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Tensor Calculus for Physics - A Concise Guide (Paperback)
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Tensor Calculus for Physics - A Concise Guide (Paperback)
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Understanding tensors is essential for any physics student dealing
with phenomena where causes and effects have different directions.
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. 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. Tensors, therefore, allow for
the convenience of coordinates while also transcending them. This
makes tensors the gold standard for expressing physical
relationships in physics and geometry. Undergraduate physics majors
are typically introduced to tensors in special-case applications.
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). Dwight E. Neuenschwander's Tensor Calculus for Physics is a
bottom-up approach that emphasizes motivations before providing
definitions. 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. It is an ideal companion for courses such
as mathematical methods of physics, classical mechanics,
electricity and magnetism, and relativity.
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