Generalized Calculus with Applications to Matter and Forces

This volume combines mathematical theory, physical principles, and engineering problems to present generalized functions from an applied point of view. It examines the Heaviside unit jump and the Dirac unit impulse and its derivatives in one and several dimensions. Containing step-by-step examples with interpretations of results and discussions of assumptions and their consequences, the text covers Gauss and Stokes’ theorems, self-adjoint and non-self-adjoint problems, multipolar expansions, Green’s functions, and more to enable readers to construct mathematical–physical models suited to new observations or novel engineering devices.