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Introduction to differential geometry for engineers /

Bibliographic Details
Main Author: Doolin, B. F. (Author)
Other Authors: Martin, Clyde F.
Format: Book
Language:English
Published: Mineola, N.Y. : Dover Publications, Incorporated, 2012.
Edition:Dover ed.
Subjects:
Geometry, Differential.
Géométrie différentielle.
Online Access:Table of contents
Publisher description
Table of Contents:
  • Machine generated contents note: 1. Introduction
  • 2. Manifolds And Their Maps
  • 2.1. Differentiable Manifolds
  • 2.2. Examples
  • 2.3. Manifold Maps
  • 3. Tangent Spaces
  • 3.1. Tangent Space of Sphere
  • 3.2. Equivalence Classes of Curves
  • 3.3. Tangent Space in General
  • 3.4. Tangent Space Maps
  • 4. Vector Fields
  • 4.1. Vector Fields
  • 4.2. Derivations
  • 4.3. Digression on Notation
  • 4.4. Isomorphism
  • 4.5. Algebra
  • 4.6. Example of a Lie Algebra
  • 5. Exterior Algebra
  • 5.1. Addition of Forms
  • 5.2. Wedge Product
  • 5.3. Contraction of Forms; Vectors
  • 5.4. Equation of a Plane
  • 5.5. Use of Determinants
  • 5.6. Solution of Linear Equations
  • 5.7. Linear Transformations
  • 6. Lie Groups And Actions
  • 6.1. Lie Groups
  • 6.2. Group Action
  • 6.3. One-Parameter Subgroups
  • 6.4. Symplectic Group
  • 7. Homogeneous Spaces
  • 8. Grassmannian Techniques
  • 8.1. Linear Optimal Control
  • 8.2. Grassmannian
  • 8.3. Application
  • 9. Concluding Remarks
  • 10. Appendix: Vector Calculus
  • 10.1. Real Euclidean Space
  • 10.2. Topological Spaces
  • 10.3. Compactness
  • 10.4. Continuity
  • 10.5. Derivative
  • 10.6. Inverse Function Theorems.