Summary of Topics

Submitted by Michael C. Ching on Tuesday, 9/6/2011, at 3:53 PM

The following is a list of the topics we plan to cover in this course. Everything is subject to change depending on how fast things go, but it should give you an idea of what is in store for you. Note that this list is not suitable for studying for exams.

Introduction: what is calculus?

Functions:

  • Ways to represent a function (1.1)
  • Functions you need to know about (1.2)
  • New functions from old (1.3)

Limits:

  • The limit of a function (1.5)
  • Limit laws (1.6)
  • The precise definition of a limit (1.7)
  • Continuity (1.8)

Derivatives:

  • Rates of change and the derivative (2.1)
  • The derivative as a function (2.2)
  • Formulas for differentiation (2.3)
  • Derivatives of trigonometric functions (2.4)
  • The chain rule (2.5)
  • Implicit differentiation (2.6)
  • Rates of change in science (2.7)
  • Related rates (2.8)
  • Linear approximation (2.9)

Applications of Differentiation:

  • Maximum and minimum values (3.1)
  • The Mean Value Theorem (3.2)
  • The relationship between derivatives and the shapes of graphs (3.3)
  • Horizontal asymptotes (3.4)
  • Curve sketching (3.5)
  • Optimization problems (3.7)
  • Antiderivatives (3.9)

Integration:

  • Areas and distances (4.1)
  • Definite integrals (4.2)
  • The Fundamental Theorem of Calculus (4.3)
  • Indefinite integrals (4.4)
  • The substitution rule (4.5)

Exponential and Logarithmic Functions:

  • Inverse functions (6.1)
  • Exponential functions and their derivatives (6.2)
  • Logarithmic functions (6.3)
  • Derivatives of logarithmic functions (6.4)

Applications of Integration:

  • Areas between curves (5.1)
  • Volumes of revolution (5.2)

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Taking Notes