Holy Cross Mathematics and Computer Science
Calculus for the Physical and Life Sciences 1 (MATH 131) is the recommended starting mathematics course at Holy Cross for students who have not taken calculus in high school, and who plan on majoring in mathematics, chemistry, physics, biology, or pursuing the premedical concentration. There is another beginning calculus course called Calculus for the Social Sciences 1 (MATH 125) which is designed for students majoring in Economics and the other social sciences. It is not possible to get credit for both this course and MATH 125 (or MATH 133, see below). MATH 125 is also frequently taken by students who simply want to fulfill part of the Science and Mathematics Common Area Requirement.
MATH 131 is a beginning calculus course and does not assume any prior exposure to this area of mathematics. If you have taken a year of calculus in high school and did reasonably well (a B or better), then this course will be almost entirely review for you. Consider starting in the one-semester MATH 136 (Advanced Placement Calculus) course if this is your situation. Students who have taken calculus before, even those who did not take the Calculus AP examination, or if you scored a 3 or lower on it, usually find that MATH 136 is a better starting point. Successful completion of MATH 136 alone also satisfies the mathematics requirement for the Biology and Economics majors.
The department also offers one ``intensive'' section of MATH 131 (called MATH 133) for students who plan on majoring mathematics, chemistry, physics, biology, or who are considering the premedical concentration, but whose high school mathematics preparation might not be as strong. That course meets five days a week rather than four and gives more opportunity for hands-on practice and review in class.
If you have any questions about which calculus class is right for you, please feel free to consult with me, or with any other member of the mathematics department.
Calculus is the mathematics of change. First developed in the 17th century, it has been a major part of mathematics since that time. Calculus is important because it is the basis for a major portion of the science and technology that shape the contemporary world. Many of the techniques used to study motion of objects in physics, kinetics of chemical reactions, growth or decline of populations of organisms in biology, growth of national economies, and many other phenomena in the real world involve calculus. Although it might sound like an exaggeration now to say it, calculus is also one of the crowning achievements of the human intellect. You are in for an exciting journey of exploration as you learn it!
Two men, Isaac Newton and Gottfried Leibniz, are given most of the credit for developing the calculus. Their contribution was primarily explaining the relation between finding the rate of change of a function (the derivative) and computing the "total accumulation" of a function over an interval (the definite integral). We will conclude this semester by studying their big result -- the Fundamental Theorem of Calculus.
The topics to be covered this semester are:
See the course schedule below for a more detailed week-by-week breakdown of the semester. This course continues to MATH 132 (Calculus for the Physical and Life Sciences 2) in the spring semester.
The primary text book for the course is Calculus, 3rd edition by Deborah Hughes-Hallett, Andrew Gleason, et al. (available in the H.C. bookstore, and elsewhere). The book comes "bundled" with a student study guide. We think you will find reading and studying this book to be challenging, but ultimately very rewarding.
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 when that seems appropriate.
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 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!
Use the textbook and study guide actively. Don't just use them 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. If necessary, make a list of questions to ask in office hours or at the next class. Another 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 -- that process is the real point, and that's what you should take away from studying the example.
Take notes and use them. This may seem obvious, but in my experience too many students seem to copy down everything on the board diligently, 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. Indeed, one technique that many students find helpful is to recopy the class notes, filling in details that might have been clear the first time, putting in extra examples, explanations or ideas that really helped them understand the material, and so forth.
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 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), 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.
Grading for the course will be 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 and on the course homepage.
Week | Dates | Class Topics | Reading (H-H, G, McC, et. al.) |
---|---|---|---|
1 | 9/1,3 | Course Introduction, Linear and Exponential Functions | 1.1-1.2 |
2 | 9/6,7,8,10 | New Functions from Old, Logarithms, Trig Functions | 1.3-1.5 |
Algebra Diagnostic Quiz Tuesday | |||
3 | 9/13,14,15,17 | Polynomials and Rational Functions, Continuity | 1.6-1.7 |
4 | 9/20,21,22,24 | Rates of Change and Limits | 2.1-2.3 |
Exam I -- Wednesday evening this week | Chapter 1 | ||
5 | 9/27,28,29,10/1 | The Derivative and Its Meaning | 2.4-6 |
6 | 10/4,5,6,8 | Continuity and Differentiability, Derivatives of Powers, Polynomials, Exponentials | 2.7, 3.1-3.2 |
7 | 13,15 | Product and Quotient Rules | 3.3 |
No class Monday and Tuesday -- Columbus Day break | |||
8 | 10/18,19,20,22 | Chain Rule, Trigonometric Derivatives, Inverse Functions | 3.4-6 |
9 | 10/25,26,27,29 | Applications, Implicit Functions, Parametric Curves | 3.6-3.8 |
Exam II -- Thursday evening this week | Chapter 2, 3.1-3.5 | ||
10 | 11/1,2,3,5 | Linear Approximation, L'Hopital's Rule | 3.9-3.10 |
11 | 11/8,9,10,12 | First and second derivative tests | 4.1-4.3 |
12 | 11/15,16,17,19 | Optimization and Modeling | 4.5 |
13 | 11/22,23 | The definite integral | 5.1-2 |
No Class Wednesday, Thursday, and Friday -- | |||
Thanksgiving break | |||
14 | 11/29,30,12/1,3 | The Fundamental Theorem of Calculus | 5.3-5.4 |
Exam III -- Wednesday evening this week | Sections 3.6-3.10, Chapter 4, 5.1-5.2 | ||
15 | 12/6,7 | Semester wrap-up |
A more detailed day-by-day schedule is posted on the course homepage.
The final exam for this course will be given Monday, December 13 at 2:30 p.m.