عنوان

Multivariable Calculus and Differential Geometry.

(Number (ISBN

3110369540

(Number (ISBN

9783110369540

Erroneous ISBN

3110369494

Erroneous ISBN

9783110369496

Title Proper

Multivariable Calculus and Differential Geometry.

General Material Designation

[Book]

Place of Publication, Distribution, etc.

Berlin/Boston, Germany :

Name of Publisher, Distributor, etc.

De Gruyter,

Date of Publication, Distribution, etc.

2015.

Date of Publication, Distribution, etc.

©2015

Specific Material Designation and Extent of Item

1 online resource (366)

Series Title

De Gruyter graduate.

Text of Note

Includes bibliographical references (page 349) and index.

Text of Note

Preface -- 1 Euclidean Space -- 1.1 Vector spaces -- 1.2 Linear transformations -- 1.3 Determinants -- 1.4 Euclidean spaces -- 1.5 Subspaces of Euclidean space -- 1.6 Determinants as volume -- 1.7 Elementary topology of Euclidean spaces -- 1.8 Sequences -- 1.9 Limits and continuity -- 1.10 Exercises -- 2 Differentiation -- 2.1 The derivative -- 2.2 Basic properties of the derivative -- 2.3 Differentiation of integrals -- 2.4 Curves -- 2.5 The inverse and implicit function theorems -- 2.6 The spectral theorem and scalar products -- 2.7 Taylor polynomials and extreme values -- 2.8 Vector fields -- 2.9 Lie brackets -- 2.10 Partitions of unity -- 2.11 Exercises -- 3 Manifolds -- 3.1 Submanifolds of Euclidean space -- 3.2 Differentiablemaps on manifolds -- 3.3 Vector fields on manifolds -- 3.4 Lie groups -- 3.5 The tangent bundle -- 3.6 Covariant differentiation -- 3.7 Geodesics -- 3.8 The second fundamental tensor -- 3.9 Curvature -- 3.10 Sectional curvature -- 3.11 Isometries -- 3.12 Exercises -- 4 Integration on Euclidean space -- 4.1 The integral of a function over a box -- 4.2 Integrability and discontinuities -- 4.3 Fubini's theorem -- 4.4 Sard's theorem -- 4.5 The change of variables theorem -- 4.6 Cylindrical and spherical coordinates -- 4.6.1 Cylindrical coordinates -- 4.6.2 Spherical coordinates -- 4.7 Some applications -- 4.7.1 Mass -- 4.7.2 Center ofmass -- 4.7.3 Moment of inertia -- 4.8 Exercises -- 5 Differential Forms -- 5.1 Tensors and tensor fields -- 5.2 Alternating tensors and forms -- 5.3 Differential forms -- 5.4 Integration on manifolds -- 5.5 Manifolds with boundary -- 5.6 Stokes' theorem -- 5.7 Classical versions of Stokes' theorem -- 5.7.1 An application: the polar planimeter -- 5.8 Closed forms and exact forms -- 5.9 Exercises -- 6 Manifolds as metric spaces.

Text of Note

6.1 Extremal properties of geodesics -- 6.2 Jacobi fields -- 6.3 The length function of a variation -- 6.4 The index formof a geodesic -- 6.5 The distance function -- 6.6 The Hopf-Rinow theorem -- 6.7 Curvature comparison -- 6.8 Exercises -- 7 Hypersurfaces -- 7.1 Hypersurfaces and orientation -- 7.2 The Gaussmap -- 7.3 Curvature of hypersurfaces -- 7.4 The fundamental theorem for hypersurfaces -- 7.5 Curvature in local coordinates -- 7.6 Convexity and curvature -- 7.7 Ruled surfaces -- 7.8 Surfaces of revolution -- 7.9 Exercises -- Appendix A -- Appendix B -- Index.

0

8

Text of Note

This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

Source for Acquisition/Subscription Address

MIL

Stock Number

802032

Title

Multivariable calculus and differential geometry.

International Standard Book Number

3110369494

Geometry, Differential.

Geometry, Differential.

MATHEMATICS-- Geometry-- General.

QA

Number

Class number

Walschap, Gerard.

Date of Transaction

20200823095500.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y