appointment

Andrea Medini: Tuesday, Thursday 8:50-9:40, and by appointment

Getting Help

The first step should always be to see your TA or Dr. Jones during office hours. If you can't make our office hours, send an email to set up an appointment with one of us. You should also check out the following resources:

• Math Lab A free drop-in tutorial program in Van Vleck staffed by TAs and undergraduate tutors.
• Mathematics Tutorial Program A free small-group tutorial program in Van Vleck. Very structured, requires a time commitment by students.
• GUTS A free student-run program covering a variety of subjects. Staffed mostly by student volunteers.
• List of Private Math Tutors

Classlist
An email Classlist has been created for important announcements about this course. All students enrolled in the course are automatically added to the list. Your @wisc.edu or @students.wisc.edu email address is the one that will be used for the list, as well as for all other official communication from the University, so check your email frequently. If you are not enrolled in the course, but would like to be added to the list, please email Dr. Jones.

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^‡From Section VI.14 of the UW Madison College of Letters and Science Handbook: "The time of a two-hour block for a class and/or the due date for a take-home examination may be changed only with the prior approval of the associate dean for Student Academic Affairs. Such changes are rare. Where a student has more than two (that is, three or more) Summary Blocks scheduled within a period of 24 hours, the instructor may, within guidelines adopted by the College faculty, reschedule a final exam for that individual student to avoid hardship."

jones@math.wisc.edu