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 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 ! |