عنوان

Aspects of differential geometry I /

شابک

1627056629

شابک

1627056637

شابک

1627057846

شابک

9781627056625

شابک

9781627056632

شابک

9781627057844

شابک اشتباه

1627056629

شابک اشتباه

1627057838

شابک اشتباه

9781627056625

شابک اشتباه

9781627057837

عنوان اصلي

Aspects of differential geometry I /

نام عام مواد

[Book]

نام نخستين پديدآور

Peter Gilkey (Univesrity of Oregon, Eugene, OR), JeongHyeong Park (Sungkyunkwan University, Suwon, Korea, Institute for Advanced Study, Seoul, Korea), Ramón Vázquez-Lorenzo (University of Santiago de Compostela, Santiago de Compostela, Spain).

محل نشرو پخش و غیره

San Rafael, California :

نام ناشر، پخش کننده و غيره

Morgan & Claypool Publishers,

تاریخ نشرو بخش و غیره

[2015]

تاریخ نشرو بخش و غیره

©2015

نام خاص و کميت اثر

1 online resource (xiii, 140 pages) :

ساير جزييات

illustrations

عنوان فروست

Synthesis lectures on mathematics and statistics,

مشخصه جلد

#15

شاپا ي ISSN فروست

1938-1751 ;

متن يادداشت

Includes bibliographical references (pages 131-133) and index.

متن يادداشت

1. Basic notions and concepts -- 1.1 Metric spaces -- 1.2 Linear algebra -- 1.3 The derivative -- 1.4 The inverse and implicit function theorems -- 1.5 The Riemann integral -- 1.6 Improper integrals -- 1.7 The change of variable theorem -- 2. Manifolds -- 2.1 Smooth manifolds -- 2.2 The tangent and cotangent bundles -- 2.3 Stokes' theorem -- 2.4 Applications of stokes' theorem -- 3. Riemannian and pseudo-Riemannian geometry -- 3.1 The pseudo-Riemannian measure -- 3.2 Connections -- 3.3 The Levi-Civita connection -- 3.4 Geodesics -- 3.5 The Jacobi operator -- 3.6 The Gauss-Bonnet theorem -- 3.7 The Chern-Gauss-Bonnet theorem.

بدون عنوان

0

متن يادداشت

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new.

منبع سفارش / آدرس اشتراک

01307586

عنوان

Aspects of differential geometry.

شماره استاندارد بين المللي کتاب و موسيقي

9781627056625

موضوع مستند نشده

Geometry, Differential.

موضوع مستند نشده

Geometry, Differential.

موضوع مستند نشده

MATHEMATICS-- Geometry-- General.

موضوع مستند نشده

MAT-- 012000

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Gilkey, Peter B.

مستند نام اشخاص تاييد نشده

Park, Jeonghyeong

مستند نام اشخاص تاييد نشده

Vázquez-Lorenzo, Ramón

تاريخ عمليات

20200823051202.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y