A Brief on Tensor Analysis: Undergraduate Texts in Mathematics
Autor James G. Simmondsen Limba Engleză Paperback – 17 oct 2012
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Paperback (1) | 370.84 lei 6-8 săpt. | |
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Springer – 19 noi 1993 | 378.57 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781461264248
ISBN-10: 1461264243
Pagini: 132
Ilustrații: XIV, 114 p.
Dimensiuni: 155 x 235 x 7 mm
Greutate: 0.2 kg
Ediția:Softcover reprint of the original 2nd ed. 1994
Editura: Springer
Colecția Springer
Seria Undergraduate Texts in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 1461264243
Pagini: 132
Ilustrații: XIV, 114 p.
Dimensiuni: 155 x 235 x 7 mm
Greutate: 0.2 kg
Ediția:Softcover reprint of the original 2nd ed. 1994
Editura: Springer
Colecția Springer
Seria Undergraduate Texts in Mathematics
Locul publicării:New York, NY, United States
Public țintă
Lower undergraduateCuprins
I Introduction: Vectors and Tensors.- Three-Dimensional Euclidean Space.- Directed Line Segments.- Addition of Two Vectors.- Multiplication of a Vector v by a Scalar ?.- Things That Vectors May Represent.- Cartesian Coordinates.- The Dot Product.- Cartesian Base Vectors.- The Interpretation of Vector Addition.- The Cross Product.- Alternative Interpretation of the Dot and Cross Product. Tensors.- Definitions.- The Cartesian Components of a Second Order Tensor.- The Cartesian Basis for Second Order Tensors.- Exercises.- II General Bases and Tensor Notation.- General Bases.- The Jacobian of a Basis Is Nonzero.- The Summation Convention.- Computing the Dot Product in a General Basis.- Reciprocal Base Vectors.- The Roof (Contravariant) and Cellar (Covariant) Components of a Vector.- Simplification of the Component Form of the Dot Product in a General Basis.- Computing the Cross Product in a General Basis.- A Second Order Tensor Has Four Sets of Components in General.- Change of Basis.- Exercises.- III Newton’s Law and Tensor Calculus.- Rigid Bodies.- New Conservation Laws.- Nomenclature.- Newton’s Law in Cartesian Components.- Newton’s Law in Plane Polar Coordinates.- The Physical Components of a Vector.- The Christoffel Symbols.- General Three-Dimensional Coordinates.- Newton’s Law in General Coordinates.- Computation of the Christoffel Symbols.- An Alternative Formula for Computing the Christoffel Symbols.- A Change of Coordinates.- Transformation of the Christoffel Symbols.- Exercises.- IV The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem.- The Gradient.- Linear and Nonlinear Eigenvalue Problems.- The Del Operator.- The Divergence, Curl, and Gradient of a Vector Field.- The Invariance of ? · v, ? × v, and ?v.- The Covariant Derivative.- The Component Forms of ? · v, ? × v, and ?v.- The Kinematics of Continuum Mechanics.- The Divergence Theorem.- Differential Geometry.- Exercises.