I Differential Calculus.- 1. Categories.- 2. Topological vector spaces.- 3. Derivatives and composition of map.- 4. Integration and Taylor's formula.- 5. The inverse mapping theorem.- II Manifolds.- 1. Atlases, charts, morphisms.- 2. Submanifolds, immersions, submersions.- 3. Partitions of unity.- 4. Manifolds with boundary.- III Vector Bundles.- 1. Definition, pull-backs.- 2. The tangent bundle.- 3. Exact sequences of bundles.- 4. Operations on vector bundles.- 5. Splitting of vector bundles.- IV Vector Fields and ...
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I Differential Calculus.- 1. Categories.- 2. Topological vector spaces.- 3. Derivatives and composition of map.- 4. Integration and Taylor's formula.- 5. The inverse mapping theorem.- II Manifolds.- 1. Atlases, charts, morphisms.- 2. Submanifolds, immersions, submersions.- 3. Partitions of unity.- 4. Manifolds with boundary.- III Vector Bundles.- 1. Definition, pull-backs.- 2. The tangent bundle.- 3. Exact sequences of bundles.- 4. Operations on vector bundles.- 5. Splitting of vector bundles.- IV Vector Fields and Differential Equations.- 1. Existence theorem for differential equations.- 2. Vector fields, curves, and flows.- 3. Sprays.- 4. The exponential map.- 5. Existence of tubular neighborhoods.- 6. Uniqueness of tubular neighborhoods.- V Differential Forms.- 1. Vector fields, differential operators, brackets.- 2. Lie derivative.- 3. Exterior derivative.- 4. The canonical 2-form.- 5. The Poincar??? lemma.- 6. Contractions and Lie derivative.- 7. Darboux theorem.- VI The Theorem of Frobenius.- 1. Statement of the theorem.- 2. Differential equations depending on a parameter.- 3. Proof of the theorem.- 4. The global formulation.- 5. Lie groups and subgroups.- VII Riemannian Metrics.- 1. Definition and functoriality.- 2. The Hilbert group.- 3. Reduction to the Hilbert group.- 4. Hilbertian tubular neighborhoods.- 5. Non-singular bilinear tensors.- 6. Riemannian metrics and sprays.- 7. The Morse-Palais lemma.- VIII Integration of Differential Forms.- 1. Sets of measure 0.- 2. Change of variables formula.- 3. Orientation.- 4. The measure associated with a differential form.- IX Stokes' Theorem.- 1. Stokes' theorem for a rectangular simplex.- 2. Stokes' theorem on a manifold.- 3. Stokes' theorem with singularities.- 4. The divergence theorem.- 5. Cauchy's theorem.- 6. The residue theorem.- The Spectral Theorem.- 1 Hilbert space.- 2 Functionals and operators.- 3 Hermitian operators.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Edition:
2nd Softcover Reprint of the Original 2nd 1985 edition
Publisher:
Springer
Published:
1988
Language:
English
Alibris ID:
18108772148
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Fine. Trade paperback (US). Glued binding. 230 p. Contains: Unspecified. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Edition:
2nd Softcover Reprint of the Original 2nd 1985 edition
Publisher:
Springer
Published:
1988
Language:
English
Alibris ID:
18108687786
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New. Trade paperback (US). Glued binding. 230 p. Contains: Unspecified. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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Very Good in Good jacket. 230pp, octavo, hc w/jacket, tight binding, clean throughout, orange cloth, tight binding, clean throughout, clean boards with sharp corners, owner's name, jacket is mild toned and soiled with tears to the edges and corners.
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Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority!
Edition:
2nd Softcover Reprint of the Original 2nd 1985 edition
Publisher:
Springer
Published:
1988
Language:
English
Alibris ID:
18078846925
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Standard Shipping: $4.71
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Fair. Connecting readers with great books since 1972. Used textbooks may not include companion materials such as access codes, etc. May have condition issues including wear and notes/highlighting. We ship orders daily and Customer Service is our top priority!
