![]() ![]() Physical grid, where it is easy to calculate products and perform other local Nonlinear terms are calculated by transforming from theĬoefficients in the spectral series to the value of each quantity on the In a spectral series of spin-weighted spherical harmonics in the angularĭirections and a scaled Jacobi polynomial basis in the radial direction, asĭescribed in Part-I. Oishi Download PDF Abstract: We present a simulation code which can solve broad ranges of partialĭifferential equations in a full sphere. Exterior Products and Differential FormsĨ.5.Download a PDF of the paper titled Tensor calculus in spherical coordinates using Jacobi polynomials, Part-II: Implementation and Examples, by Daniel Lecoanet and Geoffrey M. 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. Why Aren't Tensors Defined by What They Are?ġ.2. 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. 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. Using a clear, step-by-step approach, this book explains one of the more difficult-yet crucial-topics in physics. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |