Intermediate Algebra & Analytic Geometry

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 FormulaeSection 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 SummarySection 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 FormulaeSection 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 FormulaeAnswersIndex