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Vector Calculus [[electronic resource] /] / by Paul C. Matthews



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Autore: Matthews Paul C Visualizza persona
Titolo: Vector Calculus [[electronic resource] /] / by Paul C. Matthews Visualizza cluster
Pubblicazione: London : , : Springer London : , : Imprint : Springer, , 1998
Edizione: 1st ed. 1998.
Descrizione fisica: 1 online resource (X, 182 p. 1 illus.)
Disciplina: 515/.63
Soggetto topico: Applied mathematics
Engineering mathematics
Mathematical physics
Engineering
Applications of Mathematics
Theoretical, Mathematical and Computational Physics
Engineering, general
Note generali: Includes index.
"With 63 figures."
Nota di contenuto: 1. Vector Algebra -- 1.1 Vectors and scalars -- 1.2 Dot product -- 1.3 Cross product -- 1.4 Scalar triple product -- 1.5 Vector triple product -- 1.6 Scalar fields and vector fields -- 2. Line, Surface and Volume Integrals -- 2.1 Applications and methods of integration -- 2.2 Line integrals -- 2.3 Surface integrals -- 2.4 Volume integrals -- 3. Gradient, Divergence and Curl -- 3.1 Partial differentiation and Taylor series -- 3.2 Gradient of a scalar field -- 3.3 Divergence of a vector field -- 3.4 Curl of a vector field -- 4. Suffix Notation and its Applications -- 4.1 Introduction to suffix notation -- 4.2 The Kronecker delta ?ij -- 4.3 The alternating tensor ?ijk -- 4.4 Relation between ?ijk and ?ij -- 4.5 Grad, div and curl in suffix notation -- 4.6 Combinations of grad, div and curl -- 4.7 Grad, div and curl applied to products of functions -- 5. Integral Theorems -- 5.1 Divergence theorem -- 5.2 Stokes’s theorem -- 6. Curvilinear Coordinates -- 6.1 Orthogonal curvilinear coordinates -- 6.2 Grad, div and curl in orthogonal curvilinear coordinate systems -- 6.3 Cylindrical polar coordinates -- 6.4 Spherical polar coordinates -- 7. Cartesian Tensors -- 7.1 Coordinate transformations -- 7.2 Vectors and scalars -- 7.3 Tensors -- 7.4 Physical examples of tensors -- 8. Applications of Vector Calculus -- 8.1 Heat transfer -- 8.2 Electromagnetism -- 8.3 Continuum mechanics and the stress tensor -- 8.4 Solid mechanics -- 8.5 Fluid mechanics -- Solutions.
Sommario/riassunto: Vector calculus is the fundamental language of mathematical physics. It pro­ vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top­ ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro­ gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un­ derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.
Titolo autorizzato: Vector calculus  Visualizza cluster
ISBN: 1-4471-0597-4
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910812419403321
Lo trovi qui: Univ. Federico II
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Serie: Springer Undergraduate Mathematics Series, . 1615-2085