Differential Geometry with Applications to Mechanics and Physics. (2000)

• Record Type: Book
• Further Information: Note: Yves Talpaert.
• Authors: Talpaert, Yves
• Contents: Cover; Half Title; Title Page; Copyright Page; Dedication; PREFACE; CONTENTS; LECTURE 0: TOPOLOGY AND DIFFERENTIAL CALCULUS REQUIREMENTS; 1. TOPOLOGY; 1.1 TOPOLOGICAL SPACE; 1.2 TOPOLOGICAL SPACE BASIS; 1.2.1 Definition; 1.2.2 Example of the metric space; 1.2.3 Separable space; 1.3 HAUSSDORFF SPACE; 1.4 HOMEOMORPIDSM; 1.5 CONNECTED SPACES; 1.6 COMPACT SPACES; 1.7 PARTITION OF UNITY; 2. DIFFERENTIAL CALCULUS IN BANACH SPACES; 2.1 BANACH SPACE; 2.1.1 Norm and normed vector space; 2.1.2 Banach space; 2.1.3 Isomorphism of normed vector spaces; 2.2 DIFFERENTIAL CALCULUS IN BANACH SPACES 2.2.1 Tangent mapping2.2.2. Differentiable mapping at a point; 2.2.3 Differentiable mapping; 2.2.4 Cq diffeomorphism (q≥ 1); 2.2.5 Inverse mapping and implicit function theorems; 2.2.6 Tangent mapping; 2.2.7 Immersion 1 and submersion; 2.3 DIFFERENTIATION OF Rn INTO BANACH; 2.4 DIFFERENTIATION OF Rn INTO R; 2.4.1 Directional derivative; 2.4.2 Theorem of differentiation; 2.4.3 Linear differential forms on Rn; 2.5 DIFFERENTIATION OF Rn INTO Rm; 2.5.1 Differential and Jacobian matrix; 2.5.2 Image (in Rm) of a basis vector (of Rn) under dfx; 2.5.3 Theorems; 2.5.4 Diffeomorphism and Jacobian 2.5.5 Inverse mapping theorem2.5.6 Implicit function theorem; 2.5.7 Differentiable composite mapping theorem; 2.5.8 Constant rank theorem; 2.5.9 Immersion- Submersion; 3. EXERCISES; Exercise 1.; Exercise 2.; Exercise 3.; Exercise 4.; Exercise 5; Exercise 6.; Exercise 7.; Exercise 8.; Exercise 9.; Exercise 10.; LECTURE 1: MANIFOLDS; INTRODUCTION; 1. Coordinates on S2; 2. Stereograpbic projection; 1. DIFFERENTIABLE MANIFOLDS; 1.1 CHART AND LOCAL COORDINATES; 1.1.1 Chart; 1.1.2 Local coordinates; 1.2 DIFFERENTIABLE MANIFOLD STRUCTURE; 1.2.1 Atlas; 1.2.2 Differentiable manifold structure 1.2.3 Change of charts1.3 DIFFERENTIABLE MANIFOLDS; 1.3.1 Definitions; 1.3.2 Product manifold; 1.3.3 Examples of manifolds; 1.3.4 Orientable manifolds; 2. DIFFERENTIABLE MAPPINGS; 2.1 GENERALITIES ON DIFFERENTIABLE MAPPINGS; 2.1.1 Differentiable mapping between manifolds; 2.1.2 Properties of differentiable manifolds; 2.2 PARTICULAR DIFFERENTIABLE MAPPINGS; 2.2.1 Diffeomorphism and local diffeomorphism; 2.2.2 Immersion- Submersion- Embedding; 2.3 PULL-BACK OF FUNCTION; 2.3.1 Real-valued function on manifold; 2.3.2 Pull-back offunction under differentiable mapping; 3. SUBMANIFOLDS 3.1 SUBMANIFOLDS OF Rn3.2 SUBMANIFOLD OF MANIFOLD; 4. EXERCISES; Exercise 1.; Exercise 2.; Exercise 3.; Exercise 4.; Exercise 5.; Exercise 6.; Exercise 7.; LECTURE 2: TANGENT VECTOR SPACE; 1. TANGENT VECTOR; 1.1 TANGENT CURVES; 1.1.1 Curve; 1.1.2 ""Reading"" of a curve; 1.1.3 Tangent curves; 1.2 TANGENT VECTOR; 1.2.1 First definition of tangent vector; 1.2.2 Function along a curve and tangency; 1.2.3 Derivation in the Leibniz sense; 1.2.4 Second definition of a tangent vector; 2. TANGENT SPACE; 2.1 DEFINITION OF A TANGENT SPACE; 2.2 BASIS OF TANGENT SPACE; 2.3 CHANGE OF BASIS
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2000
• Extent: 1 online resource
• Subjects: 516.3/6; Mathematical analysis; Mathematical analysis; Electronic books
• Languages: English
• ISBNs: 9781482290004; 1482290006
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.