Math 2260: Integral Calculus

Math 2260 is an intensive integral calculus course aimed at physical science and engineering majors (though you do not have be a science or engineering major to enroll for the course). The course follows the intensive differential calculus course Math 2250, which ends with a unit on integration. The 2260 course assumes a basic knowledge of integration and teaches applications of integration, advanced techniques in integration, sequences and series leading to Taylor’s theorem and Taylor approximation, and vector geometry. The course prepares students for the multivariable calculus course Math 2270.

Class Structure

This class is a fairly conventional lecture-based calculus class, with lots of in-class interaction. There are reading assignments every night before the corresponding lecture, with a quiz at the start of class to test your reading comprehension. During class, we’ll try to minimize lecture and spend most of the time in discussion, talking about proofs and problems. There will be some in-class demonstrations based on video games. The spirit of the class is that this should be an applied calculus class, so we’ll try to point out specific and realistic applications of the material we’re learning as we go.

We will use the spaced repetition software called Anki to aid in memorizing course material. We’ll have regular quizzes on the memorization material. Mathematica is an important part of the course, and we’ll learn to use it as we go.

Grading

There will be two in-class exams and an in-class final. Grades will be assigned according to the weights:

  • 30% for each in-class exam (60% for both in-class exams)
  • 30% for the final exam
  • 10% for the WebWork and other written homework, including in-class quizzes

 

Exams

  • The first exam will be in class on Tuesday, February 28.
  • The exam covers all course material from the start of the course through Section 8.4. This includes the Anki decks “Math 2250 Review Deck”, “Math 2250 Integration Review”, “Math 2260 Chapter 6”, and “Math 2250 Chapter 8”. You are expected to have all the material in the Anki decks memorized (you won’t need to have anything else memorized).
  • You are required to bring a TI-30Xa calculator. Only this calculator will be allowed– you can’t use a TI-30Xs calculator or a graphing calculator. (Why? Making sure that everybody has the same calculator ensures that the test is fair for all students.)
  • All the exams I’ve given in this class in the last few years are available below. They may not cover exactly the same material as this year’s class, so material may be added or missing. There are no answer keys available, but you can use Mathematica or Wolfram|Alpha to check answers.
  •  Extra practice problems are open in Webwork in the Chapter 8, 9, and 11 Review assignments. These do not count for course credit.

Additional Electronic Resources

  1. The 2260 syllabusThis includes the dates of in-class quizzes.
  2. We will use a very wonderful and powerful program called Mathematica for a lot of demonstrations in class. Since you are enrolled in a math department class at UGA, you can get a free copy of the system to install on your own computer. I encourage you to do so!
  3. The course will use the WebWork online homework system. The course homework is found here. Your username comes from your UGAmail address, without the @uga.edu. So if your full email address is jbfrink@uga.edu, your WebWork username is jbfrink. Your password is your 810 number, as in 810123456. (It doesn’t include the trailing 0 in your 810 number.) You may encounter a browser error when you first visit the site, since our security certificate is not standard. It is ok to create an exception (in Firefox) or continue to site in Safari or Explorer. If you have trouble with this, please email help (at) math.uga.edu.
  4. We are going to use Anki to help us memorize some required material in the course. You need to download and install the software (it runs on Windows, Mac, Linux, Android, iPhone/iPod/iPad, and as a web-based application).
    1. First, download and install the Anki application itself.
    2. To import our decks, download the files below under Anki Decks and just double-click them.
  5. You will also probably want to experiment with Wolfram|Alpha , which is one of the truly great web resources for calculus.
  6. The book for the class is University Calculus, 3rd Edition, by Hass/Weir/Thomas.

Tutoring and Help Resources

Here is a list of resources for in-person help with the course material. These usually start on the second week of class.

  • Milledge Hall Drop-In Math Lab, Monday-Thursday 9am-5pm, Friday 9am-3pm.
  • Miller Learning Center, Room 368, Monday-Thursday 5:30pm-8:30pm.
  • Residence Hall Tutoring:
    1. Creswell Tutoring Room, Tuesdays, 7-10 pm.
    2. Russell Academic Center, Wednesdays, 7-10 pm.
    3. Brumby Conference Room, Thursdays, 7-10 pm.
  • Math Department Study Halls for Calculus, Room 222 Boyd, Monday-Thursday, 3:30-5:30pm.

Online course materials

  1. Anki Decks
    1. Math 2250 Review Deck
    2. Math 2250 Integration Review Deck
    3. Math 2260 Chapter 6 (Volume, Length, Area, Work) Deck
    4. Math 2260 Chapter 8 (Methods of Integration) Deck
    5. Math 2260 Chapter 9 (Sequences and Series) Deck
    6. Math 2260 Chapter 11 (Vectors and 3-space) Deck
  2. Lecture Notes
    1. Leibniz’s rule and the Fundamental Theorem
    2. 6.1 Volumes Using Cross-Sections
      1. Cavaleri’s Principle
      2. Solids of Revolution
      3. The Disk Method
  3. Practice Exams (no answer keys are available)
    1. First Exam Practice exams: 2005 2008 2013 2014 2015
    2. Second Exam Practice Materials (note– in 2008 and 2013, there were second AND third exams, so there are two exams for those years. In 2014 and 2015, there were only two exams.): List of trig identities Second midterm – 2007 2008-exam2 2008-exam3 2008-exam3b 2013-exam2 2013-exam3 2014 2015
    3. Practice Final Exams: 2013 2014 2015

Extra Credit: Alien Transmission.

The Tianyan radio telescope has received the following transmission.

96.1741, 20.3232, 0.543304, -32.2365, -55.5497, -50.0304, 21.0749,
28.7167, 22.8129, 35.5173, -27.6258, -11.5729, -15.8748, 15.3707,
11.3898, 26.7944, -35.6387, -21.792, -31.1044, -21.0123, 49.3058,
57.0969, 30.911, 0.100835, -19.7368, -97.054, -20.4117, 0.322845,
33.5693, 55.626, 48.6566, -22.3221, -28.5015, -23.0762, -37.0245,
25.8299, 12.0382, 13.2415, -15.4737, -11.1378, -27.5722, 36.1396,
21.9993, 28.5888, 21.258, -50.628, -56.3445, -30.8415, -0.421183,
20.7936, 94.4889, 21.1093, -0.896344, -32.2773, -55.7553, -49.4907,
22.7213, 30.33, 21.7112, 34.5471, -27.162, -11.9808, -14.3359,
16.2101, 10.8822, 26.8948, -36.1968, -23.6995, -29.108, -20.5085,
49.307, 55.5499, 31.5086, 1.65201, -19.7195, -95.6592, -21.3999,
0.339683, 31.4061, 56.6666, 51.5773, -21.0144, -30.6115, -21.7146,
-34.4277, 27.3113, 10.8639, 16.8377, -13.4488, -12.4366, -27.6268,
35.0747, 23.3858, 29.0657, 22.3302, -49.585, -54.7323, -31.0332,
-0.515375, 21.4669, 95.5698

Recently declassified evidence suggests that this transmission originates with a powerful alien civilization. We believe that the aliens were transmitting the signal

f(t) = a Cos[5t] + b Cos[9t] + c Cos[19t].

where a, b, and c are integers. However, the signal has been corrupted by the addition of random interstellar radio noise Noise(t) so that the numbers we have are samples of the signal

f(t) + Noise(t)

at times a = x_0 = 0, x_1 = h, x_2= 2h, … , x_100 = 12 Pi. We suspect that the aliens have chosen to encode a message to the people of earth using the numbers a, b, and c. Find those numbers!

Here’s a way to think about how to proceed– the sample data is enough to compute the integral of the signal using the trapezoid rule or Simpson’s rule. What might be less obvious is that you also have enough information to compute the integral of

g(t) * (f(t) + Noise(t))

over the interval [0,12pi] for any g(t) that you pick (after all, you can always evaluate g(t) at the data points yourself, and then multiply those values by the data above). So the real question is “how can you strategically choose test functions g(t) to isolate a, b, and c?”. You might consider functions of the form g(t) = Cos[K t] for various integers K. What happens if K is 5, 9, or 19? What happens if K is something else?

Bonus: There is an internet rumor that two MORE numbers are encoded in the message by functions of the form Cos[L t] and Cos[M t] for some L and M. But nobody knows L and M! Can you find them?