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

Copyright ©2013, 2017 Martin Flashman

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is included in the section entitled "GNU Free Documentation License".

Outline of Chapters (v0.7- 8/2017)

1  (VF) Visualizing Functions
VF.TTGM Technology:  Tables, Graphs, and Mapping Diagrams
VF.DTGM Dynamic Technology: Graphs, and Mapping Diagrams
X.VF:  Exercises for Visualizing Functions

   Reference   Visualizing Functions [July, 2002] https://www.math.duke.edu/education/prep02/teams/prep-12/Page0.htm

    Reference   Sensible Calculus 0.B.2 Functions-Introduction and Review. http://flashman.neocities.org/book/ch0/0B2a.htm

 2    (LF) Linear Functions - Linear Functions are an excellent beginning to understand the value of mapping Diagrams
 LF.SMR  Slope, Magnification and Rate
 LF.ID Increasing/Decreasing Linear Functions
 LF.FP Focus Point on A Mapping Diagram
 LF.COMP Composition of Linear Functions
 LF.INV Inverse of a Linear Function
 LF.FORM Forms of a Linear Function
 LF.LEq Solving Linear Equations with Linear Functions
 LF.APP Linear Function Applications (not yet ready)
 X.LF:  Exercises for Linear Functions
     

    3   (QF) Quadratic Functions
QF.FORM Forms of a Quadratic Function
QF.MA  Magnification and Addition to $x^2$
QF.ID Increasing/Decreasing for Quadratic Functions
QF.COMP Symmetry and Composition of Quadratic Functions
QF.INV "Inverse" of a Quadratic Function
QF.QEq Solving Quadratic Equations with Quadratic Functions
QF.QInEq Solving Quadratic Inequalities with Quadratic Functions
    QF.APP Quadratic Function Applications
X.QF Exercises

    4    (OAF) Other Algebraic Functions
OAF.PFF Polynomial Functions Forms: Roots and Factors
OAF.RFF Rational Functions Forms: Roots, Poles and Factors
 OAF.CPPF Core Positive Power Functions- $x^n$ where $n>0$.
 OAF.CNPF Core Negative Power Functions- $x^n$ where $n<0$.
 OAF.COMP Composition and Algebraic Functions
 OAF.BRF  (Asymptotic and Other) Behavior for Rational Functions
 OW.ICPPF Inverse for Core Positive Power Functions- $\sqrt[n] x$ where $n>0$.
            [From Section OW: Other Ways to Define Functions]
 OAF.SAE Solving Equations for Algebraic Functions
 OAF.APP Algebraic Function Applications (not yet ready)
 X.OAF Exercises


  5    (OWDF) Other Ways to Define Functions
OW.FDPC Functions Defined by Piecewise Cases
OW.ICPPF  Inverse for Core Positive Power Functions $\sqrt[n] x$ where $n>0$.
OW.IMPL Implicit Functions Defined by Equations
OW.RECF Functions Defined by Recursion
X.OW Exercises
   
    6   (ELF) Exponential and Logarithmic Functions
   ELF.ELFI Exponential and Logarithmic Functions are Important. (Not Yet Done)
   ELF.CELF Core Exponential and Logarithmic Functions
   ELF.DOM.L The Domain for Logarithmic Functions
   ELF.NEL  Natural Exponential and Logarithmic Functions
   ELF.IDA Increasing/Decreasing/Asymptotes: Exponential & Logarithmic Functions
   ELF.AP  Algebraic Properties of Exp and Log Functions
   ELF.LCOMP  Linear Composition with Core Exponential and Logarithmic Functions
   ELF.INV Inverses for Exponential and Logarithmic Functions
   LF.SEQ Solving Exponential and Logarithmic Equations
   ELF.APP Exponential and Logarithmic Function Applications (Not Yet Done)
   X.ELF Exercises (Not Yet Done)

    7    (TRIG) Trigonometric Functions
    TRIG.MA  Measurement of Angles
    TRIG.CTRIG Core Trigonometric Functions
    TRIG.OTF  Other Trigonometric Functions
    TRIG.PB Periodic Behavior for Trigonometric Functions
    TRIG.ID Increasing/Decreasing for Trigonometric Functions
    TRIG.LCOMP  Linear Composition with Core Trigonometric Functions
    TRIG.SYM Symmetry of Trigonometric Functions
    TRIG.INV Inverses for Trigonometric Functions
    TRIG.SEq Solving Trigonometric Equations
    TRIG.APP Trigonometric Function Applications-Identities and Triangle Trigonometry.  (Not Yet Done)
    X.TRIG Exercises (Not Yet Done)

    8    (AEF) Algebra and Elementary Functions
    AEF.AOEF  Arithmetic Operations and Elementary Functions (+,-,x,÷)
    AEF.COMP  Composition and Elementary Functions (∘)
    AEF.INV Inverses and Elementary Functions
    AEF.SEq Solving Equations
    AEF.NSEq Numerically Solving Equations
    X.AEF Exercises (Not Yet Done)

    9    (CCD) Calculus I (Continuity and Differentiability)
*Work in Progress! (3/20/2018)
    9.1       Limits and Continuity
    9.1.1        Definitions
    9.1.15      Limit Theory
    9.1.2        The Intermediate Value Theorem
    9.1.3        The Extreme Value Theorem
    9.2      The derivative
    9.2.1        Definitions
    9.2.2        Core Functions
    9.2.3        Calculating Rules
    9.2.3.1         Algebra Rules 
    9.2.3.5        The Chain rule
    9.2.3.7        Implicit Differentiation
    9.3.       Numerical Applications
    9.3.1         The Differential and Linear Estimation
    9.3,2         Newton’s Method
    9.4        The Mean Value Theorem
    9.4.1         Finding Extremes with Calculus
    9.4.2        The Second Derivative: Acceleration and Concavity

CCD.DLC Definitions of Limits and Continuity
CCD.LCT *Limits and Continuity Theory
CCD.DMD The Derivative: Motivation and Definition
CCD.DCF  The Derivative: Core Functions
CCD.DCR The Derivative: Calculating Rules (Not Done Yet)
CCD.NA Numerical Applications
CCD.MVT*The Mean Value Theorem
X.CCD Exercises (Not Done Yet)

    10    (CIS)  Calculus II, Differential equations, Integration, and Series
    10.1         Euler’s method
    10.2         Definite Integration
    10.3         The Fundamental Theorem of Calculus
    10.4        Taylor and MacClaurin Theory and Practice
    10.5        Sequences and Series Tests
    10.6        Power Series
*Work in Progress! (5/2018)

CIS.EM Differential Equations with Initial Conditions- Euler's Method
CIS.DI Definite Integration
CIS.FTC The Fundamental Theorem of Calculus
CIS.TM  Taylor and MacLaurin Theory and Practice
CIS.SST Sequences and Series Tests
CIS.PS  Power Series
X.CIS Exercises (Not Done Yet)

    11    Multi-variable Functions and Calculus
    11.1     1 Variable 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
 
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled GNU Free Documentation License.

Preface
Acknowledgements: Robert Beezer !