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

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

(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

QF.FORM Forms of a Quadratic Function
QF.MA  Magnification and Addition to $x^2$
QF.COMP Symmetry and Composition of Quadratic Functions
QF.INV "Inverse" of a Quadratic Function
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

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Preface
Acknowledgements: Robert Beezer !