 Spring 2002 |
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| Announcements | TF Office Hours | CA Problem Sessions | Homework: MWF TTh | Exams |
| Math1b, Spring 2002 |
 Course Content and Goals: About four hundred years ago, Galileo wrote
Although the language of mathematics has evolved over time, the statement has as much validity today as it did when it was written. In Mathematics 1b you will become more well-versed in the language of modern mathematics and learn about its applications to other disciplines. Math 1b is a second semester calculus course for students who have previously been introduced to the basic ideas of differential and integral calculus. Over the semester we will study three (related) topics, topics that form a central part of the language of modern science:
We will start the semester by studying infinite sums. You
already are aware that a rational number such as
In your previous math courses you may have seen functions
represented by integrals. For example, We will end with differential equations, equations modeling rates of change. Differential equations permeate quantitative analysis throughout the sciences (in physics, chemistry, biology, enviromental science, astronomy) and social sciences. In a beautiful and succinct way they provide a wealth of information. By the end of the course you will appreciate the power and usefulness differential equations and you will see how the work we have done with both series and integration comes into play in analyzing their solutions.
An assignment will be given at each class meeting. Unless otherwise specified, the assignment is due at the following class meeting and will be returned, graded, at the subsequent class. If you miss a class, then you are responsible for obtaining the assignment and handing it in on time. Solutions put together by the course assistants will be available on the course website. When your homework assignments are returned to you, you can consult the solutions for help with any mistakes you might have made. Problem sets must be turned in on time. When computing your final homework grade, your lowest two homework scores will be dropped if you are in a TTh section and your lowest three homework scores will be dropped if you are in a MWF section. Note that homework problems will sometimes look a bit different from problems specifically explicitly discussed in class. To do mathematics you need to think about the material, not simply follow recipes. (Following preset recipes is something computers are great at. We want you to be able to do more than this.) Giving you problems different from those done in class is consistent with our goal of teaching you the art of applying ideas of integration and differentiation to different contexts. Feel free to use a calculator or computer to check or investigate problems for homework. However, an answer with the explanation `` because my calculator says so" will not receive credit. Use the calculator as a learning tool, not as a crutch. Calculators will not be allowed on examinations due in part to equity issues. You are welcome to collaborate with other students on solving homework problems; in fact, you are encouraged to do so, and we will provided you with contact information for your classmates in order to faciliate that. However, write-ups you hand in must be your own work, you must be comfortable explaining what you have written, and there must be a written acknowledgement of collaboration with the names of you coworkers. Odd-numbered problems are solved in the Student Solution Manual; some coies will be put on reserve in the Cabot Science Library. After working on the problems on your own, you are free to consult this manual provided you acknowledge the use of this manual in your submitted work. (This is a standard rule of ethics.)
There will be an optional Technique re-Test available on Wednesday. April. 3: 7:00 - 8:00 in SC D. The higher of your two scores counts in the computation of your course grade. The first test is not optional. Calculators will not be allowed on examinations, due in part to equity issues. We will make sure that problems on the exams require minimal calculation to allow you to spend your time demostrating your mathematical knowledge as opposed to your calculating ability. We expect you to express your ideas, line of reasoning, and answers clearly.
Your course grade will be determined as follows:
A schedule of all Math 1b problem sessions will be posted on the course website. You are welcome to go to any and as many problem sessions as you like.
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can be represented by an infinite sum, (
, for
the case at hand). Actually, irrational numbers such as e and
have representations as infinite
sums as well. In fact, we will find that many functions, such as
and 
can be represented by infinite
polynomials known as power series. Polynomial approximations
based on these power series representations are widely used by
engineers, physicists, and many other scientists.
can be
represented by
. Integrals can be
used in many contexts. The definite integral enables us to
tackle many problems, including determining the net change in
amount given a varying density. In the second unit of the
course we will revisit integration. First we'll study the
integration analogues of both the Product Rule and Chain Rule
for differentiation and briefly touch on some alternative
transformations of integrals that enable us to tackle them
more efficiently. The goal is not to transform you into an
integration automaton (we live in the computer age), but to
have you acquire familiarity with the techniques and the
ability to apply them to some standard situations. More
important is the ability to apply the integration as
appropriate in problem solving; we will devote
time to developing your skill in doing this.
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Last update, 1/29/2002, math1b@fas.harvard.edu
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