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Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 0486131904
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 0486131904
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Author: Aleksandr Ivanovich Borisenko
Publisher: Courier Corporation
ISBN: 9780486638331
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 048632091X
Category : Mathematics
Languages : en
Pages : 258
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Book Description
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Author: Louis Brand
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 472
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Book Description
Author: Eutiquio C. Young
Publisher: CRC Press
ISBN: 9780824787899
Category : Technology & Engineering
Languages : en
Pages : 530
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Book Description
Revised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved.
Author: Robert C. Wrede
Publisher: Courier Corporation
ISBN: 0486137112
Category : Mathematics
Languages : en
Pages : 436
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Book Description
Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.
Author: Mikhail Itskov
Publisher: Springer Science & Business Media
ISBN: 3540939075
Category : Technology & Engineering
Languages : en
Pages : 253
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Book Description
There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
Author: L. P. Lebedev
Publisher: World Scientific
ISBN: 9814313998
Category : Mathematics
Languages : en
Pages : 378
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Book Description
1. Preliminaries. 1.1. The vector concept revisited. 1.2. A first look at tensors. 1.3. Assumed background. 1.4. More on the notion of a vector. 1.5. Problems -- 2. Transformations and vectors. 2.1. Change of basis. 2.2. Dual bases. 2.3. Transformation to the reciprocal frame. 2.4. Transformation between general frames. 2.5. Covariant and contravariant components. 2.6. The cross product in index notation. 2.7. Norms on the space of vectors. 2.8. Closing remarks. 2.9. Problems -- 3. Tensors. 3.1. Dyadic quantities and tensors. 3.2. Tensors from an operator viewpoint. 3.3. Dyadic components under transformation. 3.4. More dyadic operations. 3.5. Properties of second-order tensors. 3.6. Eigenvalues and eigenvectors of a second-order symmetric tensor. 3.7. The Cayley-Hamilton theorem. 3.8. Other properties of second-order tensors. 3.9. Extending the Dyad idea. 3.10. Tensors of the fourth and higher orders. 3.11. Functions of tensorial arguments. 3.12. Norms for tensors, and some spaces. 3.13. Differentiation of tensorial functions. 3.14. Problems -- 4. Tensor fields. 4.1. Vector fields. 4.2. Differentials and the nabla operator. 4.3. Differentiation of a vector function. 4.4. Derivatives of the frame vectors. 4.5. Christoffel coefficients and their properties. 4.6. Covariant differentiation. 4.7. Covariant derivative of a second-order tensor. 4.8. Differential operations. 4.9. Orthogonal coordinate systems. 4.10. Some formulas of integration. 4.11. Problems -- 5. Elements of differential geometry. 5.1. Elementary facts from the theory of curves. 5.2. The torsion of a curve. 5.3. Frenet-Serret equations. 5.4. Elements of the theory of surfaces. 5.5. The second fundamental form of a surface. 5.6. Derivation formulas. 5.7. Implicit representation of a curve; contact of curves. 5.8. Osculating paraboloid. 5.9. The principal curvatures of a surface. 5.10. Surfaces of revolution. 5.11. Natural equations of a curve. 5.12. A word about rigor. 5.13. Conclusion. 5.14. Problems -- 6. Linear elasticity. 6.1. Stress tensor. 6.2. Strain tensor. 6.3. Equation of motion. 6.4. Hooke's law. 6.5. Equilibrium equations in displacements. 6.6. Boundary conditions and boundary value problems. 6.7. Equilibrium equations in stresses. 6.8. Uniqueness of solution for the boundary value problems of elasticity. 6.9. Betti's reciprocity theorem. 6.10. Minimum total energy principle. 6.11. Ritz's method. 6.12. Rayleigh's variational principle. 6.13. Plane waves. 6.14. Plane problems of elasticity. 6.15. Problems -- 7. Linear elastic shells. 7.1. Some useful formulas of surface theory. 7.2. Kinematics in a neighborhood of [symbol]. 7.3. Shell equilibrium equations. 7.4. Shell deformation and strains; Kirchhoff's hypotheses. 7.5. Shell energy. 7.6. Boundary conditions. 7.7. A few remarks on the Kirchhoff-Love theory. 7.8. Plate theory. 7.9. On Non-classical theories of plates and shells
Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 0486139239
Category : Mathematics
Languages : en
Pages : 290
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Book Description
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author: James G. Simmonds
Publisher: Springer Science & Business Media
ISBN: 1441985220
Category : Mathematics
Languages : en
Pages : 124
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Book Description
In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.
