Applied Calc 1 Spring 2012  Course Information in Detail

This sheet provides additional information to supplement what appears on the one page course information sheet.

Course Overview and Learning Objectives

Calculus involves a collection of concepts and techniques for analyzing the behavior of real functions.  Traditionally, a first course in calculus put a significant emphasis on mastering the techniques --  so that  a student's primary  goal was to learn a  set of procedures applicable to solve certain kinds of problems.  Modern computer resources make this sort of procedural mastery much less important than it once was.  Computer programs and websites can carry out the procedures of calculus instantly and essentially flawlessly.  These resources are much more reliable than hand calculation. 

If mastering the procedures of calculus is no longer to be the primary focus, what should calculus students focus on?  The most important objective is to develop an understanding of and familiarity with the major concepts of calculus: derivatives, integrals, limits, continuous functions.  These have multiple representations, in terms of formal definitions, informal conceptualizations, algebraic, numeric, and pictorial properties.  At the end of the course you should have a comfortable command of all of these variations.  This will provide a background for understanding and critically examining applications of calculus to other other fields, such as economics, biology, environmental science, etc.  In Applied Calculus the emphasis will be on acquiring the background that makes this kind of understanding possible.

The second main objective is to learn how and when to apply the methods of calculus to answer questions about functions.  Calculus provides a set of analytical tools, and you are supposed to learn which tools can be applied in what contexts.  Part of this is being able to interpret the results of using calculus methods.  It will also be important to know the correct statements of definitions and theorems.  These represent the factual knowledge base of calculus, and at the end of the course you should be able to demonstrate a technically correct knowledge of this factual knowledge.

Finally, you should have an understanding of the logical structure of calculus.  In mathematics, we only accept two forms of truth: Definitions and conditions that are assumed to be true, and theorems that can be logically proved  to be true.  We need instances of the first kind of knowledge as a starting point for analysis.  Then, once we have explicitly stated our starting assumptions, we discover conclusions that are logical consequences  of the assumptions.  The prior learning objective indicates that at the end of the course you should know the importatnt statements of assumptions (definitions) and derived conclusions (theorems).  In addition you should understand how these fit together into the logical structure of the subject.  You should also understand and be able to reproduce the proofs of some of the main theorems.

Tentative Schedule

This web site includes a very tentative schedule for what topics will be considered at each class meeting. It is to be expected that we may deviate from the schedule, spending more time on some subjects and less time on others. However, we should cover all the material listed by the end of the course. As a general rule, once a section of the text has been discussed in class the first time, the homework problems assigned for that section should be completed by the following class meeting. Even if no specific assignment is announced in class, you will be expected to work on the appropriate problems. See the additional comments below about Homework.

Grades

As stated on the one page course information sheet, grades will be based on three in-class exams (20% each), a final exam (20%) and class participation, homework, and quizzes (20%). This last category is optional, and cannot lower your exam average. Here is how it works. During the semester, you are expected to keep a portfolio as detailed below. It will contain completed homework assignments, quizzes and exams, and corrections for quizzes and exams. The portfolio will be handed in at the time of the final exam, and I will review it before determining a subjective grade for both the portfolio and class participation. If this grade is lower than your exam average, (or if you do not turn in a portfolio), it will NOT be counted as part of your grade. If the subjective grade is higher than your exam average, it will be included in your grade, with a weight of 20%. If you elect not to turn in a portfolio, your grade will be based on the average of your four exam scores, equally weighted.

If you are forced to miss an in-class exam for reasons beyond your control (such as an illness, family emergency, etc.), a makeup may be arranged, but ONLY if I am informed in advance. I will NOT approve requests to reschedule an exam for reasons of convenience. For example, if you plan to travel during a school break and leave early or return late, that is not a valid reason to reschedule an exam. Similarly, avoidable conflicts for recreational, entertainment, social, or work activities are generally not valid reasons to miss an exam. The exam dates are listed on the overview webpage. Be sure to plan other activities around them.  Note in particular that we have an exam on the Thursday before Spring Break, so make travel plans with that in mind.

Attendance in this course is not required; I will not keep track of days you miss class. However, you are responsible for anything presented in class, including announced schedule changes, modifications to assignments, and material that supplements what is in the text. Note also that the class work component of your grade will depend on regular participation in class activities. If you elect to skip these activities, your final grade will be based almost completely on your exam average.

Homework

Generally, you are expected to hand in homework at each Monday and Thursday. Homework assignments will be posted on the internet, and additions or modifications will be announced in class. For each assignment there are two due dates, one for you to ask questions and a second when papers will be collected.  You should complete as much of the homework as you can by the first due date, so that you can identify any questions you have about the problems.  Then, using what you learn in that discussion, you can correct, complete, or extend your solutions in time to be collected on the second due date.  Unless instructed otherwise, assume that the first homework due date for each section of the text will be the class meeting following the first time that section is discussed in class.  The second due date will be the first Monday or Thursday class after the first due date.

For most people, learning mathematics involves two stages: understanding and retention. At first, doing the exercises will help you to understand the ideas. But it is not enough to understand - when it comes to the exam you will also have to remember. That requires practice and drill, even after you understand the concepts involved. The homework assignments are intended to serve as a guide, and they should be modified to suit your personal needs. If you find that you need more drill and practice to remember important ideas and procedures, then do not limit yourself to the homework that will be collected. On the other hand, you may wish to do less than the assigned amount of drill and practice if you learn and retain the material quickly.

In some cases you may not complete an entire assignment, either because you do not understand all of the questions, or because you run out of time. In all cases, hand in as much of the assignment as you have completed when it is collected in class.

If you get stuck on an exercise, DO NOT SPEND HOURS SPINNING YOUR WHEELS!!! Sometimes a few short minutes with a classmate, tutor or with me can get you back on track again. This can even be done over the phone. Please feel free to call me in my office if you have a question. In any case, DO NOT LET IT SLIDE. Get the help you need right away, so you don't fall behind. Working with another person, or in a group, can be very helpful in this regard.

Although you are encouraged to work with others, you are expected to work actively on the problems. Do not let someone else do all the work, or just copy their answers. This will not contribute to your understanding, and will result in poor exam grades. Remember, handing in assignments is not an end in itself. The assignments are there to help you learn the material.  In any case, copying another student's solution to any homework problem, or allowing someone to copy any of your solutions, is not permitted and will be considered a violation of the academic integrity rules (ie, a form of cheating).  This can have serious consequences.  Be sure you have reviewed the University's Academic Integrity code, available at http://www1.american.edu/academics/integrity/index.htm.

Homework Format
Homework should be written neatly on lined binder paper. Leave a wide margin on the left side of the page -- close to half the page width, so that there is room to write comments. Be sure that the work is written neatly. Do not put multiple problems side by side. Please also indicate clearly at the top of the page the section of the text for the problem set, something like this: Section 2.3. And did I mention that I would like the work to be done neatly?  Here is a sample showing the format.

Examinations

The midterm examinations will contribute a major portion to your grade. The first assignment after the exam will be to correct all your errors. The exam corrections will be put into your portfolio, and will be reviewed as part of the evaluation of the portfolio.

Course Portfolio

For full credit on the class participation part of your grade, you will be expected to keep a course portfolio. It should be in a three ring binder,  with separate sections for the following four categories:

These should be organized with tabbed separators so that it is easy for me to turn to which ever section I want to review. Notes from class or your reading, assignment sheets, and any materials I hand out can optionally be included in the portfiolio, but these will not be reviewed.  Please clearly designate this material so I don't have to search through it to find the parts I am looking for.

I will review portfolios during each midterm exam, and will put a comment sheet in your portfolio at that time. The comment sheet is required to stay in the portfolio. For full credit, your portfolio must be up to date at each review. Do not neglect your portfolio all semester, and then try to put it together just before finals. It is supposed to be a consistent record of your work in the course over the entire semester.

For more information, see portfolioQA.html.