Matrix and Tensor Calculas: With Applications to Mechanics, Elasticity and Aeronautics - Brossura

Michal, Aristotle D.

Brossura

ISBN 10: 0486462463 ISBN 13: 9780486462462

Casa editrice: Dover Pubns, 2008

Riassunto

This volume offers a working knowledge of the fundamentals of matrix and tensor calculus that can be applied to a variety of fields. Relevant to mathematicians, physicists, meteorologists, and electrical engineers, its contents are of particular value to mechanical and aeronautical engineers, who will find information on vibrations, aircraft flutter, elasticity, hydrodynamics, and fluid mechanics.
Each section of the two-part treatment is self-contained. The first part concerns matrix calculus and its applications; the second, tensor calculus and its applications. Both sections feature an introduction with a concise presentation of mathematical concepts, and more advanced mathematical ideas are developed within the context of applications. Students and professionals alike will appreciate this book's skillful combination of clear, precise mathematical statements and immediate practical applications.

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Contenuti

Part I. Matrix Calculus and its Applications 1.-2. Algebraic Preliminaries 3.-4. Differential and Integral Calculus of Matrices 5.-6. Matrix Methods in Problems of Small Oscillations 7. Matrix Methods in the Mathematical Theory of Aircraft Flutter 8. Matrix Methods in Elastic Deformation Theory Part II. Tensor Calculus and its Applications 9. Space Line Element in Curvilinear Coordinates 10. Vector Fields, Tensor Fields, and Euclidean Christoffel Symbols 11. Tensor Analysis 12. Laplace Equation, Wave Equation, and Poisson Equation in Curvilinear Coordinates 13. Some Elementary Applications of the Tensor Calculus to Hydrodynamics 14. Applications of the Tensor Calculus to Elasticity Theory 15. Homogeneous and Isotropic Strains, Strain Invariants, and Variation of Strain Tensor 16. Stress Tensor, Elastic Potential, and Stress-Strain Relations 17. Tensor Calculus in Riemannian Spaces and the Fundamentals of Classical Mechanics 18. Applications of the Tensor Calculus to Boundary-Layer Theory Notes on Part I Notes on Part II References for Part I References for Part II Index

Product Description

Book by Aristotle D Michal

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2008
• ISBN 10: 0486462463
• ISBN 13: 9780486462462
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 132