Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics

Overview


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...
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Overview


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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Product Details

  • ISBN-13: 9780486462462
  • Publisher: Dover Publications
  • Publication date: 7/24/2008
  • Series: Dover Books on Engineering Series
  • Pages: 144
  • Sales rank: 968,415
  • Product dimensions: 5.30 (w) x 8.40 (h) x 0.40 (d)

Table of Contents


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
 
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