2008 June 11 / E-Mail Me

Introduction To Calculus

Carleton College Math 111, Spring 2008, Prof. Joshua R. Davis


This is a first course in calculus, focusing on the basic concepts of limit, derivative, and integral. Applications to the natural and social sciences are woven throughout. We also expend significant effort on writing mathematics well. The class is aimed at students with a firm grasp of high-school algebra and geometry but no experience in calculus. That said, we move fast. You can expect to spend at least 10 hours per week on this course outside class. The basic materials are

Our class meets in CMC 209 during period 1A (MW 08:30AM-09:40AM, F 08:30AM-09:30AM). Here's how you get in contact with me:

Dr. Joshua R. Davis (call me Josh if you like)
E-mail: See here
Office: CMC 221, x4366
Office hours: Mon 1:40-2:40, Wed 3:30-4:30, Thu 8:30-9:30, and Thu 1:10-2:10. You can also make an appointment; simply pick a free time from my weekly schedule and e-mail me. You can also talk to me after class.


Final grades (A, B, C, etc.) are assigned according to an approximate curving process. By this I mean that there are no predetermined percentages (90%, 80%, 70%, etc.) required for specific grades. The following elements contribute to the final grade.

Notice that you are allowed to use a "note sheet" on each exam. By this I mean a single, standard-size (8.5 by 11 inches) sheet of paper, on which you may record whatever notes you like, on both sides. The notes must be your own creation; using a sheet of notes created by another student is prohibited. I recommend you create a new note sheet for each exam; it's helpful for studying.


You are encouraged to work with others on all assignments. Work together to figure out the problems, and then write them up separately, in your own words. You may not copy someone else's work or allow them to copy yours.

Homework is graded for correctness and for presentation. Depending on time constraints, perhaps only a subset of the work is graded; in order to ensure full credit, do all of the assigned problems. Make your paper easy to grade. The problems must be answered in the order they were assigned. Do not write them in multiple columns; just use one column, going down the page. Clearly write each problem's number on the left side of the page. If your paper is messy or disorganized from revisions or erasures, then you may need to recopy it. Staple each week's assignment into a single packet.

How much work should you show? The answer is simple: Write your solutions as if the intended audience is your fellow students. By doing so, you show enough detail that your grader can ascertain whether you yourself understand the material. Your solutions should also be self-explanatory; the grader should not have to refer to the book, to determine whether your solution is correct. In short, if a classmate were to read one of your solutions, then she or he should be able to understand what the problem was and how you solved it.

In order to help you develop your math writing skill, I have designed a sequence of short writing assignments that we will complete throughout the term. They are not intended to be difficult.

  1. An Equation Is A Statement (due on Day 2)
  2. A String Of Equations Is A String Of Statements (due on Day 5)
  3. The Arrow "=>" Indicates That One Equation Implies Another (due on day 8)
  4. Make Your Solutions Self-Explanatory (due on day 13)
I have also made a short Writing Sample that incorporates the lessons of all of the writing assignments. You should try to mimic its style. For more examples of good style, simply read your math book. (The only caveat there is that Stewart doesn't always end sentences in punctuation. We always do.)

Special Accommodations

During the term, you have one free pass to hand in an assignment late. Here is how you activate it. Instead of handing in your assignment, send me e-mail declaring that you are using your late pass and proposing a new due date. If the due date is extended only a couple of days, then no explanation is necessary; if you need longer, then convince me. Use your free pass wisely. Otherwise, no late assignments are accepted, except in extreme circumstances that are truly beyond the student's control.

If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class, so that we can make arrangements. You may want to visit the dean's Disability Services/Resources page first.


Frequently I am asked, "How should I study for this course? What do you recommend?" I have compiled my answers into

Here are the exams we've taken so far. Certainly you should review them for later exams.

Here are my Math 111 exams from winter term. Our schedule this term is similar but not identical. Exam 1 has no material from 5.1, but ours will. Exam 2 has material from 5.2 (#5), but ours will not.

Here are my Math 111 exams from fall term. Our schedule this term is somewhat different, so the exams come with some warnings. On Exam 1, ignore #6, and study #1B, #7, #8 for our Exam 2, not our Exam 1.

Differentating functions is a basic skill that you are expected to master in this course. To help you, I have constructed a web page that gives you as many differentiation problems as you want:

Several years ago I compiled these brief reviews of basic topics. Some you already know; we study the others in this course. They are much too terse to learn from, but perhaps they can refresh your memory or point out key concepts.


I want all of my students to work hard, learn a lot of math, and earn a good grade. Here are my recommendations:

Each term I asked my students, "What advice would you give to future students in this course?" The overwhelming top two responses are versions of

  1. "Don't procrastinate on homework until the night before it's due. Do it right away."
  2. "Always read the book before class."