ERROR

Chúng tôi xin lỗi - mặc dù chúng tôi đã cố gắng hết sức: đã xảy ra lỗi
Typedatabase
MessageYou have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near "AND SUBSTRING(categories_id,4,1) != "0") AS cat4, (SELECT categorie..." at line 5
QuerySELECT (SELECT categories_id FROM categories_description WHERE language_id = 20 AND categories_id = 000) AS cat1, (SELECT categories_id FROM categories_description WHERE language_id = 20 AND categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2, (SELECT categories_id FROM categories_description WHERE language_id = 20 AND categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3, (SELECT categories_id FROM categories_description WHERE language_id = 20 AND categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4, (SELECT categories_name FROM categories_description WHERE language_id = 20 AND categories_id = 000) AS cat1name, (SELECT categories_name FROM categories_description WHERE language_id = 20 AND categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2name, (SELECT categories_name FROM categories_description WHERE language_id = 20 AND categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3name, (SELECT categories_name FROM categories_description WHERE language_id = 20 AND categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4name, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = 000) AS cat1url, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2url, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3url, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4url, (SELECT wod_count_products FROM categories WHERE categories_id = 000) AS cat1cnt, (SELECT wod_count_products FROM categories WHERE categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2cnt, (SELECT wod_count_products FROM categories WHERE categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3cnt, (SELECT wod_count_products FROM categories WHERE categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4cnt

Louis Auslander & Robert E. MacKenzie 
Introduction to Differentiable Manifolds [EPUB ebook] 

Support

The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary differential equations. The authors offer a coherent treatment of the fundamental concepts of Lie group theory, and they present a proof of the basic theorem relating Lie subalgebras to Lie subgroups. Additional topics include fiber bundles and multilinear algebra. An excellent source of examples and exercises, this graduate-level text requires a solid understanding of the basic theory of finite-dimensional vector spaces and their linear transformations, point-set topology, and advanced calculus.

€17.05
payment methods
Buy this ebook and get 1 more FREE!
Language English ● Format EPUB ● ISBN 9780486158082 ● Publisher Dover Publications ● Published 2012 ● Downloadable 3 times ● Currency EUR ● ID 5824462 ● Copy protection Adobe DRM
Requires a DRM capable ebook reader

More ebooks from the same author(s) / Editor

5,049,822 Ebooks in this category