Instructor
Calculus, Single Variable (2nd Edition), Hughes-Hallett, Gleason, et al.
A graphing calculator. I recommend the TI-83 or the TI-86.
Student Solution Manual (solutions to every other odd problem)
A copy is on reserve in the library.
• Learn to examine mathematical concepts graphically, numerically, and algebraically.
• Be able to define, describe, and apply the concepts of calculus to include definite and indefinite integrals, antiderivatives, and differential equations.
• Learn to work with the basic computations of integral calculus.
• Develop skills in problem analysis and problem solving.
• Learn to use and trust your intuition to better understand how to interpret and solve problems.
• Learn to interpret real-world problems in the language of mathematics.
• Be able to use graphing calculators and computer software as computational tools for understanding and solving problems in calculus and its applications
• Learn to communicate mathematics effectively, both verbally and in writing.
• The Definite Integral: brief review of chapter 3
• Constructing Antiderivatives: Chapter 6, sections 1, 2, 4, 3 (note order!)
• Integration: Chapter 7, sections 1-3, 5-8
• Using the Definite Integral: Chapter 8, sections 1, 2, Focus on Modeling (Probability)
• Approximations and Series: Chapter 9, sections 1-4
• Differential Equations: Chapter 10, sections 1-6, as time permits
I do not have regularly scheduled office hours. Rather, you are encouraged to stop by my office at any time when you have questions or problems and if I am not too busy I will be happy to work with you. You may also stop by to make an appointment for a time that is mutually convenient. Another good way to contact me is through email, particularly during the evenings or weekends. I promise to respond to your email as quickly as I can.
Several study sessions are scheduled each week (details and location to be announced). These are times when you are encouraged to drop in and work alone or with others and chat about your progress. Students who attend these sessions weekly on a regular basis often find them beneficial. You are also encouraged to work with the learning assistants assigned to this course, in the evenings in Buttrick. Their hours and location will be on the weekly learning support schedule.
In this course, it is absolutely essential that you do the reading assignments. Your experience with previous math courses may make this seem unlikely, since it may have been possible to avoid reading the text, yet do adequately well by copying down the examples the instructor did in class and then doing the homework exercises by just changing the numbers in those "pattern examples" and the pattern examples given in the text. Unfortunately, this approach resulted in students being able to do the mechanical computations quite well, but having no real understanding of the material and no real ability to apply it in situations that are even a little bit different from that covered by the pattern examples. This is one factor that led to the national movement toward reformed courses, like Math 119, stressing understanding. This modern approach to learning requires new methods in the classroom emphasizing learning rather than lecturing, as well as new texts such as the one for this course.
The difference between the text for this course and an old-style calculus text is apparent from even a cursory scanning of the first chapter. If you open the text to page 2 and just begin turning pages, you will probably be struck by the following:
1. The amount of text to be read outside of examples is much greater than in old-style books. Older books would typically have brief explanations, sometimes single paragraphs, followed by one or more pattern examples. This book has longer explanations that attempt to convey understanding of the concepts involved rather than just the mechanics of how to do computations.
2. There are far fewer examples than in an old-style text, but the examples tend to be much longer ones that arise from actual real–world problems.
3. There are far fewer homework problems than in an old-style text, but the exercises are much longer, are often quite different from each other and from the examples in the text, and use real–world numbers that are not as "nice" as the made–up numbers in the shorter exercises typical of older texts.
Doing the problems requires an understanding of the material in the text, not just the ability to change numbers in pattern examples. Also, I will be counting on you to read the text since I will not be lecturing very much and will be relying on you to have seen the material before we work with it in class.
Since the reading is so important, some hints on how to do it might be helpful. You may find that slight variations on the following scheme will work for you.
a. Plan on doing the reading more than once, and do not make it an essential goal to understand everything in the reading the first time through it. The first reading should be devoted only to getting a general overview of the material of the section.
b. After the first reading, stop for a few minutes and attempt to summarize to yourself, in your own words, what the section is all about. Then immediately reread the section.
c. During the second reading, make a serious effort to understand all of the material in the section. This does not mean to memorize it, but rather to understand all of the points before going on.
d. If you do not understand something during the second reading, put the book aside awhile and return to it later when your mind is fresher. If you still do not understand it after returning to it, ask me or some other members of the class about it. Do make sure you eventually understand all of the material. You will probably get tripped up in later reading, in doing the homework, or on tests if you treat material you don’t quite understand as "probably not all that important."
e. Do not get discouraged if some points require some time to understand. It is not uncommon to have to think about a point in a math text for a half hour (or more, for more complicated concepts) before it becomes clear what is really going on.
Do not just accept mathematical statements or graphs of functions depicted in the text, but try to verify these statements and graphs yourself. Working with your graphing calculator while you read the text is a good way to do this. Often the book will ask you to try something. When it does, try answering the book’s question before reading further. If you have questions, ask in class, stop by my office, or send me email.
You will be given (almost) daily problem assignments, which you will be expected to complete even though this work will probably not be checked unless you ask for help with it. You are encouraged to work with others on these assignments and check each other’s work. You will receive additional problems that will be collected. Some assignments will be done collectively in small collaborative groups; for others you will be encouraged to work together but asked to write up (and understand) your own solution.
The problems can be found at http://ecademy.agnesscott.edu/Mathematics/mathfacpgs/riddle/courses/math119/
There will several projects that will be turned in for a grade. These will usually be done in groups of 2 or 3. As with the homework problems, each member of a group is expected to not only understand the work submitted by the group, but to take the responsibility to insure that all members of her group participate and understand the solutions to the problems. The group assignments will require you to express mathematical ideas in English in a written format. To explain a solution in writing requires a good understanding of the concepts and procedures involved, and is an important ability to develop. Take your written work seriously.
Class involvement is important. This includes your attendance and punctuality, your attitude, your willingness to contribute ideas and questions, to listen to your peers, and to be a contributing partner in collaborative efforts. There will be three tests, the first covering up through chapter 6, the second covering chapter 7 and chapter 8, and the third on chapter 9. The final will review material from the entire course.
We will make frequent and important use of calculator and technology to help us learn about functions and to work with functions to solve real problems. You will use a graphing calculator for much of the work in the course. The computer program Maple will be used for the symbolic exploration of data and functions. The philosophy we will take can be summarized by the following unauthorized adaptation of a quote from Elementary Differential Equations, 5th Edition, by William Boyce and Richard DiPrima:
"For you, the student, these various computing resources have an effect on how you should study functions. It is still essential to understand the behavior of standard functions, and this understanding is achieved, in part, by working out a sufficient number of examples in detail. However, eventually you should plan to delegate as many as possible of the routine (often repetitive) details to a computer while you focus more attention on the proper formulation of the numeric, graphic, and analytic methods so as to attain maximum understanding of the behavior of functions and of the underlying processes that the functions model. Our viewpoint is that you should always try to use the best tools available for each task. Sometimes this is a pencil and paper; sometimes, a computer or calculator. Often a judicious combination is best."
Regular attendance for this class will be very important since much of our class time will be spent on discussing problems or working in small groups on problems or computing experiments. It is therefore expected that you will attend and be prepared for every class, but it is also recognized that circumstances may occasionally necessitate that you miss a class. However, you are still responsible for all material discussed in class whether you are there or not, and for submitting all work before the due date. Approval for extensions must be obtained in advance.
Your grade will be determined by applying the most favorable of the following two weighting schemes.
Your two best exams (80 points each) 160 points
The remaining exam 40 points
Final exam 120 points
Homework and Projects 150 points
Class participation 30 points
Total 500 points
or
Three exams (80 points each) 240 points
Final exam 80 points
Homework and Projects 150 points
Class participation 30 points
Total: 500 points