Mathematic Functions Basics HomePage

An Approach to Mathematic Functions Basics

by Frank C. Fung ( 1st published in December, 2014. )

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SUMMARY and KEY FINDINGS :

Summary :

Key Finding One :

Key Finding Two :

Table of Content

Table Of Content
Part I --- Introduction and Preliminaries
Section IIntroduction
Part II --- The Logarithmic Functions
Section IIA Statement of Purpose for Part II
Section IIIDeriving the Logarithmic Functions
Section IVDefining Natural Logarithms
Section VFlexibility inherent within the Logarithmic Class of Functions
Section VIEvaluating Logarithms via an Infinite Series
Section VIIThe Logarithms of Natural Numbers
Part III --- Understanding the Hyperbola
Section VIIIA Statement of Purpose for Part III
Section IXThe Hyperbola in Cartesian Co-ordinates
Section XThe Geometric Definition of the Hyperbola
Section XIEquation of the Hyperbola in [ U-V Axis Co-ordinates ]
Section XIIEquation of the Hyperbola in [ Polar Co-ordinates ]
Section XIIIThe Hyperbola via [ Focal-Point based Co-ordinates ] - Part I
Section XIVThe Hyperbola via [ Focal-Point based Co-ordinates ] - Part II
Section XVThe Asymptotes for the Hyperbola - Part I
Section XVIThe Asymptotes for the Hyperbola - Part II
Part IV --- The Ellipse , the Circle and the Parabola
Section XVIIA Statement of Purpose for Part IV
Section XVIIIGeometric Definition of the Ellipse
Section XIXEquation for the Ellipse - Part I
Section XXEquation for the Ellipse - Part II
Section XXIEquation for the Circle
Section XXIIEquation for the Parabola
Part V --- A Single Type of Equation for the Circle / Ellipse / Parabola / Hyperbola
Section XXIIILinkage System for the Circle / Ellipse / Parabola / Hyperbola
Section XXIVThe Reasons for bringing-in the Orbit of a Satellite
Part VI --- Orbit of a Satellite moving under a Central Force
Section XXVA Statement of Purpose for Part VI
Section XXVISetting up the Polar Co-ordinates Reference Frame
Section XXVIISetting up the Central Force influencing the Satellite
Section XXVIIIThe Differential Equation involving [ R ] and [ Theta ]
Section XXIXSetting up the Standardized Set of Initial Conditions
Section XXXThe Case of the Circular Orbit as the Base Scenerio
Section XXXIThe Case of the Central Force disappearing totally
Section XXXIISolving for [ R ] in terms of [ Theta ]
Section XXXIIISummarizing on the Orbit of a Satellite
Section XXXIVOther Central Forces of a Similar Nature
Section XXXVRe-doing the Differential Equation for [ N = 2 ]
Section XXXVIDoing the Differential Equation for [ N = 3 ]
Section XXXVIIA Graphic Look at the Solutions for [ N = 3 ]
Section XXXVIIISome Observations on the Orbits of the Satellite
Section XXXIXA Proposal for Further Study of Orbital Shapes
Part VII --- The Tangent Addition Formula
Section XLA Statement of Purpose for Part VII
Section XLIDeriving the Tangent Addition Formula
Section XLIIThe Tangent Addition Formula in Action
Section XLIIITangent Additions and the Pascal Triangle
Section XLIVAlgebraic Equations arising from { Tangent of [ Pi-over-4 ] = 1 }
Part VIII --- The Arctangent Function
Section XLVA Statement of Purpose for Part VIII
Section XLVIDeriving the Arctangent Function
Section XLVIIUsing the Ratio of Areas to define an Angle
Section XLVIIISome Graphics related to the Arctangent Function
Part IX --- Concluding Remarks
Section XLIXConcluding Remarks

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Original dated 2014-12-07