Martin E. Flashman
http://flashman.neocities.org

Copyright ©2013

Outline of Chapters (v0.1- 10/2012)

1    Introduction to Mapping Diagrams (2 weeks)
1.1    See web pages:
    1.1.1    Visualizing Functions [July, 2002] https://www.math.duke.edu/education/prep02/teams/prep-12/Page0.htm
    1.1.2     Sensible Calculus 0.B.2 Functions-Introduction and Review. http://flashman.neocities.org/book/ch0/0B2a.htm

    2    Linear Functions - Linear Functions are an excellent beginning to understand the value of mapping Diagrams (2 weeks)
    2.1     Function Features
    2.1.1        Magnification (slope), rate
    2.1.2         Increasing and Decreasing
    2.1.3        Forms for linear functions: initial values and rates.   
    2.1.4                Focus Points
    2.1.5        Composition
    2.1.6                 Inverses
    2.1.7        “Intercepts”
    2.2    Solving Linear Equations
    2.3    Fixed Points

    3    Quadratic Functions (1 week)
    3.1     Function Features
    3.1.1        Magnification and rates
    3.1.2        Linear Composition
    3.1.3        “Intercepts”
    3.1.4        Extremes   
    3.2    Solving quadratic equations
    3.3    Fixed Points

    4    Other Algebraic Functions (2 weeks)
    4.1    Reciprocal
    4.1.1        Domain Issues
    4.1.2        Linear Composition
    4.1.3         Asymptotic Behavior
    4.2    Cubic
    4.3    Polynomials
    4.4    Rational Functions
    4.5    Roots (Function Inverses)
   
    5    Other ways to define Functions (½ week)
    5.1         Cases
    5.2         Implicit Functions
   
    6    Exponential and Logarithmic Functions (1 week)
    6.1                 Linear vs geometric growth
    6.1.1                 linear composition
    6.1.2            Inverses
    6.1.3    Logarithms
    6.1.4         Domain
    6.1.5         Linear Composition
    6.1.6         Asymptotic Behavior
    6.1.7         Algebra Properties of Logs and Exponential Functions

    7    Trigonometric Functions: This class of functions has some major uses of mapping diagrams to make visual connections with their properties. (3 weeks)
    7.1         Definitions Triangles and the Unit Circle
    7.2         Domain and Measurement of Angles
    7.3         Extremes and “Intercepts”
    7.3.1         Asymptotic Behavior
    7.3.2         Periodic Behavior
    7.3.3        Linear Composition
    7.4    Trigonometric Equations
    7.4.1         Inverses
    7.4.2         Identities
    7.4.3         Triangle Geometry


    8    The Algebra of Functions (½ week)
    8.1         Composition
    8.2        Inverses
    8.3         Roots - Estimation with Linearity

    9    Calculus (3 weeks)
    9.1         Limits and Continuity      
    9.1.1        The Intermediate Value Theorem
    9.2         The derivative
    9.3          Calculating Rules
    9.3.1               The chain rule
    9.3.2         The Differential and Linear Estimation
    9.3.3         Newton’s Method
    9.3.4         The Mean Value Theorem
    9.3.5         Extremes

    10    Differential equations (1 week)
    10.1         Euler’s method
    10.2         Definite Integration
    10.3         The Fundamental Theorem of Calculus

    11    Multi-variable Functions and Calculus (2 weeks)
    11.1     1Variable Controlling 2 (3) Variables
    11.1.1         Vectors
    11.1.2         Limits and Continuity
    11.1.3         Derivative
    11.2    2 (3) Variables Controlling 1 Variable
    11.2.1           Vectors
    11.2.2         Limits and Continuity
    11.2.3         Partial Derivatives
    11.2.4         Extremes
    11.2.5         The Differential and Linear Estimation 
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Preface
Acknowledgements: Robert Beezer !