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
Page : 292 pages
File Size : 45,70 MB
Release : 2012-08-28
Category : Mathematics
ISBN : 0486131904
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
Page : 292 pages
File Size : 46,8 MB
Release : 1968-01-01
Category : Mathematics
ISBN : 9780486638331
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
Page : 258 pages
File Size : 42,44 MB
Release : 2013-09-26
Category : Mathematics
ISBN : 048632091X
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 :
Page : 472 pages
File Size : 27,65 MB
Release : 1947
Category : Calculus of tensors
ISBN :
Author : Robert C. Wrede
Publisher : Courier Corporation
Page : 436 pages
File Size : 45,64 MB
Release : 2013-01-30
Category : Mathematics
ISBN : 0486137112
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 : Richard L. Bishop
Publisher : Courier Corporation
Page : 290 pages
File Size : 35,69 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486139239
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author : Ralph Abraham
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 24,52 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461210291
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
Author : Mikhail Itskov
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 12,89 MB
Release : 2009-04-30
Category : Technology & Engineering
ISBN : 3540939075
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
Page : 378 pages
File Size : 33,94 MB
Release : 2010
Category : Mathematics
ISBN : 9814313998
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 : James G. Simmonds
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 14,9 MB
Release : 2012-10-31
Category : Mathematics
ISBN : 1441985220
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.