Test Bank for Elementary Differential Geometry, (2nd Edition) by Barrett O’neill

  • ISBN-10:  120887355 / ISBN-13:  9780120887354
  • Ebook Details

    • Edition: 2nd Edition
    • Format: Downloadable ZIP Fille
    • Resource Type : Testbank
    • Publication: 2006
    • Duration: Unlimited downloads
    • Delivery: Instant Download

    $35.00 $30.00

    SKU: e70c3de852f3 Categories: ,

    Table of content:

    Chapter 1: Calculus on Euclidean Space:
    Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings.

    Chapter 2: Frame Fields:
    Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations.

    Chapter 3: Euclidean Geometry:
    Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves.

    Chapter 4: Calculus on a Surface:
    Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds.

    Chapter 5: Shape Operators:
    The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution.

    Chapter 6: Geometry of Surfaces in R3:
    The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces.

    Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet.

    Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard.


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