Math 1aIntroduction to

CalculusFall 2006 Introductory

MeetingBret Benesh

Why attend Harvard?

i.e. What should you expect from you tuition money?

High School

• Consumer of Knowledge• Teacher shows you how to do it.

At Harvard

• Producer of Knowledge• Teacher guides you, but you do a lot of work on your own.

General Relativity

Polio Vaccine

Real Estate

Quote• “Merely accumulating information is of little value to students. Facts are soon forgotten, and the sheer volume of information has grown to the point that it is impossible to cover all the important material or even to agree on what is most essential. Concepts and theories have little value unless one can apply them to new situations.”

• -Derek Bok, President of Harvard University

About Math 1a

• The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium.

About Math 1a

• This course will help you see the greatness of calculus by introducing:

1. How differential calculus treats rates of change.

2. How integral calculus treats accumulation.

3. How the Fundamental Theorem of Calculus links the two.

Course Goals

• To build a mathematical foundation for future study.

• To be better able to solve new problems.

• To build a founded confidence in your problem solving abilities.

• To appreciate the utility and logic of mathematics.

• To improve communication skills• To become more skillful in evaluating the validity of an argument.

Prerequisites

• A solid knowledge of precalculus and a satisfactory score on the Math Placement Exam.

The text

• James Stewart. Essential Calculus: Early Transcendentals, first edition. Thomson Brooks/Cole, Belmont CA, 2007. ISBN-10: 0495014281.

Calculators

• Any graphing calculator will be helpful.

• If you would like to buy one, we recommend a TI-84, TI-86, or a TI-89.

• Calculators will be allowed on homework but not on exams.

Course Topics

• Differentiation: rates of change, linear approximations to functions, optimization

• Integration: The definite integral, Riemann sums, the Fundamental Theorem of Calculus

Final Exam Problem

Grading

• Homework: 20%• Precalculus Exam: 5%• Midterm I: 20%• Midterm II: 20%• Final Exam: 35%

Exam Dates

• Precalculus Exams: October 2nd - 13th

• Midterm I: October 24th• Midterm II: December 12th

• Final Exam: January 22nd?

Homework

• Everyone does the same homework.

• Homework is due at the beginning of class.

• We drop your three lowest homework scores.

• You will hand in homework reports on some of the problems.

Problem Solving

• Explicit Instruction on how to go about solving new problems.

• Heuristics• Time Management• Beliefs

Sections and Problems Sessions• Each 1a section has an undergraduate course assistant.

• CAs hold 90 minute problem sessions each week.

• You can go to any problem session.

Getting Help with Math 1a

• Other 1a students.• Your CA’s problem session• Your TF’s Office Hours• The Math Question Center (MQC) in SC B-10 (8:30 pm - 10:30 pm Sunday through Thursday)

Advising

• Math advising hours can be found at: http://www.math.harvard.edu/sectioning/index.html

Math 1a or Xa?

• Most students in Math 1a will have taken calculus already.

• Math 1a will assume a good knowledge of precalculus.

• Math Xa will take time to teach precalculus.

• The courses are about the same amount of work.

Sectioning

• Math 1a is taught in small sections.

• You must section by 1:00 pm on Wednesday, September 20th.

• Sectioning directions are on: http://www.math.harvard.edu/sectioning/index.html

Precalculus Warm-Up

• There will be a warm up session on precalculus today from 2:00 pm - 3:30 pm in SC Hall A.

Your Homework

• The Bottle Calibration Problem.

• Due Page 1 for before the first day of class.

Important Emails

• Bret Benesh (Course Head)benesh@math.harvard.edu

• Janet Chen (Assistant Course Head) jjchen@math.harvard.edu