College of the Holy Cross Mathematics and Computer Science
College of the Holy Cross Mathematics and Computer Science
This course is an intensive section of MATH 132 (Calculus for the Physical and Life Sciences 2). We will use the same textbook and cover essentially the same material (chapters 6 - 10 of the text) as the regular sections of MATH 132. Both MATH 134 and MATH 132 form the second half of the first-year calculus sequence. Both are intended for students planning to major in mathematics or the sciences, or planning to enter the premedical program. 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 us 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.
This semester will be devoted mostly to techniques and applications of integration. We introduced the beginnings of this story at the end of the first semester. This semester we will study many additional ways to compute integrals of various functions and study 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:
See the course schedule below for a more detailed week-by-week breakdown of the semester.
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.
Come to class. Unless you are deathly ill, have a genuine family emergency, etc. plan on showing up here at 10:00 am every day 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 result 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. Even though MATH 134 meets 5 hours/week, 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.
Jodi Marani, class of '01 will be continuing as Teaching Assistant for this course. She will be attending class and helping to answer questions on some group discussion days, and grading the weekly problem sets. If there is interest, we may be able to set up some review sessions with Jodi outside of class time as well.
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 several quizzes and exams when the goal is to make sure you know how to do certain things "by hand". The TI-82 and similar models are sufficient. The TI-86 contains some calculus features, but we will be using a program called Maple in the PC lab for many of these things, so it is definitely not necessary to have such a powerful calculator. The TI-89, TI-92 and other calculators with symbolic computation features are definitely not necessary. Because over-dependence on calculators can hinder your learning of mathematics, these will never be allowed on quizzes and exams.
The text book for the course is the same as last semester -- Calculus, 2nd edition by Deborah Hughes-Hallett, Andrew Gleason, et al. See me as soon as possible if you do not have a copy.
Most weeks, we will be following a schedule something like this:
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.
Several times during the semester the class will meet in the Haberlin 408 PC laboratory for ``math lab'' classes. 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 (the developers of the program come from the University of Waterloo in Canada, which explains the name). We will use Maple to produce graphs of functions, calculate numerical approximations to integrals, and compute symbolic derivatives and integrals of functions. But 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, and finance. Being able to use them effectively is also a valuable skill to have!
Grading for the course will be based on
For all exams and quizzes, the topics to be covered and a list of practice problems will be given out well in advance of the date. The Thursday meetings of "exam weeks" will be used for review for the exam, since no problem sets will be due those weeks.
If you ever have a question about the grading policy or your standing in the course, don't hesitate to ask me.
The following is an approximate schedule. Some rearrangement, expansion, or contraction of topics may become necessary. I will announce any changes in class and here.
| Week | Dates | Class Topics | Reading (H-H, G, et. al.) |
|---|---|---|---|
| 1 | 1/16,17,18,19 | Review of definite integral, FTC | Chapter 3, 6.1 |
| 2 | 1/22,23,24,25,26 | Antiderivatives | 6.2,6.3,6.4 |
| Quiz 1 Friday | |||
| 3 | 1/29,30,31, 2/1,2 | Integrals by substitution | 7.1,7.2 |
| Quiz 2 Friday | |||
| 4 | 2/5,6,7,8,9 | Integrals by parts, tables | 7.3,7.4 |
| Quiz 3 Friday | |||
| 5 | 2/12,13,14,15,16 | Numerical integration, improper integrals | 7.5,7.7 |
| Exam 1 Friday | 6.1-6.4, 7.1-7.4 | ||
| 6 | 2/19,20,21,22,23 | Begin applications of integrals | 7.8, 8.1 |
| Quiz 4 Friday | |||
| 7 | 2/26,27,28,3/1,2 | Applications of integrals, cont. | 8.2,8.4 |
| Quiz 5 Friday | |||
| 3/5,6,7,8,9 | No class -- Spring Break | ||
| 8 | 3/12,13,14,15,16 | Applications to probability | Chapter 8 Focus on Modeling |
| Quiz 6 Friday | |||
| 9 | 3/19,20,21,22,23 | Taylor polynomials and series | 9.1,9.2 |
| Exam 2 Friday | 7.5, 7.7, 7.8, Chapter 8 | ||
| 10 | 3/26,27,28,29,30 | More on infinite series | 9.3, 9.4 |
| Quiz 7 Friday | |||
| 11 | 4/2,3,4,5,6 | Differential equations | 10.1,10.2 |
| Quiz 8 Friday | |||
| 12 | 4/9,10,11 | Differential Equations, cont. | 10.3,10.4 |
| No Quiz this week -- Easter Break | |||
| 13 | 4/16,17,18,19,20 | Growth and decay | 10.5,10.6 |
| Quiz 9 Friday | |||
| 14 | 4/23,24,25,26,27 | Population growth models | 3.4 |
| Exam 3 Friday | Chapters 9, 10 | ||
| 15 | 4/30 | Semester wrap-up |
The final exam for this course will be given Saturday, May 5 at 8:30am in the regular classroom.