Intermediate Algebra & Analytic Geometry

Intermediate Algebra & Analytic Geometry

1st Edition - January 1, 1965

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  • Authors: William R. Gondin, Bernard Sohmer
  • eBook ISBN: 9781483278209

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Description

Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, systems involving quadratics, and determinants. Topics include determinants of higher order, application of Cramer's rule, second-order determinants, systems linear in quadratic terms, systems treatable by substitution, systems with a linear equation, and other systems treated by comparison. The manuscript ponders on trigonometric functions and equations, straight lines, and points, distances, and slopes, including intersection points of lines, perpendicular distances, angles between lines, positions of points, inverse trigonometric functions, and trigonometric equations. The publication is a valuable source of data for readers interested in intermediate algebra and analytic geometry.

Table of Contents


  • Section One—Introduction

    1 Preliminary Review

    The Purpose of These Books

    What is Advanced Mathematics?

    Advanced Approaches to Mathematics

    Recommended Sequence of Study

    Recommended Pace of Study

    Recommended Use of Practice Exercises

    Assumed Background of the Reader

    Note on Tables of Formulae

    Review Table of Elementary Formulae

    R-Series Formulae

    Section Two—Intermediate Algebra

    2 Linear Equations in Two Unknowns

    Preliminary Definitions

    Systems of Two Equations

    Determinate and Indeterminate Systems

    Consistent and Inconsistent Equations

    Independent and Dependent Equations

    Defective and Redundant Systems

    Summary

    3 Variables, Functions, and Graphs

    Algebra and Geometry

    Variables and Functions

    Tables of Values

    Explicit and Implicit Functions

    First Quadrant Graphs

    Rectangular Co-Ordinates

    Graphic Interpretations

    Summary

    Note on Sequence of Study

    4 Quadratic Equations in One Variable

    A Different Type of Problem

    Preliminary Definitions

    Solution by Extracting Square Roots

    Solution by Factoring

    Solution by Completing the Square

    Solutions by Formula

    'Imaginary' Roots

    Equations Equivalent to Quadratics

    Graphic Interpretation of Quadratic Roots

    Physical Interpretation of Quadratic Roots

    Summary

    5 Systems Involving Quadratics

    Preliminary Definitions

    Note on Sequence of Topics

    Defective Systems

    Systems with a Linear Equation

    Systems Quadratic in Only One Variable

    Other Systems Treated by Comparison

    Systems Linear in Quadratic Terms

    Systems with Only One Linear Term

    Systems of Other Special Types

    Systems Treatable by Substitution

    Summary

    Note on Sequence of Study

    6 Linear Equations in N Variables

    Systems in N Variables

    Linear Dependence and Independence

    Linear Consistency and Inconsistency

    Geometric Interpretation in Schematic Form

    Summary

    7 Determinants

    A Note on Sequence of Topics

    Second-Order Determinants

    Determinants of Higher Order

    Expansion by Minors

    Further Properties of Determinants

    Applications of Cramer's Rule

    Properties of Determinants, Continued

    Exceptions to Cramer's Rule

    Summary

    Table of Determinant Formulae

    8 Trigonometric Functions and Equations

    Trigonometric Equations

    Preliminary Algebraic Treatment

    Inverse Trigonometric Functions

    Angles of Any Magnitude

    Radian Measure of Angles

    Trigonometric Functions of Any Angle

    Table: Typical Values of Trigonometric Functions

    Applications of Generalized Trigonometric Functions

    Complete Solution of Trigonometric Equations

    Graphs of Trigonometric Functions

    Variations of Trigonometric Functions

    Summary

    Section Three—Plane Analytic Geometry

    9 Points, Distances, and Slopes

    What is Analytic Geometry?

    Positions of Points

    Distances or Lengths

    Slopes

    Angles Between Lines

    Problem-Solving Technique

    Summary with Formulae

    10 Straight Lines

    Point-Slope Line Formulae

    Two-Point Line Formulae

    Points on Lines

    Intersection Points of Lines

    Parallel Lines

    Perpendicular Lines

    Perpendicular Distances

    Problem-Solving Technique

    Summary with Formulae

    11 Conic Sections—Parabolas

    Conic Sections as Loci

    Parabolas: Definitions and Construction

    Standard Equations for Parabolas

    Applications of Parabola Formulae

    12 Ellipses and Circles

    Ellipses: Definitions and Construction of Ellipses

    Eccentricity of Ellipses

    The Standard Equation for an Ellipse

    Applications of Ellipse Formulae

    Circles: Formula and Applications

    13 Hyperbolas

    Definitions and Construction

    Eccentricity of Hyperbolas

    Standard Equation for a Hyperbola

    Applications of Hyperbola Formulae

    Summary (Chapters XI, XII, XIII) with Formulae

    Section Four—Solid Analytic Geometry

    14 Points and Directions in Space

    Three-Dimensional Rectangular Co-Ordinates

    Point and Length Formulae

    Direction Numbers and Cosines

    Parallel and Perpendicular Directions

    15 Surfaces and Lines in Space

    Normal Plane-Formulae

    Parallel and Perpendicular Planes

    Point Plane-Formulae

    Lines as Intersections of Planes

    Quadric Surfaces

    Footnote on Hyper-Geometry

    Summary (Chapters XIV and XV) with Formulae

    Answers

    Index

Product details

  • No. of pages: 288
  • Language: English
  • Copyright: © Made Simple 1967
  • Published: January 1, 1965
  • Imprint: Made Simple
  • eBook ISBN: 9781483278209

About the Authors

William R. Gondin

Bernard Sohmer

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