
Intermediate Algebra & Analytic Geometry
Free Global Shipping
No minimum orderDescription
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
Ratings and Reviews
There are currently no reviews for "Intermediate Algebra & Analytic Geometry"