Math 115a

Course Number:	Math 115a - Section 1
Course Name:	Enriched Calculus II: Series, Complex Numbers, Applications
Instructor:	Curtis Greene
Semester and Year:	Fall 2009

Course Description:

Math 115a is a one-semester course. This is a change from previous years, in which the first half was taught as a half-semester course -- this year, the two halves will be combined. The first half (roughly) covers the last quarter of a standard BC Calculus course. Principal topics include: improper integrals, sequences and series, Taylor series and Taylor polynomials, and a brief introduction to complex numbers. The second half (roughly) covers applications, with the topic varying depending on the instructor. This fall in this section, the topic will be applications of series in combinatorics and probability, primarily focusing on the theory of generating functions.

Math 115 is for students whose prior experience includes a substantial amount of calculus, but not enough to place directly into Math 121 (Calculus III: Multivariable Calculus). The course includes a brief review of integration techniques, but assumes that students have seen most of this material previously. Students who need a more extensive review of integration might consider Math 114 instead. Math 115 is ideal for students who have had a solid AB calculus course, but have not been exposed to infinite series.

Math 115 is especially recommended for students whose interests may lead them to courses beyond calculus. Homework exercises will include a mix of routine and challenging problems, designed to expose students to a wide range of mathematical ideas. It is not intended to be a "terminal" math course.

Textbooks:

For the first half-semester: Chapter 12 (Infinite Sequences and Series, p. 710-799) of Calculus, 6th Edition, by James Stewart, Thomson-Brooks/Cole 2008. This is available for $8.99 as a single-chapter electronic download from ichapters.com at this link. You may also buy the hardcopy edition of the text, but it is much more expensive. Please be careful to get the correct edition (6th), the correct version of the book (Calculus, not Calculus: Early Transcendentals or Elements of Calculus, and the correct chapter (12). If you somehow end up with the wrong chapter (paper or electronic), you may still be able to use it. But you should be aware that the page- and problem-numbering may not be the same.
For the second half-semester: I will provide and handouts and electronic links in lieu of a text.

Course Schedule:

Math 115a is taught MWF 10:30-11:30. There will not be an formal discussion/lab hour, but I encourage you to reserve time in your schedule to meet with me informally, either in the Math Question Center Monday nights or during my office hours (see below).

A second section is offered MWF 2:00-3:00, taught by Prof. Clay Shonkwiler. Enrollment in both sections is limited to 25 students each.

Homework, Tests, etc.:

Weekly homework, two midterm tests, occasional quizzes (usually on Friday during class), and a final exam (self-scheduled) These will be weighted as follows in determining the final course grade:

Homework	10%
Quizzes	10%
Tests	50%
Final	30%

The weekly homework will contain a mixture of basic and challenging problems, the latter indicated by a star (*). All of the homework should be handed in for grading. Basic problems are designed to help you learn the essential concepts and practice new techniques. Mastery of the basic problems will be sufficient to guarantee at least a 3.0 in the course.

The first homework assignment is due on Friday, September 4. Assignments after the first week will be due on Wednesdays.

Office Hours:

You can find me in my office at the following times: Monday and Wednesday 11:30-12:00 (after class), and Friday 3:00-4:00. I am happy to arrange other consultation times by appointment.

Math Question Center (MQC):

I encourage collaboration on the homework, and many students find it useful to work together in the Math Question Center (Sunday through Thursday 7-9PM, Hilles 011/012). I will be in the Math Question Center on Monday evenings -- it's a good time to come and ask me questions about the course.

Electronic Resources:

(1) Blackboard will be the primary source for course materials. You are responsible for getting the weekly homework assignments from Blackboard. I will also post solutions to homework and tests, handouts, links to course-related websites, and other materials that might be quite important (e.g. corrections to and hints to homework assignments, reminders of test dates, etc.). Please check Blackboard regularly.

(2) Mathematica is a powerful software system for doing symbolic calculation and displaying graphics, and we will use it extensively. Since it may also be useful in other courses, it is worthwhile becoming adept with Mathematica at an early stage of your Haverford career. If you are not familiar with Mathematica, please acquaint yourself with it as soon as possible, e.g., by coming to the Math Question Center. In this course you will especially want to acquaint yourself with the Sum and Limit commands.

Haverford has a site license for Mathematica that permits unlimited use by students, as long as they are on the campus network. Complete details on how to download Mathematica and install it on your own computer can be found at http://www.haverford.edu/math/Mathematica/. The installation process requires obtaining a password from the publishers. If you have any difficulty doing this, please come to the MQC and/or contact David Lippel (Math Department lab support person) for assistance.

Calculators:

Math 115d does not require the use of graphing calculators. The "official" computing platform of choice in this course is Mathematica. Students who already own graphing calculators usually find them useful. But you need not buy a calculator especially for this course. There will be no homeworks, labs, or exams that require a calculator. I urge you to explore the capabilities of Mathematica, and I hope that you will eventually discover that it is a very powerful resource.

Collaboration:

I encourage collaboration on the homework, both standard and special problems. Indeed, I expect you will learn a great deal about this course from each other. It will be to your advantage to form study groups, and many students facilitate this by working together in the Math Question Center.

Collaboration on homework naturally raises the question, "how much is OK?" I expect that you will share ideas, and perhaps work together at a blackboard, but eventually each student must write up his/her work independently, without reference to another students work or to written work that has been produced jointly. Verbatim copying from another person's paper or blackboard work is definitely "not OK". The safest approach is to write up your final solutions in a different place, and on a fresh sheet of paper.

It's important not to misunderstand these guidelines, so please ask me if you have any questions. You might also want to refer to the department's published guidelines on homework collaboration, which are available on the department website.

It goes without saying that collaboration on tests is never permitted. All inquiries about problems on the tests should be directed to me.

Honor code principle:

You must never present others' work as your own. If you have used other students' work in the preparation of homework you must acknowledge it. If you obtain solutions to assigned problems (on homework or take-home tests) from sources other than the textbook or class notes, you must acknowledge such sources. This especially applies to material obtained electronically, e.g., on the web.

If there are questions about honor code issues, you should seek clarification and guidance from me.