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Coordinate geometry 坐标几何

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Coordinate geometry 坐标几何

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定 价：￥361.00

作 者：LutherPfahlerEisenhart　著 著

出 版 社：

出版时间：2005-5-1

I S B N：0486442616

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    内容简介
    A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. In contrast to other studies, which cover all aspects of the second dimension before going on to the third, Professor Eisenhart advances in dimension within each topic. The sphere and circle are treated together; three-dimen-sional coordinate systems are introduced along with polar coordi-nates; and quadric surfaces directly follow conic sections.
    This approach makes extensive use of determinants, but no previous knowledge is assumed; they are introduced from the beginning as a natural tool for coordinate geometry, lnvariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed and carried farther than is usual in algebra courses. Throughout the book,results are formulated precisely, with clearly stated theorems.
    Professor Eisenhart discusses the axiomatic basis of analytic geome-try, an unusual procedure in an introductory text. He presents axioms for coordinate geometry and shows that they are the algebraic equiv-alent of Hilbert's axioms for synthetic geometry.

    作者简介

    目录
    INTRODUCTION
    CHAPTER 1 Points and Lines in the PIane
    1. The Equation of the First Degree in x and y
    2. Cartesian Coordinates in the Plane
    3. Distance between Two Points·Direction Numbers and Di-rection Cosines·Angle between Directed Line Segments
    4. Internal and External Division of a Line Segment
    5. An Equation of a Line·Parametric Equations of a Line
    6. Direction Numbers and Direction Cosines of a Line·Angle between Two Lines
    7. The Slope of a Line
    8. Directed Distance from a Line to a Point
    9. Two Equations of the First Degree in x and y·Determinants of the Second Order
    10. The Set of Lines through a Point
    11. Oblique Axes
    12. The Circle
    13. R6sum6·Line Coordinates
    CHAPTER 2 Lines and PIanes in Space·Determinants
    14. Rectangular Coordinates in Space
    15. Distance between Two Points·Direction Numbers and Di-rection Cosines of a Line Segment·Angle between Two Line Segments
    16. Equations of a Line·Direction Numbers and Direction Co-sines of a Line·Angle of Two Lines
    17. An Equation of a Plane
    18. The Directed Distance from a Plane to a Point·The Dis-tance from a Line to a Point
    19. Two Equations of the First Degree in Three Unknowns·A Line as the Intersection of Two Planes
    20. Two Homogeneous Equations of the First Degree in Three Unknowns
    21. Determinants of the Third Order·Three Equations of the First Degree in Three Unknowns
    22. Three Homogeneous Equations of the First Degree in Three Unknowns
    23. Equations of Planes Determined by Certain Geometric Con-ditions·Shortest Distance between Two Lines
    24. The Configurations of Three Planes
    25. Miscellaneous Exercises·The Sphere
    26. Determinants of Any Order
    27. Solution of Equations of the First Degree in Any Number of Unknowns·Space of Four Dimensions
    CHAPTER 3 Trans[ormafions o[ Coordinates
    28. Transformations of Rectangular Coordinates
    29. Polar Coordinates in the Plane
    30. Transformations of Rectangular Coordinates in Space
    31. Spherical and Cylindrical Coordinates
    CHAPTER 4 The Conics·Locus Problems
    CHAPTER 5 The Quadric Surfaces
    APPENDIX TO CHAPTER
    INDEX

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