Analytic Geometry

By David A. Smith

Analytic geometry presents the following topics: lines, planes, circles, conics, vectors, rectangular coordinates, polar coordinates, cylindrical coordinates, spherical coordinates, translations, and rotations. The goal is to be able to construct correct and rigorous solutions to exercises in algebra, geometry, and trigonometry. Analytic geometry often starts with a detailed introduction to the Cartesian plane, which some readers may have seen, with the idea of having a more detailed analytic approach than say in a basic algebra course. Then vectors, lines, and conic sections are explored at the same level of detail. Analytic geometry usually also covers transformations of coordinate systems and curve sketching which are important topics for any analytic geometry student preparing for calculus. Other important topics include solid analytic geometry including different coordinate systems and a survey of types of surfaces in analytic geometry.