Math 1a: Introduction to Calculus, Spring 2005

Goals

Welcome to Math 1a! In this course, we will study the foundations of calculus, the study of functions and their rates of change. Along the way, we hope you will learn to appreciate the ubiquity of mathematics in our daily lives; to read, write, and critique mathematical arguments; and to analyze new problems with mathematical modeling.

Topics

The derivative measures the instantaneous rate of change of a function. The definite integral measures the accumulation of a function over an interval. These two ideas form the basic for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way.

Course Details

Staff

Instructor

Dr. Matthew Leingang, Preceptor in Mathematics.

Office:Science Center 323
Phone:(617-49)5-5334
E-mail:leingang@math.harvard.edu
Office hours:2:00-4:00pm Tuesdays and Wednesdays

Sections

There is only one section of Math 1a this term. Unlike Math Xb, 1b, 21a, and 21b, you will not need to choose a section by computer.

Course Assistants

The class will be assigned a course assistant, typically an undergraduate. The course assistant conducts a weekly problem session to supplement the section meeting and answer questions, and grades homework.

Class Meetings

Class meets Mondays, Wednesdays, and Fridays, 10:00-11:00AM. There will also be a weekly 90-minute problem session. Be prepared to ask and answer questions, as the goal of a small-section class is to learn through discussion.

Factors Determining your Grade

Reading Assignments

We will generally require that you read the material in the textbook before we discuss it in class, as opposed to reading it after the class. Before class you will go online to the course web site and answer a question or two. One question will always be the same: What part of the reading did you find most difficult? This question in particular will help me prepare the day's class.

In order to reward your effort in doing pre-class reading assignments the assignments will be graded and that grade figured into your course grade. Free-response questions will be graded on effort.

Homework

Homework will be assigned each class meeting and due the next class meeting. It will be returned, graded, at the following class meeting. Solutions will be made available on the course web site. Late homework will not be accepted. Three assignments will be dropped in the final grade calculation.

Homework problems are themselves an extension of the course material. This is not like high school in which there are a limited number of "types" of problems in mathematics and your teacher is responsible for showing you how to do each type. Some problems will require you to apply the concepts of the class and the textbook to solve problems not explicitly covered in class.

By all means you may work in groups on the homework assignments. However, each student must turn in his or her own write-up of the solutions, with an acknowledgment of collaborators. This is in line with good habits of scholarship in general.

Exams

There are three one-hour midterm examinations, currently scheduled for March 7, April 18, and May 5. There will be a final examination as well, tentatively scheduled for Thursday, May 26. No calculators will be allowed on the exams.

Exams are to test your mastery of the course topics. Exam problems may be like homework problems but may also synthesize various parts of the course.

Grades

Your course grade will be determined as the following weighted average:

Pre-Class Reading Assignments 5%
Homework 15%
Midterm I 15%
Midterm II 15%
Midterm III 15%
Final 35%
Total 100%

Miscellaneous

Prerequisites

The department recommends into Math 1a those with an 18 or higher on the first part (precalculus) of the Harvard Math Placement Test. Our research has shown that 1a students who do not heed the precalculus prerequisites often do poorly. Be sure you are comfortable with the following topics before you register in Math 1a:

  • Algebra
  • Graphing
  • Trigonometry
  • Exponentials
  • Logarithms

An optional precalculus primer has been made available in case you would like a book to study from. There are also precalculus books in the textbook reference section of Cabot Library, and a host of precalculus references on the course web site.

Texts

  • Calculus: Concepts and Contexts, 2nd edition, by James Stewart. Brooks/Cole, ISBN 0-534-37862-5. There is a companion web site to the text, and you may find the Review of Algebra2 linked there useful.
  • Schaum's Outlines: Precalculus, by Fred Safier, ISBN 0-07-057261-5. This is available only if you want something to study from for the precalculus quizzes.

Calendar

A detailed calendar is available on the course web site.

First Assignment

An initial quiz/survey, "Getting to Know You," can be found on the Online Quizzes section of the course web site.

Conclusion

We look forward to seeing you in Math 1a!