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Tensor Calculus for Physics : A Concise Guide by Dwight E. Neuenschwander (2014, Trade Paperback)

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Unlike most tensor textbooks, he says, he introduces tensors in vernacular English rather than in mathematical language that beginners might not understand. Annotation ©2015 Ringgold, Inc., Portland, OR ().

About this product

Product Identifiers

PublisherJohns Hopkins University Press

ISBN-101421415658

ISBN-139781421415659

eBay Product ID (ePID)202486010

Product Key Features

Number of Pages248 Pages

Publication NameTensor Calculus for Physics : a Concise Guide

LanguageEnglish

SubjectCalculus, Physics / Mathematical & Computational, Applied

Publication Year2014

TypeTextbook

Subject AreaMathematics, Science

AuthorDwight E. Neuenschwander

FormatTrade Paperback

Dimensions

Item Height0.6 in

Item Weight12.6 Oz

Item Length8.8 in

Item Width7.1 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2014-936825

ReviewsAn introductory Tensor Calculus for Physics book is a most welcome addition... Professor Neuenschwander's book fills the gap in robust fashion., ""An introductory Tensor Calculus for Physics book is a most welcome addition... Professor Neuenschwander's book fills the gap in robust fashion."", This book is well written and has sufficient rigor to allow students to use it for independent study.

Dewey Edition23

Grade FromCollege Freshman

IllustratedYes

Grade ToCollege Graduate Student

Dewey Decimal515.63

Table Of ContentPreface Acknowledgments 1. Tensors Need Context 1.1. Why Aren't Tensors Defined by What They Are? 1.2. Euclidean Vectors, without Coordinates 1.3. Derivatives of Euclidean Vectors with Respect to a Scalar 1.4. The Euclidean Gradient 1.5. Euclidean Vectors, with Coordinates 1.6. Euclidean Vector Operations with and without Coordinates 1.7. Transformation Coefficients as Partial Derivatives 1.8. What Is a Theory of Relativity? 1.9. Vectors Represented as Matrices 1.10. Discussion Questions and Exercises 2. Two-Index Tensors 2.1. The Electric Susceptibility Tensor 2.2. The Inertia Tensor 2.3. The Electric Quadrupole Tensor 2.4. The Electromagnetic Stress Tensor 2.5. Transformations of Two-Index Tensors 2.6. Finding Eigenvectors and Eigenvalues 2.7. Two-Index Tensor Components as Products of Vector Components 2.8. More Than Two Indices 2.9. Integration Measures and Tensor Densities 2.10. Discussion Questions and Exercises 3. The Metric Tensor 3.1. The Distinction between Distance and Coordinate Displacement 3.2. Relative Motion 3.3. Upper and Lower Indices 3.4. Converting between Vectors and Duals 3.5. Contravariant, Covariant, and ""Ordinary"" Vectors 3.6. Tensor Algebra 3.7. Tensor Densities Revisited 3.8. Discussion Questions and Exercises 4. Derivatives of Tensors 4.1. Signs of Trouble 4.2. The Affine Connection 4.3. The Newtonian Limit 4.4. Transformation of the Affine Connection 4.5. The Covariant Derivative 4.6. Relation of the Affine Connection to the Metric Tensor 4.7. Divergence, Curl, and Laplacian with Covariant Derivatives 4.8. Disccussion Questions and Exercises 5. Curvature 5.1. What Is Curvature? 5.2. The Riemann Tensor 5.3. Measuring Curvature 5.4. Linearity in the Second Derivative 5.5. Discussion Questions and Exercises 6. Covariance Applications 6.1. Covariant Electrodynamics 6.2. General Covariance and Gravitation 6.3. Discussion Questions and Exercises 7. Tensors and Manifolds 7.1. Tangent Spaces, Charts, and Manifolds 7.2. Metrics on Manifolds and Their Tangent Spaces 7.3. Dual Basis Vectors 7.4. Derivatives of Basis Vectors and the Affine Connection 7.5. Discussion Questions and Exercises 8. Getting Acquainted with Differential Forms 8.1. Tensors as Multilinear Forms 8.2. 1-Forms and Their Extensions 8.3. Exterior Products and Differential Forms 8.4. The Exterior Derivative 8.5. An Application to Physics: Maxwell's Equations 8.6. Integrals of Differential Forms 8.7. Discussion Questions and Exercises Appendix A: Common Coordinate Systems Appendix B: Theorem of Alternatives Appendix C: Abstract Vector Spaces Bibliography Index

SynopsisUnderstanding 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., 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., Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarisation in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to ......, Using a clear, step-by-step approach, this book explains one of the more difficult--yet crucial--topics in physics. 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., Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarisation 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: 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 Classical Mechanics, 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. The book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. As such, the book is an ideal companion for courses such as Mathematical Methods of Physics, Classical Mechanics, Electricity and Magnetism, and Relativity.

LC Classification NumberQC20.7.C28