Martin E. Flashman
http://users.humboldt.edu/flashman
Copyright ©2013 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 (v0.5- 11/2013)
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 Sensible
Calculus 0.B.2 Functions-Introduction and Review.
http://users.humboldt.edu/flashman/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.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 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
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
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 ! |