Course Information
Course Content and Goals
Calculus is the mathematics of change and motion; it enables us
to apply our knowledge of static situations to dynamic
situations. We know how to find the slope of a line; calculus
enables us to find the slope of a curve. We know how to find the
area of a rectangle; calculus enables us to find the area between
curves. We know how to find average rates of change; calculus enables
us to calculate instantaneous rates of change. Derivatives, which measure
instantaneous rate of change or the slope of a curve, and
integrals, which can be used to compute areas between curves
or net accumulation, together form the basis of our
study of onevariable calculus this semester.
Differentiation and integration are intimately related to
oneanother. This relationship is the focus of the
Fundamental Theorem of Calculus. In Mathematics 1a we will explore
the ideas of calclus and apply them to problems of optimization,
graphing and problems from many disciplines.
The approach taken
throughout the development of calculus is to get
successively better and better approximations of a quantity
we wish to compute. These successive approximations, when
followed by a limiting process, allow us to get a handle on
problems that originally may seem intractable. So in essense
it is limits that enable us to apply our knowledge of static
situations to dynamic ones.
The roots of calculus go back to the ancient Greek
mathematicians Eudoxus and Archimedes, but it wasn't until
the mid to late 1600s that Newton began to talk about limits,
albeit informally, and that Leibniz introduced much of the
notation in use today. Later mathematicians put Newton's
notions on firmer ground.
Today the applicability of calculus is so broad that fluency
in calculus is essential for not only mathematicians, but also
for biologists, environmental scientists, physicists,
economists, engineers, and many others. When you leave Math
1a, you will carry with you concepts and ideas from calculus
that you can apply in your further studies, both in
mathematics and in other fields.
The fundamental topics in this course, the derivative, the
integral, and the limit, are presented and analyzed from
several vantage points: symbolically, graphically, numerically,
and as relationships between quantities. All of these
perspectives are important to gaining a deep and thorough
understanding of calculus. Your job, with the help of your
instructor, is to learn calculus by reading about, thinking
about, and experimenting with its ideas and practicing what
you learn.
Necessary Background
If this is a typical
Math 1a group, many of you have had exposure to calculus
before. However, those of you who haven't need not be
alarmed: in the past students without a calculus background
have done as well as those with it. Doing well in Math 1a
requires a solid background in precalculus, as demonstrated
by a score of 18 or more on part 1 of the Harvard Math
Placement Test.
Text
Single Variable Calculus:
Concepts and Contexts by James Stewart. Second edition,
Brooks/Cole 2001. This text is available at the Harvard
Coop. There will be supplementary material available as well.
Class and Problem Sessions
Math 1a is
taught in sections that meet three hours per week. Each
section of Math 1a has a Course Assistant who will be in
class, collect and correct homework assignments, and hold
weekly problem sessions. You are strongly encouraged to
attend these problem sessions as they are an integral part
of the course and will be generally be devoted to working
problems and amplifying the lecture material. The pace of
the course is rather fast, so these sessions should be
particularly valuable to you in learning the material. A
schedule of all problem sessions will be posted on the
course web site; feel free to go to any Math 1a Course
Assistant's Problem Session.
Homework
Problems are an integral part of
the course; it is unlikely that you will learn the material
and do well in the course without working through the
homework problems in a thoughtful manner. Don't just crank
through computations and write down answers; {\it think}
about the problems posed, the strategy you employ, the
meaning of the computations you perform, and the answers you
get. It is often in this reflection that the greatest
learning takes place.
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 goals of
teaching you the art of problem solving and applying ideas of
calculus 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.
You are welcome to collaborate with other students on solving
homework problems; in fact, you are encouraged to do so.
However, writeups you hand in must be your own work, you
must be comfortable explaining what you have written, and
there should be a written acknowledgement of collaboration
with the names of you coworkers.
Oddnumbered problems are solved in the Student
Solution Manual. 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.
Math Help
The following sources of math help are
available without any appointment:
weekly problem sessions lead by course assistants: go to as
many as you like
office hours held by your section leader
the Math Question Center: in Loker Common 810 pm every night
except Friday and Saturday.
Exams
Exams are common and given in the
evenings. Please keep these exam dates free from conflicts:
Exam 1 
Tuesday, October 21 
7:009:00 pm 
SC C and SC D 
Exam 2 
Monday, Nov. 24 
6:008:00 pm 
Boylston 110 [Fong] and 2 Divinity Ave 18 [Yenching] 
Final Exam 
Tuesday, January 27, 2004 
TBA 
TBA 
There will also be a short quiz before the drop/add date; the quiz score will count towards your homework grade.
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 demonstrating your mathematical knowledge as
opposed to your calculating ability. We expect you to
express your ideas, line of reasoning, and answers clearly. If, for
some reason you have an unmovable conflict with an exam time you are
expected to email the course head at least one full week in advance
so we can make an attempt at accommodation. Please do not schedule
Thanksgiving departures for before the date of the exam.
Grading Policy
Your course grade will be determined as follows:
Take the higher of
45% Final Exam + 20% Exam 1 + 20% Exam 2 + 15% Homework
35% Final Exam + 25% Exam 1 + 25% Exam 2 + 15% Homework
30% Final Exam + 25% Exam 1 + 25% Exam 2 + 20% Homework
You must pass the final to earn more than a C in the course.
Course Head
Robin Gottlieb
Office: Science Center 430
Phone: (617) 4957882
Email: gottlieb@math.harvard.edu
