This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.

This book will prove useful to undergraduate trigonometric students.

Contenu

Preface

The Coordinate System-Fundamental Relations
1-1 Introduction
1-2 Directed Lines
1-3 Cartesian Coordinates
1-4 Projections of a Line Segment on Horizontal and Vertical Lines
1-5 Point of Division on a Line Segment
1-6 Distance between Two Points
1-7 Slope of a Line
1-8 Parallel and Perpendicular Lines
1-9 Angle Formed by Intersecting Lines
1-10 Analytic Proofs of Geometric Theorems
The Straight Line
2-1 Equation and Locus
2-2 The Graph of an Equation
2-3 The Graph of a Linear Equation
2-4 The Point-Slope Equation
2-5 The Two-Point Equation
2-6 The Slope-Intercept Equation
2-7 The First-Degree Equation
2-8 Intersection of Lines
2-9 The Normal Equation of the Straight Line
2-10 Distance from a Line to a Point
2-11 Families of Lines
2-12 Families of Lines through the Intersection of Two Lines
Graphs of Nonlinear Equations
3-1 Introduction
3-2 Intercepts
3-3 Symmetry
3-4 Extent
3-5 Horizontal and Vertical Asymptotes
3-6 Graphing Equations
Transformation of Coordinates
4-1 Introduction
4-2 Translation of Axes
4-3 Rotation of Axes
Graphing the Equation Ax2 + By2 + Cx + Dy + E = 0
5-1 Introduction
5-2 Case I: A = B
5-3 Case II: Either A = 0 or B = 0
5-4 Case III: A and B of the Same Sign, A B
5-5 Case IV: A and B of Different Signs
The Conic Sections
6-1 Introduction
6-2 The Circle
6-3 Families of Circles
6-4 The Parabola
6-5 Applications
6-6 The Ellipse
6-7 Applications
6-8 The Hyperbola
6-9 General Definition of the Conic Sections
The General Second-Degree Equation
7-1 Introduction
7-2 The Reduction of (7-1) to the Form (5-1)
7-3 Invariants and Identification
Parametric Equations
8-1 Some Basic Concepts
8-2 Parametric Representation-Introduction
8-3 Parametric Representation-Some Examples
Polar Coordinates
9-1 Introduction
9-2 Definitions
9-3 Sketching Polar Curves
9-4 Intersection of Polar Curves
9-5 Polar Equations of the Conics
Rectangular Coordinates in Three Dimensions
10-1 The Coordinate System
10-2 The Distance Formula
10-3 Planes Parallel to the Coordinate Planes
10-4 Directions on a Line
Surfaces and Curves
11-1 Introduction
11-2 Traces and Sections
11-3 Intercepts and Symmetry
11-4 Sketching Surfaces
11-5 Cylindrical Surfaces
11-6 Projections of Curves on the Coordinate Planes
11-7 Surfaces of Revolution
11-8 Cylindrical Coordinates
11-9 Spherical Coordinates
Lines and Planes
12-1 Parametric Equations of a Line
12-2 Symmetric Equations of a Line
12-3 The Plane
12-4 Distance from a Point to a Plane
12-5 More about Lines