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Tensor Calculus on Time Scales

Name: Tensor Calculus on Time Scales
Brand: De Gruyter
SKU: 9783112228487
Price: 28847 HUF
Availability: InStock

Dynamic Calculus and Riemannian Spaces

Szerző: Svetlin G. Georgiev

Nyelv:

Kötés: Puha kötésű

Kiadó: De Gruyter

Elérhetőség: 50 % esély

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In chapter 1 N dimensional spaces, contravariant vectors, covariant vectors and invariants are intro...

Információk a könyvről

Szerző

Svetlin G. Georgiev

Nyelv

Angol

Kötés

Könyv - Puha kötésű

Kiadva

2026

oldal

300

EAN

9783112228487

Enbook ID

50793218

Kiadó

De Gruyter

Súly

519

Méretek

170 x 240

Teljes leírás

In chapter 1 N dimensional spaces, contravariant vectors, covariant vectors and invariants are introduced. Some of their properties are deduced. Transformations of coordinates are investigated. Chapter 2 provides an informative introduction concerning the origin and nature of the tensor concept and the scope of the tensor calculus. The tensor algebra has been developed in an N dimensional space. Contravariant, covariant and mixed tensors of arbitrary order are defined. Some of their properties are deduced. The quotient law of the tensors is formulated and proved. Outer product and contractions are introduced. In Chapter 3, an N dimensional Riemannian space has been chosen for the development of tensor calculus. Metric and associated tensors are defines and some of their properties are explored. Affine and curvalinear coordinates are introduced. In Chapter 4, the Christoffel symbols of the first and second kinds are defined. Some of their basic properties are established. Covariant derivatives are introduced. The divergence, Laplace operator and curl are defined and explored. Intrinsic differentiation is studied. Chapter 5 is devoted to Riemann-Christoffel tensor, Ricci tensor, covariant curvature tensor, Riemann curvature and Einstein tensor and we deduct some of their properties. In Chapter 6, we represent some applications of tensor calculus in relativistic dynamics and relativistic kinematics. Lorentz transformations are derived on arbitrary time scales.

Velocity and acceleration vectors are defined and developed. Lagrange equations are deducted. Conservation laws for the energy momentum vector and angular momentum tensor are obtained.

The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text material of this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques.

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Leggyakrabban keresett

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Tensor Calculus on Time Scales

Dynamic Calculus and Riemannian Spaces

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