عنوان

Multivariable Calculus and Differential Geometry.

شابک

3110369540

شابک

9783110369540

شابک اشتباه

3110369494

شابک اشتباه

9783110369496

عنوان اصلي

Multivariable Calculus and Differential Geometry.

نام عام مواد

[Book]

محل نشرو پخش و غیره

Berlin/Boston, Germany :

نام ناشر، پخش کننده و غيره

De Gruyter,

تاریخ نشرو بخش و غیره

2015.

تاریخ نشرو بخش و غیره

©2015

نام خاص و کميت اثر

1 online resource (366)

عنوان فروست

De Gruyter graduate.

متن يادداشت

Includes bibliographical references (page 349) and index.

متن يادداشت

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.

متن يادداشت

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.

بدون عنوان

0

بدون عنوان

8

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

MIL

شماره انبار

802032

عنوان

Multivariable calculus and differential geometry.

شماره استاندارد بين المللي کتاب و موسيقي

3110369494

موضوع مستند نشده

Geometry, Differential.

موضوع مستند نشده

Geometry, Differential.

موضوع مستند نشده

MATHEMATICS-- Geometry-- General.

موضوع مستند نشده

QA

شماره

شماره رده

مستند نام اشخاص تاييد نشده

Walschap, Gerard.

تاريخ عمليات

20200823095500.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y