College of the Holy Cross Mathematics and Computer Science
College of the Holy Cross Mathematics and Computer Science
MATH 132 is the second half of the first-year calculus sequence intended for students planning to major in mathematics or the sciences, or planning to enter the premedical program. Only students who have taken MATH 131 at Holy Cross or an equivalent course elsewhere should be enrolled in this class. There is also an intensive section of MATH 132 called MATH 134 (Intensive Calculus) that some of you may want to consider. The most obvious difference between MATH 132 and MATH 134 is that Intensive Calculus meets 5 days a week rather than 4. The extra hour allows you to spend a little more time on difficult topics, to review precalculus topics as necessary, to spend more time discussing homework problems, and to work on problems in groups. It is designed for those who feel that they could benefit from the extra class time and those whose backgrounds in mathematics may not be as strong.
This semester will be devoted mostly to techniques and applications of integration. We will study many ways to compute integrals of various functions and applications of integration to problems such as computing volumes and centers of mass of certain solids, probabilities, solving differential equations and others.
The topics to be covered this semester are:
A week-by-week schedule may be found at the end of this syllabus, and a more detailed day-by-day breakdown of the semester is posted on the course homepage. Any modifications will be announced in class and on the course homepage.
The following is the same advice as in the syllabus for the first semester of the class, but it bears repeating!
A good "work ethic" is key. You do not need to be a "math genius" to master this material and do well. But you will need to put in a consistent effort and keep up with the course. (Note: This is especially true if you found the material in the first semester to be largely review. We will be studying a significant amount of material this semester that you will probably not have seen previously.)
Come to class. Unless you are deathly ill, have a genuine family emergency, etc. plan on showing up here at 8:00 am every Monday, Tuesday, Wednesday, and Friday this semester. If attending class wasn't important, all college courses would be by correspondence, and your tuition would be much lower!
Read the textbook. Don't just use it to look for worked problems similar to ones on the problem sets. You will find alternate explanations of concepts that may help you past a "block" in your understanding. Reading a math book is not like reading a novel, though. You will need to read very carefully, with pencil and paper in hand, working through examples in detail and taking notes. Make a list of questions to ask in office hours or at the next class. One thing to bear in mind while reading your text is that the answer at the end of an example is often secondary to the process used in obtaining the result.
Take notes and use them. This may seem obvious, but in my experience too many students diligently copy down everything on the board, and then never look at their notes again. Used intelligently, your notes can be a valuable resource as you work on problem sets and prepare for exams.
Set up a regular study schedule and work at a steady pace. It's not easy to play catch-up in a mathematics course, since every day builds on the previous one. You should still expect to budget at least 6 hours in a typical week for work outside of class. The best way to use your time is to do a few problems, a little reading from the book, and reviewing of class notes every day.
Most importantly, if you are having difficulty learning something, get help as soon as possible. You can do this by asking questions during class (any time something isn't clear, but especially in the Thursday problem sessions), seeing me during office hours, or attending the Calculus Workshop in the evenings Sunday-Thursday.
It is certainly true that a decent graphing calculator is a good investment for this and your other science courses. However a calculator will not be required and you will not be allowed to use one on exams where the goal is to make sure you know how to do certain things "by hand". The department has a supply of "basic" (i.e. non-graphing) calculators that will be provided for your use on exams when some ``number-crunching'' may be required.
The text book for the course is the same as last semester -- Calculus, 3nd edition by Deborah Hughes-Hallett, Andrew Gleason, et al. See me as soon as possible if you do not have a copy.
In order for students to get as much as possible out of this or any course, regular active participation and engagement with the ideas we discuss are necessary. And working through questions in a group setting is a good way to develop a deeper understanding of the mathematics involved, if you approach the enterprise as a truly collaborative effort. That means asking questions of your fellow students when you do not understand something they say or think they do see, and being willing to explain your own ideas carefully when you see something that someone else does not. Looking to the future as well, working effectively in a group is also a valuable skill to have.
So with these points in mind, regularly throughout the semester the class will break down into groups of 3 or 4 students for one or more days, and each group will work individually for most of those class periods on a group discussion exercise. I will be responsible for designing and preparing these exercises, and I will be available for questions and other help during these periods. At the conclusion of each discussion, the class as a whole may reconvene to talk about what has been done, to sum up the results, to hear short oral reports from each group, etc. Each group will keep a written record of their observations, results, questions, etc. which will be handed in. I will make copies of these, and return them with comments, for all members of the group.
Regularly during the semester the class will meet in the Haberlin 408 PC laboratory for ``math lab'' classes. Each of these sessions will lead to a lab writeup assignment. (The due date will be announced when the assignment is given out.) We will be using an excellent, extremely powerful, general-purpose mathematical software system called Maple. We will use Maple to produce graphs of functions, calculate numerical approximations to integrals, and compute symbolic derivatives and integrals of functions. In fact Maple is so powerful that we will be using only a small fraction of what it can do. If you take additional mathematics courses at Holy Cross, you will probably use many other features of this same program. And programs like this are now a standard tool in many areas of science, engineering, even finance. Being able to use them effectively is also a valuable skill to have!
The other meetings of the class will be structured as lectures. I will try to provide plenty of opportunities to ask questions in class. I will also regularly call on students in the class to answer questions as we move through the day's lesson so that everyone stays involved.
Grading for the course will be the same as last semester, based on:
The following is an approximate schedule. Some rearrangement, expansion, or contraction of topics may become necessary. I will announce any changes in class, on the course homepage, and here.
| Week | Dates | Class Topics | Reading (H-H, G, et. al.) |
|---|---|---|---|
| 1 | 1/19,21 | Review of the definite integral | Chapter 5 |
| 2 | 1/24,25,26,28 | Antiderivatives | 6.1, 6.2, 6.3 |
| 3 | 1/31,2/1,2,4 | More on antiderivatives, begin methods of integration | 6.4, 7.1, 7.2 |
| 4 | 2/7,8,9,11 | More on methods of integration | 7.2, 7.3, 7.4 |
| 5 | 2/14,15,16,18 | Partial Fractions, Trigonometric Substitution | 7.4 |
| 6 | 2/21,22,23,25 | Numerical integration, "improper" integrals | 7.5, 7.6, 7.7 |
| Exam 1 Wednesday, 2/23 | |||
| 7 | 2/28,3/1,2,4 | More on "improper" integrals, begin applications to volumes | 7.8, 8.1, 8.2 |
| 3/7,8,9,11 | No class -- Spring Break | ||
| 8 | 3/14,15,16,18 | Arc length, density, center of mass | 8.2, 8.3 |
| 9 | 3/21,22,23 | Probability | 8.6, 8.7 |
| 3/25,28 | No class -- Easter Break | ||
| 10 | 3/29,30,4/1 | Geometric series | 9.1 |
| Exam 2 Thursday, 3/31 | |||
| 11 | 4/4,5,6,8 | Convergence of infinite series | 9.2, 9.3 |
| 12 | 4/11,12,13,15 | Power series, Taylor polynomials and series | 9.4, 10.1, 10.2 |
| 13 | 4/18,19,20,22 | Error in Taylor approximation, begin differential equations | 10.3, 10.4, 11.1, 11.2 |
| 14 | 4/25,26,27,30 | Differential equations | 11.3, 11.4, 11.5 |
| Exam 3 Wednesday, 4/27 | |||
| 15 | 5/2,3 | Modeling with Differential equations | 11.7 |
The final exam for this course will be given Tuesday, May 10 at 2:30pm, in the regular classroom.