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Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics by Aristotle D. Michal

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About this book :-
Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics written by Aristotle D. Michal .
This textbook is best for the topic matrix and tensor calculus. Since the beginnings of the modem age of the aeronautical sciences a close cooperation has existed between applied mathematics and aeronautics. Engineers at large have always appreciated the help of applied mathematics in furnishing them practical methods for numerical and graphical solutions of algebraic and differential equations. However, aeronautical and also electrical engineers are faced with problems reaching much further into several domains of modem mathematics. As a matter of fact, these branches of engineering science have often exerted an inspiring influence on the development of novel methods in applied mathematics.
One branch of applied mathematics which fits especially the needs of the scientific aeronautical engineer is the matrix and tensor calculus. The matrix operations represent a powerful method for the solution of problems dealing with mechanical systems" with a certain number of degrees of freedom. The tensor calculus gives admirable insight into complex problems of the mechanics of continuous media, the mechanics of fluids, and elastic and plastic media.
(Aristotle D. Michal)

Book Detail :-
Title: Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics
Edition:
Author(s): Aristotle D. Michal
Publisher: Dover Publications
Series: Dover Books on Engineering
Year: 2008
Pages: 141
Type: PDF
Language: English
ISBN: 978-0-486-46246-2,0486462463
Country: US
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About Author :-
Author Aristotle D. Michal
After graduating fellow, receiving a master's degree in 1921, then he studied at Rice Institute, Houston, Texas, where he was influenced particularly by Griffith C. Ecans and his work on functionals. He received the doctorate from Rice Institute and married Luddye Kennerly of Houston, Texas.
In 1927 Dr. Michal was appointed Assistant Professor of Mathematics at the Chio State University. Two year later he joined the faculty of the California Institute of Technology. After 2 years e promoted to a Professorship in 1938.


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Book Contents :-
Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics written by Aristotle D. Michal cover the following topics.
1. ALGEBRAIC PBELlMINARIES
2. ALGEBRAIC PRELIMINARIES (Continued)
3. DIFFERENTIAL AND INTEGRAL CALCULUS OF MATRICES
4. DIFFERENTIAL AND INTEGRAL CALCULUS OF MATRICES (Continued)
5. MATRIX METHODS IN PROBLEMS OF SMALL OSCILLATIONS
6. MATRIX METHODS IN PROBLEMS OF SMALL OSCILLATIONS (Continued)
7. MATRIX METHODS IN THE MATHEMATICAL THEORY OF AIRCRAFT FLUTTER
8. MATRIX METHODS IN ELASTIC DEFORMATION THEORY I
9. SPACIAl LINE ELEMENT IN CURVILINEAB COORDINATES
10. VECTOR FIELDS, TENSOR FIELDS, AND EUCLIDEAN GHlWITOFFiL SYMBOLS
11. TENSOR ANALYSIS
12. LAPLACE EQUATION, WAVE EQUATION, AND POISSON EQUATION IN KURVI LINEAR 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 RELATION OF STRAIN TENSOR
16. STRESS TENSOR, ELASTIC POTENTIAL, AND STRESS-8TaAJN RELATIONS
17. TENSOR CALCULUS IN RIEmANNiAN SPACES AND TBJD FuNDAMENTALS OF CLASSICAL MECHANICS
18. APPLICATION OF THE TENSOR CALCULUS TO BOUNDARY-LAYER TBlDOBY
Index


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