| Part I --- Introduction and Preliminaries |
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Section I | Introduction |

| Part II --- The Logarithmic Functions |
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Section II | A Statement of Purpose for Part II |

Section III | Deriving the Logarithmic Functions |

Section IV | Defining Natural Logarithms |

Section V | Flexibility inherent within the Logarithmic Class of Functions |

Section VI | Evaluating Logarithms via an Infinite Series |

Section VII | The Logarithms of Natural Numbers |

| Part III --- Understanding the Hyperbola |
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Section VIII | A Statement of Purpose for Part III |

Section IX | The Hyperbola in Cartesian Co-ordinates |

Section X | The Geometric Definition of the Hyperbola |

Section XI | Equation of the Hyperbola in [ U-V Axis Co-ordinates ] |

Section XII | Equation of the Hyperbola in [ Polar Co-ordinates ] |

Section XIII | The Hyperbola via [ Focal-Point based Co-ordinates ] - Part I |

Section XIV | The Hyperbola via [ Focal-Point based Co-ordinates ] - Part II |

Section XV | The Asymptotes for the Hyperbola - Part I |

Section XVI | The Asymptotes for the Hyperbola - Part II |

| Part IV --- The Ellipse , the Circle and the Parabola |
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Section XVII | A Statement of Purpose for Part IV |

Section XVIII | Geometric Definition of the Ellipse |

Section XIX | Equation for the Ellipse - Part I |

Section XX | Equation for the Ellipse - Part II |

Section XXI | Equation for the Circle |

Section XXII | Equation for the Parabola |

| Part V --- A Single Type of Equation for the Circle / Ellipse / Parabola / Hyperbola |
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Section XXIII | Linkage System for the Circle / Ellipse / Parabola / Hyperbola |

Section XXIV | The Reasons for bringing-in the Orbit of a Satellite |

| Part VI --- Orbit of a Satellite moving under a Central Force |
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Section XXV | A Statement of Purpose for Part VI |

Section XXVI | Setting up the Polar Co-ordinates Reference Frame |

Section XXVII | Setting up the Central Force influencing the Satellite |

Section XXVIII | The Differential Equation involving [ R ] and [ Theta ] |

Section XXIX | Setting up the Standardized Set of Initial Conditions |

Section XXX | The Case of the Circular Orbit as the Base Scenerio |

Section XXXI | The Case of the Central Force disappearing totally |

Section XXXII | Solving for [ R ] in terms of [ Theta ] |

Section XXXIII | Summarizing on the Orbit of a Satellite |

Section XXXIV | Other Central Forces of a Similar Nature |

Section XXXV | Re-doing the Differential Equation for [ N = 2 ] |

Section XXXVI | Doing the Differential Equation for [ N = 3 ] |

Section XXXVII | A Graphic Look at the Solutions for [ N = 3 ] |

Section XXXVIII | Some Observations on the Orbits of the Satellite |

Section XXXIX | A Proposal for Further Study of Orbital Shapes |

| Part VII --- The Tangent Addition Formula |
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Section XL | A Statement of Purpose for Part VII |

Section XLI | Deriving the Tangent Addition Formula |

Section XLII | The Tangent Addition Formula in Action |

Section XLIII | Tangent Additions and the Pascal Triangle |

Section XLIV | Algebraic Equations arising from { Tangent of [ Pi-over-4 ] = 1 } |

| Part VIII --- The Arctangent Function |
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Section XLV | A Statement of Purpose for Part VIII |

Section XLVI | Deriving the Arctangent Function |

Section XLVII | Using the Ratio of Areas to define an Angle |

Section XLVIII | Some Graphics related to the Arctangent Function |

| Part IX --- Concluding Remarks |
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Section XLIX | Concluding Remarks |