Generalized calculus with applications to matter and forces
Author(s)
Bibliographic Information
Generalized calculus with applications to matter and forces
(Mathematics and physics for science and technology / series editor, L.M.B.C. Campos)
CRC Press, c2014
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables.
As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as:
Gauss and Stokes' theorems in the differential geometry, tensor calculus, and theory of potential fields
Self-adjoint and non-self-adjoint problems for linear differential equations and nonlinear problems with large deformations
Multipolar expansions and Green's functions for elastic strings and bars, potential and rotational flow, electro- and magnetostatics, and more
This third volume in the series Mathematics and Physics for Science and Technology is designed to complete the theory of functions and its application to potential fields, relating generalized functions to broader follow-on topics like differential equations. Featuring step-by-step examples with interpretations of results and discussions of assumptions and their consequences, Generalized Calculus with Applications to Matter and Forces enables readers to construct mathematical-physical models suited to new observations or novel engineering devices.
Table of Contents
List of Classifications, Diagrams, Lists, Notes, and Tables. Mathematical Symbols. Physical Quantities. Limit of a Sequence of Functions. Shape of a Loaded String. Functionals over Test Functions. Bending of Bars and Beams. Differential Operators and Geometry. Axisymmetric Flows and Four Sphere Theorems. Convolution, Reciprocity, and Adjointness. Electric/Magnetic Multipoles and Images. Multidimensional Harmonic Potentials. Twenty Examples.
by "Nielsen BookData"