Synopses & Reviews
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.
This volume offers a working knowledge of the fundamentals of matrix and tensor calculus that can be applied to a variety of fields, particularly scientific aeronautical engineering. Mathematicians, physicists, and meteorologists as well as engineers will benefit from its skillful combination of mathematical statements and immediate practical applications. 1947 edition.
This volume offers a working knowledge of the fundamentals of matrix and tensor calculus. Relevant to several fields, particularly aeronautical engineering, the text skillfully combines mathematical statements with practical applications. 1947 edition.
Table of Contents
Part I. Matrix Calculus and its Applications1.-2. Algebraic Preliminaries3.-4. Differential and Integral Calculus of Matrices5.-6. Matrix Methods in Problems of Small Oscillations7. Matrix Methods in the Mathematical Theory of Aircraft Flutter8. Matrix Methods in Elastic Deformation TheoryPart II. Tensor Calculus and its Applications9. Space Line Element in Curvilinear Coordinates10. Vector Fields, Tensor Fields, and Euclidean Christoffel Symbols11. Tensor Analysis12. Laplace Equation, Wave Equation, and Poisson Equation in Curvilinear Coordinates13. Some Elementary Applications of the Tensor Calculus to Hydrodynamics14. Applications of the Tensor Calculus to Elasticity Theory15. Homogeneous and Isotropic Strains, Strain Invariants, and Variation of Strain Tensor16. Stress Tensor, Elastic Potential, and Stress-Strain Relations17. Tensor Calculus in Riemannian Spaces and the Fundamentals of Classical Mechanics18. Applications of the Tensor Calculus to Boundary-Layer TheoryNotes on Part INotes on Part IIReferences for Part IReferences for Part IIIndex