College of the Holy Cross Mathematics and Computer Science
College of the Holy Cross Mathematics and Computer Science
Calculus for the Social Sciences 2 is the second semester of the calculus sequence designed for Economics majors and minors and Economics/Accounting majors. Many other non-science majors who wish to continue their study of mathematics or who want to satisfy one portion of the Natural Science/Mathematics common area requirement also take this course. The fall sections of this course are intended for students who have studied calculus in high school (usually for a year), but who have not seen the topics described below. In most cases, students taking this course will not take further mathematics courses at Holy Cross.
Calculus is the mathematics of change. First developed in the 17th century, it has been at the center of mathematics and natural science ever since. Calculus is the basis for a major portion of the science and technology that shape the contemporary world. More recently, the mathematical tools provided by calculus have been applied to study problems from the social and managerial sciences as well.
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 begin 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 day-by-day timetable for 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 2:00 pm every Monday, 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 result of an example is often secondary to the process used in obtaining the result. Be sure you can carry out the process yourself on similar examples before moving on.
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 expect to budget at least 6-9 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 course. However a calculator will not be required and you will not be allowed to use one on exams when the goal is to make sure you know how to do certain things "by hand". The TI-83 and similar models are sufficient. The TI-86 contains some calculus features, but 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 exams.
The text book for the course is Applied Calculus, 5th edition by S.T. Tan (available in the H.C. bookstore). Please feel free to let me know whether or not you find this book helpful to study.
Most of the class meetings will be structured as lecture/discussions, with plenty of opportunities for you to ask questions if something is not clear. I will present new material, work through examples, and ask you questions as we go along to see how well you are grasping the material and to keep you involved. I will expect everyone to participate, and I may call on you by name if the class is unresponsive.
In order for students to get as much as possible out of a course, regular active participation and engagement with the ideas are necessary. 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, knowing how to work effectively in a group is also a valuable skill because almost all jobs involve this kind of work.
So with these points in mind, several times 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.
Grading for the course will be based on
For all exams, the topics to be covered and a list of practice problems will be given out well in advance of the date.
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.
| Date | Class Topic | Reading (Tan) |
|---|---|---|
| 8/29 | Review of functions | 2.1-2.5 |
| 8/31 | Review of derivatives | 2.6,3.1-3.3 |
| 9/3 | Exponential and logarithm functions | 5.1-5.5 |
| 9/5 | Antiderivatives | 6.1 |
| 9/7 | Antiderivatives by substitution | 6.2 |
| 9/10 | More on substitution | 6.2 |
| 9/12 | Area and the definite integral | 6.3 |
| 9/14 | The Fundamental Theorem of Calculus | 6.4 |
| 9/17 | More on the FTC | 6.4 |
| 9/19 | Evaluating integrals | 6.5 |
| 9/21 | Finding areas | 6.5 |
| 9/24 | Areas between curves | 6.6 |
| 9/26 | Economic applications | 6.7 |
| 9/28 | Exam I | Chapter 6, sections 1 - 5 |
| 10/1 | Integration by parts | 7.1 |
| 10/3 | More on integrals by parts | 7.1 |
| 10/5 | Integration by tables | 7.2 |
| 10/8 | No Class - Columbus Day Recess | 7.3 |
| 10/10 | Numerical integration | 7.3 |
| 10/12 | Improper integrals | 7.4 |
| 10/15 | Differential equations | 9.1 |
| 10/17 | Separation of variables | 9.2 |
| 10/19 | Applications | 9.3 |
| 10/22 | Euler's method | 9.4 |
| 10/24 | Begin Probability | 10.1 |
| 10/26 | Exam II | 6.6-6.7, Chapters 7, 9 |
| 10/29 | Probability density functions | 10.1 |
| 10/31 | The cumulative distribution function | class notes |
| 11/2 | Expected value, standard deviation | 10.2 |
| 11/5 | The normal distribution | 10.3 |
| 11/7 | Cartesian coordinates in space | 8.1 |
| 11/9 | Functions of several variables | 8.1 |
| 11/12 | Partial derivatives | 8.2 |
| 11/14 | More on partial derivatives | 8.2 |
| 11/16 | Maxima and minima for functions of several variables | 8.3 |
| 11/19 | More on Max/Min | 8.3 |
| 11/21,23 | No Class - Thanksgiving Recess | 8.4 |
| 11/26 | Constrained Max/Min and Lagrange Multipliers | 8.4 |
| 11/28 | More on Lagrange Multipliers | 8.4 |
| 11/30 | Exam III | Chapter 10, 8.1-8.3 |
| 12/3 | Semester wrap-up |
The final exam for this course will be given Friday, December 7, 2001 at 8:30 a.m. in the regular classroom.