Math 1a Introduction to Calculus

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Math 1aIntroduction to Calculus

• Fall 2006 Introductory Meeting
• Bret Benesh

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Why attend Harvard?

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

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High School

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

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At Harvard

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

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General Relativity
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Polio Vaccine
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Real Estate
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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

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About Math 1a

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

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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.

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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.

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Prerequisites

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

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The text

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

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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.

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Course Topics

• Differentiation rates of change, linear
  approximations to functions, optimization
• Integration The definite integral, Riemann
  sums, the Fundamental Theorem of Calculus

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Final Exam Problem
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Grading

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

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Exam Dates

• Precalculus Exams October 2nd - 13th
• Midterm I October 24th
• Midterm II December 12th
• Final Exam January 22nd?

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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.

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Problem Solving

• Explicit Instruction on how to go about solving
  new problems.
• Heuristics
• Time Management
• Beliefs

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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.

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Getting Help with Math 1a

• Other 1a students.
• Your CAs problem session
• Your TFs Office Hours
• The Math Question Center (MQC) in SC B-10 (830
  pm - 1030 pm Sunday through Thursday)

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Advising

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

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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.

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Sectioning

• Math 1a is taught in small sections.
• You must section by 100 pm on Wednesday,
  September 20th.
• Sectioning directions are on http//www.math.har
  vard.edu/sectioning/index.html

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Precalculus Warm-Up

• There will be a warm up session on precalculus
  today from 200 pm - 330 pm in SC Hall A.

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Your Homework

• The Bottle Calibration Problem.
• Due Page 1 for before the first day of class.

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Important Emails

• Bret Benesh (Course Head)
• benesh_at_math.harvard.edu
• Janet Chen (Assistant Course Head)
• jjchen_at_math.harvard.edu