Space Analytic Geometry (Second Edition)

Author: Yang Wenmao
Publisher: Wuhan University Press
Book Description:
Since its publication, this book has been nearly a decade old. Although it has been revised over the years, it still feels like it can be further improved. For the second edition, considering that some majors have reduced the teaching hours for the "Spatial Analytic Geometry" course and combining my teaching practices over the past decade, the following revisions and deletions have been made:
1. The two chapters "Spatial Coordinate Systems" and "Vector Algebra," which serve as prerequisite knowledge for this course, have been combined into one chapter after some content has been removed.
2. Chapter 7 "Projective Geometry," which was only used as an extension and enhancement in the first edition, has been deleted due to limited teaching hours.
3. The new version features more concise wording and more standardized mathematical terms and symbols (e.g., "vector" is changed to "vector," and "projection" in formulas is changed to "Prj," etc.).
4. Some examples and illustrations have been modified and added.
5. Chapters marked with "" in the book are optional and not required.
Table of Contents:
Chapter 1: Spatial Coordinate Systems and Vector Algebra
1.1 Spatial Rectangular Coordinate Systems
1.1.1 Concept of Spatial Rectangular Coordinate Systems
1.1.2 Two Simple Problems
1.1.3 Cylindrical and Spherical Coordinate Systems
1.2 Equations of Surfaces and Curves
1.2.1 Equations of Surfaces
1.2.2 Equations of Curves
1.3 Concepts of Vectors and Linear Operations on Vectors
1.3.1 Vectors and Their Geometric Representation
1.3.2 Vector Addition
1.3.3 Scalar Multiplication of Vectors
1.3.4 Collinear or Coplanar Vectors
1.4 Projection of Vectors on Axes and Coordinates of Vectors
Chapter 1: Spatial Coordinate Systems and Vector Algebra
1.1 Spatial Rectangular Coordinate Systems
1.1.1 Concept of Spatial Rectangular Coordinate Systems
1.1.2 Two Simple Problems
1.1.3 Cylindrical and Spherical Coordinate Systems
1.2 Equations of Surfaces and Curves
1.2.1 Equations of Surfaces
1.2.2 Equations of Curves
1.3 Concepts of Vectors and Linear Operations on Vectors
1.3.1 Vectors and Their Geometric Representation
1.3.2 Vector Addition
1.3.3 Scalar Multiplication of Vectors
1.3.4 Collinear or Coplanar Vectors
1.4 Projection of Vectors on Axes and Coordinates of Vectors
1.4.1 Projection of Vectors on Axes
1.4.2 Coordinates of Vectors
1.4.3 Linear Operations on Vectors Using Coordinates
1.5 Inner Product of Vectors
1.5.1 Concept of Inner Product of Vectors
1.5.2 Inner Product Operation Using Coordinates
1.5.3 Direction Cosines
1.6 Outer Product and Mixed Product of Vectors
1.6.1 Concept of Outer Product and Mixed Product of Vectors
1.6.2 Outer Product Operation Using Coordinates
1.6.3 Calculation of Mixed Product Using Coordinates
1.6.4 Double Outer Product Formula
Chapter 2: Planes and Lines
2.1 Equations of Planes
2.1.1 Point-Perpendicular Form of Plane Equations
2.1.2 General Equation of a Plane
2.1.3 Intercept Form of Plane Equations
2.1.4 Parametric Equation of a Plane
2.2 Normal Form of Plane Equations
2.2.1 Definition of Normal Form of Plane Equations
2.2.2 Distance from a Point to a Plane
2.3 Equations of Lines
2.3.1 Several Standard Forms of Line Equations
2.3.2 General Equation of a Line
2.3.3 Bundle of Planes
2.4 Positional Relationships Between Planes and Lines
2.4.1 Positional Relationships Between Two Planes
2.4.2 Positional Relationships Between Two Lines
2.4.3 Positional Relationships Between a Line and a Plane
2.4.4 Distance from a Point to a Line, Distance Between Two Skew Lines
Chapter 3: Special Surfaces
3.1 Parametric Equations of Spatial Curves and Surfaces
3.1.1 Parametric Equation of Spatial Curves
3.1.2 Parametric Equation of Surfaces
3.2 Cylindrical, Conical, Quadratic Cylindrical, and Quadratic Conical Surfaces
Chapter 4: Quadratic Curves and Quadratic Surfaces
Chapter 5: Orthogonal Transformations and Affine Transformations
Appendix: Conditional Extremum
Solutions and Hints to Exercises