It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity. 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. This version allows the user to perform many tensor operations, including derivatives and series expansions, along with routines to obtain the typical General Relativity tensors. Introduction Lie algebras and the Lie groups which they generate. Pytearcat syntax resembles the usual physics notation for tensor calculus, such as the Einstein notation for index contraction. 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. Linear algebra forms the skeleton of tensor calculus and differential geometry. 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. Integrals of Differential Forms8.7.Using a clear, step-by-step approach, this book explains one of the more difficult-yet crucial-topics in physics. An Application to Physics: Maxwell's Equations8.6. Exterior Products and Differential Forms8.4. Getting Acquainted with Differential Forms8.1. Discussion Questions and ExercisesChapter 8. Derivatives of Basis Vectors and the Affine Connection7.5. Metrics on Manifolds and Their Tangent Spaces7.3. Tangent Spaces, Charts, and Manifolds7.2. An introductory Tensor Calculus for Physics book is a most welcome addition to the libraries of both young students in physics and instructors with teaching duties at the advanced undergraduate level. Discussion Questions and ExercisesChapter 7. Discussion Questions and ExercisesChapter 6. Tensor Calculus for Physics: A Concise Guide by Neuenschwander, Dwight E. Disccussion Questions and ExercisesChapter 5. Divergence, Curl, and Laplacian with Covariant Derivatives4.8. Relation of the Affine Connection to the Metric Tensor4.7. Transformation of the Affine Connection4.5. Discussion Questions and ExercisesChapter 4. Contravariant, Covariant, and "Ordinary" Vectors3.6. This booklet contains an explanation about tensor calculus for students of physics and engineering with a basic knowledge of linear algebra. The Distinction between Distance and Coordinate Displacement3.2. Tensor Calculus Taha Sochi OctoDepartment of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT. Discussion Questions and ExercisesChapter 3. Integration Measures and Tensor Densities2.10. Two-Index Tensor Components as Products of Vector Components2.8. Discussion Questions and ExercisesChapter 2. Neuenschwanders Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. Transformation Coefficients as Partial Derivatives1.8. Euclidean Vector Operations with and without Coordinates1.7. Derivatives of Euclidean Vectors with Respect to a Scalar1.4. Euclidean Vectors, without Coordinates1.3. Why Aren't Tensors Defined by What They Are?1.2.
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