Calculus‎ > ‎

00 Pre-Requisites

Before launching into calculus, let's make sure to review the fundamentals of algebra, trigonometry, analytic functions. This will be mostly a self-paced unit with the bulk of the practice done on Khan Academy. I'll will do a few lectures illustrating how I approach the topics, and will spend a lot of time working with you one-on-one to get ready for calculus.

The following table summarizes the pre-requisite content of chapter 1 and provides links to online tutorials that may be helpful to you.
 

 Important Concepts

 Video Tutorials
 
Khan Academy tutorials

Algebra 1
Algebra 2
Trigonometry

 

Unit 1.1: Four Ways to Represent a Function

  • Understanding the interplay between the four ways of representing a function (verbally, numerically, visually, algebraically).
  • Finding the domain and range of a function, regardless of representation. 
  • Investigating even and odd functions. 
  • Working with piecewise defined functions.
     
     
    Function Introduction
    Function Expressions
    Domain and Range
    Recognizing Functions

     

    Unit 1.2: Mathematical Models - A Catalog of Essential Functions

    • The modeling process: developing, analyzing, and interpreting a mathematical model. 
    • Classes of functions: linear, power, rational, algebraic, trigonometric, exponential and transcendental functions. Include the special characteristics of each class of functions.
         
       
      Polynomial and Rational Functions
      Rational Expressions
      Exponential and Logarithmic Functions
      Logarithms
      Basic Trigonometry
      Unit Circle Definition of Trig Functions
      Graphs of Trig Functions
      Trigonometric Identities





       

      Unit 1.3: New Functions from Old Functions

      • The mechanics and geometry of transforming functions. 
      • The mechanics and geometry of adding, subtracting, multiplying, and dividing functions. 
      • The mechanics and geometry of composing functions. 
           

        Composing Functions

        Function Inverses

        Piecewise Functions

        Shifting and Reflecting Functions

        Properties and Features of Functions

        Comparing and Interpreting Functions

         
        The links below  take you to algebra and trig review videos, which students have found helpful and provides a link to download a copy of the Yellow Book.

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        TopicURL
        The Yellow Book (review of algebra, geometry, and pre-calculus)  
        Patrick JMT Algebra Tutorials http://patrickjmt.com/#algebra 
        Patrick JMT Trig http://patrickjmt.com/#trigonometry 
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