Math S-1ab - Calculus I and II
Harvard University
Summer School
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Math S-1ab - Calculus I and II |
Harvard University |
Syllabus |
| Topics: | Differential and integral Calculus in one real variable including sequences and series and differential equations. Major ideas include limits, derivatives, functions and graphing, linear approximation, optimization, definite and indefinite integrals, sequences, series, differential equations, and applications of all of these to the physical, biological, and social sciences. | ||
| Instructors: | John Mackey, SC 331, 496-5211, jfm@math.harvard.edu Robert Winters, SC 435, 495-4744, rwinters@math.harvard.edu |
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| Course Meetings: | The course meets M-F from 10am-noon in Science Center 110. There will also
be discussion sections M-F from 1-2pm with Course Assistant Nick Ramsey, location to be
announced. The course meets from Tuesday, July 26, through Friday, August 10, with a final exam on Tuesday, Aug 14. There is no class meeting on July 4. |
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| Grades: | Your course grade will be determined as follows: first midterm (Friday, July 6) 15% second midterm (Friday, July 20) 15% third midterm (Friday, August 3) 15% final exam (Tuesday, August 14) 30% homework 25% |
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| Text: | For most of the course we will closely follow the textbook "Calculus
with Early Transcendentals (4th Ed.)" by James Stewart, published by Brooks/Cole and
available at the Harvard COOP in a package with the supplementary "Student Solutions
Manual." This is a very fast-paced course which covers a lot of material. We will cover more than one section of the text per lecture, and hence it will be impossible to cover some topics in class as thoroughly as they deserve to be. Therefore, reading the text is an integral part of the course. While it would be ideal to read through the material before it is covered in class and then again after it has been covered, this is impractical. You should think of your text as a super-resource, with more examples, different explanations, and greater depth than can be presented even in two-hour lectures. |
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| Homework: | Doing problems is essential to learning and understanding mathematics.
Many ideas which seem clear when presented in class can only be completely understood once
you have studied them yourself with pencil and paper at the ready, and consequently,
homework problems are an important part of this course. Working collaboratively is also an important component to learning mathematics. The best way to learn something is to try to explain it to someone else, and you are encouraged to discuss problems with other students, the instructors, and the course assistants. However, you should always write out your homework solutions yourself in your own words. Perhaps more than any other, mathematics is a subject in which the ideas build quickly one upon the other. Therefore, homework will be assigned daily and will be due at 2pm the next day after section. Falling behind will present serious difficulties, and we urge you to keep up with your homework sets. This is especially important given the fast pace of this course. Because the course moves so quickly, the homework burden would become too great if we were to assign as many problems as we would like or as many as would thoroughly cover a topic in all its subtleties. As the course moves forward, some problems will be listed as recommended instead of being assigned and graded. You should nevertheless make certain that you know how to do these problems, even if we are not asking you to write out complete solutions. We must stress that this is only because of the practical considerations imposed by a short summer term. Additionally, there will occasionally be "challenge" problems posed that go beyond the requirements of the course. Some will be accessible using techniques you will have learned, and some will give you a glimpse of yet higher level mathematics. They are intended to spark your interest, and we hope that you consider them. |
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| Attendance: | While attendance is not a required part of the course as far as your grade is concerned, it is sure to be a determining factor in your success in this course. Missing even one class and falling a day behind will present a significant challenge. | ||
Technology: |
Technology can be a wonderful aid to learning mathematics, but too often, students use it as a crutch. We aim to give you a complete theoretical and computational understanding of Calculus, and the use of calculators and computers can provide a part of that understanding, but only after the ideas themselves are in place. You are encouraged to use technology to solve computational problems and to check your work, but there is no substitute for thinking. No calculators will be allowed in the exams. | ||
| Chapter-by-Chapter Syllabus: |
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Greater detail may be derived from the homework assignments as the course proceeds.
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Page maintained by Robert Winters.
Last updated: June 25, 2001.