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Analytic Geometry with Calculus by Robert C. Yates



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Analytic Geometry with Calculus by Robert C. Yates , University of South Florida.
Certain features of the book are listed here as a guide to the reader before he begins a detailed study of the text. In the geometry of the plane, rectangular and polar coordinates are introduced at the same time and used interchangeably throughout. Lines are characterized by direction numbers for wider application and to facilitate transition to three-space geometry. The concepts of derivative and its inverse are presented early so that their applications to direction of a curve, motion of points, plane areas, tangents and normals to surfaces and curves in three-space, and volumes bounded by surfaces considerably enhance the subject matter. Discussion of the conies begins with the fundamental consideration of plane sections of a right circular cone, thus establishing their proper designation as conic sections. The customary `higher plane
curves make their natural appearance as important loci connected with various mechanical devices such as cams, gears, and linkages. There are treatments of diameters of the conics and diametral planes of the quadrics which provide a firm foundation for further study of geometry. The usual treatment of transformations is amplified and extended to plane mappings, some given in matrix form. Ruled surfaces are studied and attention is focused upon their important application in the construction of space gears.

Analytic Geometry with Calculus by Robert C. Yates cover the following topics.

  • I.THE PLANE
    1. The Real Number System-Graphs
    2. Measures
    3. Variables, Functions, Limits, Continuity
    4. The Derivative
    5. Functions Whose Derivatives Are Known
    6. The Straight Line
    7. The Circle
    8. Conics
    9. The Conies: Their Properties and Applications
    10. Some Mechanical Motions and Loci
    11. Transformations
    12. * Mapping

  • II.THREE -Space
    13. Coordinate Systems-Measures
    14. Planes and Lines
    15. Surfaces and Curves
    16. Tangents and Normals
    17. Special Surfaces
    18. * Volumes
    19. Quadric Surfaces

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