Analytic Geometry

Tailored for a first course in the study of analytic geometry, the text emphasizes the essential elements of the subject and stresses the concepts needed in calculus. This new edition was revised to present the subject in a modern, updated manner. Color is used to highlight concepts. Technology is integrated with the text, with references to the Calculus Explorer and tips for using graphing calculators.

Several new topics, including curve fitting involving mathematical modeling, were added. Exercises were updated. New and varied applications from medicine to navigation to public health were added.

FEATURES:

• Historical comments and real-world examples and exercises add to student interest.
• A strong graphing emphasis effectively prepares students for calculus. Tips on the use of a graphing calculator are included.
• Curve sketching, including mathematical modeling, are emphasized.
• Many new topics were added to enrich the text.
• End-of-chapter material now includes Key Terms, Chapter Review exercises, and a Chapter Test.

Chapter 1: Fundamental Concepts

Basic Concepts
Inclination and Slope of a Line
Division of a Line Segment
Analytic Proofs of Geometric Theorems
Relations and Functions
The Equation of a Graph

Chapter 2: The Straight Line and the Circle

Lines and First-Degree Equations
Other Forms of First-Degree Equations
Intersection of Lines
Directed Distance from a Point to a Line
Families of Lines
Circles
Families of Circles
Translation of Axes

Chapter 3: Conics

The Parabola
Parabolas With Vertex at (h, k)
The Ellipse
The Hyperbola

Chapter 4: Simplification of Equations

Simplification by Translation
Rotation of Axes
Simplification by Rotations and Translations
Identification of a Conic

Chapter 5: Algebraic Curves

Polynomials
Rational Functions
Slant Asymptotes
Fractional Equations

Chapter 6: Transcendental Functions

Trigonometric Functions
The Exponential Function
Logarithms
Addition of Ordinates

Chapter 7: Polar Coordinates

The Polar Coordinate System
Relations Between Rectangular and Polar Coordinates
Graphs of Polar-Coordinate Equations
Aids in Graphing Polar-Coordinate Equations
Polar Equations of Lines and Circles
Polar Equations of Conics
Trigonometric Equations
Intersections of Polar-Coordinate Graphs

Chapter 8: Parametric Equations

Parametric Equations
Applications of Parametric Equations

Chapter 9: Space Coordinates and Surfaces

Space Coordinates
Surface of Revolution and Quadric Surfaces
Cylindrical and Spherical Coordinates

Chapter 10: Vectors, Planes, and Lines

Operations on Vectors
Vectors in Space
The Scalar Product of Two Vectors
The Equation of a Plane
Vector Equation of a Line
The Vector Product

Chapter 11: Curve Fitting

Method of Least Squares
Exponential Models