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Generalized Calculus with Applications to Matter and Forces (Paperback)
Loot Price: R1,955
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Generalized Calculus with Applications to Matter and Forces (Paperback)
Series: Mathematics and Physics for Science and Technology
Expected to ship within 12 - 17 working days
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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.
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