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추가 및 수정(2003년 8월) 최진원 김래용 임숙빈


  1. Differentiable manifold

    1. Definition [ps] [pdf] [TeX]
    2. Examples and review of implicit function theorem [ps] [pdf] [TeX]
    3. Further examples [ps] [pdf] [TeX]
    4. Smooth maps [ps] [pdf] [TeX]
    5. Quotient smooth manifold [ps] [pdf] [TeX]

  2. Tangent bundle and differential

    1. Tangent vector [ps] [pdf] [TeX]
    2. Tangent bundle [ps] [pdf] [TeX]
    3. Differential of a smooth map [ps] [pdf] [TeX]

  3. Submanifolds

    1. Definitions [ps] [pdf] [TeX]
    2. Regular value and transversality [ps] [pdf] [TeX] [flash]
    3. Examples [ps] [pdf] [TeX]

  4. Vector fields and flow

    1. Vector fields [ps] [pdf] [TeX]
    2. Fundamental theorem of ODE [ps] [pdf] [TeX]
    3. Local flow [ps] [pdf] [TeX]
    4. Global flow [ps] [pdf] [TeX]

  5. Distribution & Frobenius theorem

    1. Lie Bracket [ps] [pdf] [TeX]
    2. Lie derivative and phi - related vector fields [ps] [pdf] [TeX]
    3. Distribution and Frobenius theorem(local part) [ps] [pdf] [TeX]
    4. Frobenius theorem(global part) [ps] [pdf] [TeX]
    5. Foliation [ps] [pdf] [TeX]

  6. Review of Multilinear Algebra

    1. Tensor Product [ps] [pdf] [TeX]
    2. Tensor as multilinear functions [ps] [pdf] [TeX]

  7. Tensor bundles and Differential Forms

    1. Vector Bundles [ps] [pdf] [TeX]
    2. Construction of new vector bundles from a given one [ps] [pdf] [TeX]
    3. Tensor fields and forms [ps] [pdf] [TeX]
    4. Exterior Derivative [ps] [pdf] [TeX]
    5. Effect of mappings [ps] [pdf] [TeX]
    6. de Rham cohomology [ps] [pdf] [TeX]
    7. Lie derivative and Interior derivative [ps] [pdf] [TeX]

  8. Topology of Manifold

    1. Topology of Manifold and Partition of Unity [ps] [pdf] [TeX]
    2. Manifold with Boundary [ps] [pdf] [TeX]
    3. Orientation [ps] [pdf] [TeX]

  9. Integration on manifolds

    1. Integration of n-forms on n-dimensional oriented manifold M [ps] [pdf] [TeX]
    2. Stoke's Theorem [ps] [pdf] [TeX]
    3. Classical Versions in R^n [ps] [pdf] [TeX]
    4. Integration of a function on M [ps] [pdf] [TeX]