Exterior Products and Differential FormsĨ.5. Getting Acquainted with Differential FormsĨ.3. ![]() Derivatives of Basis Vectors and the Affine ConnectionĬhapter 8. Metrics on Manifolds and Their Tangent Spacesħ.4. Tangent Spaces, Charts, and Manifoldsħ.2. Divergence, Curl, and Laplacian with Covariant Derivativesħ.1. Relation of the Affine Connection to the Metric TensorĤ.7. Transformation of the Affine ConnectionĤ.6. Contravariant, Covariant, and "Ordinary" VectorsĤ.4. The Distinction between Distance and Coordinate Displacementģ.4. Integration Measures and Tensor Densitiesģ.1. Two-Index Tensor Components as Products of Vector ComponentsĢ.9. Transformation Coefficients as Partial DerivativesĢ.5. Euclidean Vector Operations with and without Coordinatesġ.7. Derivatives of Euclidean Vectors with Respect to a Scalarġ.6. Euclidean Vectors, without Coordinatesġ.3. Srivastava 1992 This book presents a systematic introduction to the subject of tensor calculus and includes within its scope tensors, algebra of tensors, convariant differentiation of tensors and techniques of tensor methods in continuum mechanics. Why Aren't Tensors Defined by What They Are?ġ.2. numerous worked-out examples to aid in understanding. It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.ġ.1. Using a clear, step-by-step approach, the book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. Neuenschwander's Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism, they encounter the "polarization tensor." However, this piecemeal approach can set students up for misconceptions when they have to learn about tensors in more advanced physics and mathematics studies (e.g., while enrolled in a graduate-level general relativity course or when studying non-Euclidean geometries in a higher mathematics class).ĭwight E. ![]() Undergraduate physics majors are typically introduced to tensors in special-case applications. I am working through a fluid dynamics paper and came across this equation: v t +v v T 1 (1) (1) v t + v v T 1. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Tensors, therefore, allow for the convenience of coordinates while also transcending them. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. A horizontal electric field producing vertical polarization in dielectrics an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts-these are some situations where physicists employ tensors. ![]() Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. The notation tensotrial can get very complicated because we are dealing with covariant and contravariant coordinates of different dimensions, such as the Riemann tensor is a tensor (1.Using a clear, step-by-step approach, this book explains one of the more difficult-yet crucial-topics in physics. There is a tensorial product denoted por ⊗, defined as follows, if T is a tensor (r, s) and S is a tensor (m, n), tensorial product is a (r + m, s + n) tensor consisting of
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