libristo the absolute differential calculus calculus of tensors 1258452
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Calculus Of Tensors And Differential Forms
Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Calculus
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Introduction To Differential Geometry - With The Use Of Tensor Calculus Read Books
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AN INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH USE OF THE TENSOR CALCULUS By LUTHER PFAHLER EISENHART. Preface: Since 1909, when my Differential Geometry of Curves and Surfaces was published, the tensor calculus, which had previously been invented by Ricci, was adopted by Einstein in his General Theory of Relativity, and has been developed further in the study of Riemannian Geometry and various generalizations of the latter. In the present book the tensor calculus of cuclidean 3-space is developed and then generalized so as to apply to a Riemannian space of any number of dimensions. The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and the content of the tensor calculus. LUTHER PFAHLER EISENHART. Contents include: CHAPTER I CURVES IN SPACE SECTION PAGE 1. Curves ami surfaces. The summation convention 1 2. Length of a curve. Linear element , 8 3. Tangent to a curve. Order of contact. Osculating plane 11 4. Curvature. Principal normal. Circle of curvature 16 5. TBi normal. Torsion 19 6r The Frenet Formulas. The form of a curve in the neighborhood of a point 25 7. Intrinsic equations of a curve 31 8. Involutes and evolutes of a curve 34 9. The tangent surface of a curve. The polar surface. Osculating sphere. . 38 10. Parametric equations of a surface. Coordinates and coordinate curves trT a surface 44 11. 1 Tangent plane to a surface 50 tSffDovelopable surfaces. Envelope of a one-parameter family of surfaces. . 53 CHAPTER II TRANSFORMATION OF COORDINATES. TENSOR CALCULUS 13. Transformation of coordinates. Curvilinear coordinates 63 14. The fundamental quadratic form of space 70 15. Contravariant vectors. Scalars 74 16. Length of a contravariant vector. Angle between two vectors 80 17. Covariant vectors. Contravariant and covariant components of a vector 83 18. Tensors. Symmetric and skew symmetric tensors 89 19. Addition, subtraction and multiplication of tensors. Contraction.... 94 20. The Christoffel symbols. The Riemann tensor 98 21. The Frenet formulas in general coordinates 103 22. Covariant differentiation 107 23. Systems of partial differential equations of the first order. Mixed systems 114 CHAPTER III INTRINSIC GEOMETRY OF A SURFACE 24. Linear element of a surface. First fundamental quadratic form of a surface. Vectors in a surface 123 25. Angle of two intersecting curves in a surface. Element of area 129 26. Families of curves in a surface. Principal directions 138 27. The intrinsic geometry of a surface. Isometric surfaces 146 28. The Christoffel symbols for a surface. The Riemannian curvature tensor. The Gaussian curvature of a surface 149 29. Differential parameters 155 30. Isometric orthogonal nets. Isometric coordinates 161 31...
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Tensors, Differential Forms and Variational Principles Dover Publications Inc.
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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
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Essential Calculus with Applications Dover Publications Inc.
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To the Instructor; To the StudentChapter 1. Mathematical Background1.1 Introductory Remarks1.2 Sets1.3 Numbers1.4 Inequalities1.5 The Absolute Value1.6 Intervals and Neighborhoods1.7 Rectangular Coordinates1.8 Straight Lines1.9 More about Straight LinesChapter 2. Differential Calculus2.1 Functions2.2 More about Functions2.3 Graphs2.4 Derivatives and Limits2.5 More about Derivatives2.6 More about Limits2.7 Differentiation Technique2.8 Further Differentiation Technique2.9 Other Kinds of LimitsChapter 3. Differentiation as a Tool3.1 Velocity and Acceleration3.2 Related Rates and Business Applications3.3 Properties of Continuous Functions3.4 Properties of Differentiable Functions3.5 Applications of the Mean Value Theorem3.6 Local Extrema3.7 Concavity and Inflection Points3.8 Optimization ProblemsChapter 4. Integral Calculus4.1 The Definite Integral4.2 Properties of Definite Integrals4.3 The Logarithm4.4 The Exponential4.5 More about the Logarithm and Exponential4.6 Integration Technique4.7 Improper IntegralsChapter 5. Integration as a Tool5.1 Elementary Differential Equations5.2 Problems of Growth and Decay5.3 Problems of MotionChapter 6. Functions of Several Variables6.1 From Two to n Dimensions6.2 Limits and Differentiation6.3 The Chain Rule6.4 Extrema in n DimensionsTables; Selected Hints and Answers; Supplementary Hints and Answers; Index
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Elementary Differential Geometry Springer London Ltd
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Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum nothing beyond first courses in linear algebra and multivariable calculus and the most direct and straightforward approach is used throughout. §§New features of this revised and expanded second edition include:§§§§a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. §§§Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.§§§Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com
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Mathematical Tools for Physics Dover Publications
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Preface to the Dover Edition Introduction Bibliography 1. Basic Stuff 2. Infinite Series 3. Complex Algebra 4. Differential Equations 5. Fourier Series 6. Vector Spaces 7. Operators and Matrices 8. Multivariable Calculus 9. Vector Calculus 1 10. Partial Differential Equations 11. Numerical Analysis 12. Tensors 13. Vector Calculus 2 14. Complex Variables 15. Fourier Analysis 16. Calculus of Variations 17. Densities and Distributions Index
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Manifolds, Tensor Analysis, and Applications Springer-Verlag New York Inc.
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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 mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.
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Smooth Functions and Maps Springer Nature Switzerland AG
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The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus.The scope of notions includes, among others, Lagrange inequality, Taylor's formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings.In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor's formula in a nonconvex area (Chapter I, 8), Whitney's extension theorem for smooth function (Chapter I, 11) and some of its corollaries, global diffeomorphism theorem (Chapter II, 5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV).The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations.Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
Sklep: Libristo.pl
Smooth Functions and Maps Springer Nature Switzerland AG
Książki / Literatura obcojęzyczna
The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus.The scope of notions includes, among others, Lagrange inequality, Taylor's formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings.In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor's formula in a nonconvex area (Chapter I, 8), Whitney's extension theorem for smooth function (Chapter I, 11) and some of its corollaries, global diffeomorphism theorem (Chapter II, 5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV).The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations.Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
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t1=0.026, t2=0, t3=0, t4=0, t=0.027