تانسورها ، رياضيات نظريه نسبيت و مكانيك پيوسته

كتاب تانسورها - رياضيات نظريه نسبيت و مكانيك پيوسته (Tensors - The Mathematics of Relativity Theory and Continuum Mechanics)، مشتمل بر 300 صفحه، در 7 فصل، با فرمت PDF، به زبان انگليسي، همراه با مثال ها و تمرينات متعدد به ترتيب زير گردآوري شده است:

Chapter 1: Finite Dimensional Vector Spaces and Linear Mappings

• Fields
• Finite-Dimensional Vector Spaces
• Linear Mappings of a Vector Space
• Dual or Covariant Vector Spaces

Chapter 2: Tensor Algebra

• Second-Order Tensors
• Higher Order Tensors
• Exterior or Grassmann Algebra
• Inner Product Vector Spaces and the
• Metric Tensor

Chapter 3: Tensor Analysis on a Differentiable Manifold

• Differentiable Manifolds
• Tangent Vectors, Cotangent Vectors, and Parametrized Curves
• Tensor Fields over Differentiable Manifolds
• Differential Forms and Exterior Derivatives

Chapter 4: Differentiable Manifolds with Connections

• The Affine Connection and Covariant Derivative
• Covariant Derivatives of Tensors along a Curve
• Lie Bracket, Torsion, and Curvature Tensor

Chapter 5: Riemannian and Pseudo-Riemannian Manifolds

• Metric Tensor, Christoffel Symbols and Ricci Rotation Coefficients
• Covariant Derivatives and the Curvature Tensor
• Curves, Frenet Serret Formulas and Geodesics
• Special Coordinate Charts

Chapter 6: Special Riemannian and Pseudo-Riemannian Manifolds

• Flat Manifolds
• The Space of Constant Curvature
• Einstein Spaces
• Conformally Flat Spaces

Chapter 7: Hypersurfaces, Submanifolds, and Extrinsic Curvature

• Two-Dimensional Surfaces Embedded in a Three Dimensional Space
• (N −1)-Dimensional Hypersurface
• D-Dimensional Submanifolds

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تانسورها ، رياضيات نظريه نسبيت و مكانيك پيوسته