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."
General
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