Holy Cross Mathematics and Computer Science



Mathematics 136 -- AP Calculus, section 4

Syllabus Fall 2003

Professor: John Little
Office: Swords 335
Office Phone: 793-2274
Email: little@mathcs.holycross.edu (preferred), or jlittle@holycross.edu
Office Hours: MWF 10-12, T 3-5, and by appointment
Course Homepage: http://mathcs.holycross.edu/~little/AP03/AP.html

Table of Contents

  1. Is This The Right Course For You?
  2. Course Description
  3. Textbook
  4. What Will Class Meetings Be Like?
  5. Advice On How To Succeed In This Class
  6. Notes On Calculators
  7. Grading Policy
  8. Academic Integrity Policy
  9. Course Schedule
  10. Final Examination

Is This The Right Course For You?


AP Calculus is the recommended starting mathematics course at Holy Cross for students who taken most 1 year calculus courses in high school. If you took the Calculus AB Advanced Placement exam and received a score of 4 or above (or the BC Advanced Placement exam and an AB subscore of 4 or above), then you earn one semester course credit, and this is almost certainly the right course for you to take if you want to continue with calculus at Holy Cross. Even if you did not take an AP exam, if you took a year of high school calculus and earned a grade of B or better, this is probably the correct place for you to start. If you scored a 4 or higher on the BC exam, or if your high school calculus course was stronger than average and you did well in it, you may want to consider starting with Mathematics 241 -- Multivariable Calculus. It is also possible, though not recommended, to start with Calculus for the Physical and Life Sciences 1 (Mathematics 131). Be aware that if you decide to take that option, you will be repeating a large portion of the material from your high school course, and you will lose your advanced placement credit. 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.

Course Description


The course will cover the following topics. (Also see the detailed course schedule at the end of this syllabus.)

  1. Functions, Differentiation
  2. Integration and applications
  3. Differential Equations
  4. Taylor polynomials and series, approximation
Much of the material from Units 1 and 2 will be familiar, but we may be approaching it from a different viewpoint from the one you have seen before -- we will not just be repeating your high school calculus course.

Textbook


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). 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.

What Will Class Meetings Be Like?


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.

The other meetings of the class will be structured as lectures when that seems appropriate.

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!

Advice On How To Succeed In This Class


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, 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!

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. 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.

Notes on Calculators


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 use on exams.

Grading Policy


Grading for the course will be based on

  1. Three in-class tests, each worth 15% of the course grade,
  2. A two-hour final exam, worth 30% of the course grade,
  3. Written reports from small group discussions and computer labs -- one report from each group, together, worth 15% of the course grade.
  4. Individual homework assignments, given out in class. The homework will count as 10% of your course grade, if it is to your benefit, that is, if your homework average is greater than or equal to the average of your other grades. Otherwise, it will be discounted, and your average will be the average of your other grades. No credit will be given for late homework, except in the case of an excused absence, or with my permission.
  5. A 5-page paper may be substituted for one of the in-class exams. I will prepare a list of possible topics and distribute it later in the semester.
If you ever have a question about the grading policy or your standing in the course, don't hesitate to ask me.

Departmental Statement on Academic Integrity


Why is academic integrity important?


All education is a cooperative enterprise between teachers and students. This cooperation works well only when there is trust and mutual respect between everyone involved. One of our main aims as a department is to help students become knowledgeable and sophisticated learners, able to think and work both independently and in concert with their peers. Representing another person's work as your own in any form (plagiarism or ``cheating''), and providing or receiving unauthorized assistance on assignments (collusion) are lapses of academic integrity because they subvert the learning process and show a fundamental lack of respect for the educational enterprise.

How does this apply to our courses?


You will encounter a variety of types of assignments and examination formats in mathematics and computer science courses. For instance, many problem sets in mathematics classes and laboratory assignments in computer science courses are individual assignments. While some faculty members may allow or even encourage discussion among students during work on problem sets, it is the expectation that the solutions submitted by each student will be that student's own work, written up in that student's own words. When consultation with other students or sources other than the textbook occurs, students should identify their co-workers, and/or cite their sources as they would for other writing assignments. Some courses also make use of collaborative assignments; part of the evaluation in that case may be a rating of each individual's contribution to the group effort. Some advanced classes may use take-home examinations, in which case the ground rules will usually allow no collaboration or consultation. In many computer science classes, programming projects are strictly individual assignments; the ground rules do not allow any collaboration or consultation here either.

What are the responsibilities of faculty?


It is the responsibility of faculty in the department to lay out the guidelines to be followed for specific assignments in their classes as clearly and fully as possible, and to offer clarification and advice concerning those guidelines as needed as students work on those assignments. The Department of Mathematics and Computer Science upholds the College's policy on academic honesty. We advise all students taking mathematics or computer science courses to read the statement in the current College catalog carefully and to familiarize themselves with the procedures which may be applied when infractions are determined to have occurred.

What are the responsibilities of students?


A student's main responsibility is to follow the guidelines laid down by the instructor of the course. If there is some point about the expectations for an assignment that is not clear, the student is responsible for seeking clarification. If such clarification is not immediately available, students should err on the side of caution and follow the strictest possible interpretation of the guidelines they have been given. It is also a student's responsibility to protect his/her own work to prevent unauthorized use of exam papers, problem solutions, computer accounts and files, scratch paper, and any other materials used in carrying out an assignment. We expect students to have the integrity to say ``no'' to requests for assistance from other students when offering that assistance would violate the guidelines for an assignment.

Specific Guidelines for this Course


In this course, all examinations will be closed-book and given in-class. No sharing of information with other students in any form will be permitted during exams. On group discussion write-ups, close collaboration is expected. On the problem sets, discussion of the questions with other students in the class, and with me during office hours is allowed, even encouraged. If you do take advantage of any of these options, you will be required to state that fact in a "footnote" accompanying the problem solution. Failure to follow this rule will be treated as a violation of the College's Academic Integrity policy.

Course Schedule


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.

DateClass Topic Reading (H-H, et. al.)
9/3 Course introduction Chapter 1
9/5 Review of the ``library of functions'' Chapter 1
9/8 Review of the ``library of functions'' Chapter 1
9/9 Rates of change 2.1
9/10 Limits 2.2
9/12 Definition of the derivative 2.3
9/15 Lab 1: Getting started with Maple
9/16 Lab 1, continued: differentiability = local linearity 2.3
9/17 Meaning of the derivative 2.4, 2.6
9/19 Computing derivatives (review) 3.1 - 3.5
9/22 Computing derivatives, continued 3.6, 3.7
9/23 Lab 2: Parametric curves 3.8
9/24 More on parametric curves 3.8
9/26 Critical points 4.1
9/29 Optimization 4.3, 4.5
9/30 Exam I (material through 9/24)
10/1 Lab 3: An applied optimization problem 4.5
10/3 Total change of a function 5.1
10/6 Riemann sums, the definite integral 5.2
10/7 Lab 4: Riemann sums 5.2
10/8 Meaning of the definite integral 5.3
10/10 Theorems about definite integrals 5.4
10/13,14 Columbus Day Break -- NO CLASS
10/15 Antiderivatives 6.1-6.3
10/17 2nd Fundamental Theorem of Calculus 6.4
10/20 Integrals by substitution 7.1
10/21 Integrals by parts 7.2
10/22 Tables of integrals 7.3
10/24 Algebraic identities and trig substitution 7.4
10/27 More on algebraic identities and trig substitution 7.4
10/28 Applications of integration 8.1
10/29 Volumes by slices 8.2
10/31 Exam II (9/26 - 10/27)
11/3 More applications of integrals 8.2
11/4 Lab 5: Arc length, numerical approximations 8.2 , 8.3
11/5 What is a differential equation? 11.1
11/7 Slope fields 11.2
11/10 Euler's Method 11.3
11/11 Lab 6: Slope fields and Euler's Method 11.3
11/12 Separation of variables 11.4
11/14 Growth and decay 11.5
11/17 Other population models 11.7
11/18 Lab 7: Modelling populations
11/19 Lab 7: continued
11/21 Geometric series 9.1
11/24 Convergence 9.2
11/25 Power series 9.3
11/26,28 Thanksgiving Recess -- NO CLASS
12/1 Taylor polynomials 10.1
12/2 Taylor series 10.2, 10.3
12/3 Error in Taylor approximation 10.4
12/5 Exam III (11/4 - 12/1)
12/8 Semester wrap-up

Final Examination


The final exam for this course will be given Friday, December 19 at 8:30 a.m.

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