i-SMOOTH ANALYSIS
A totally new direction in mathematics, this revolutionary new study
introduces a new class of invariant derivatives of functions and
establishes relations with other derivatives, such as the Sobolev
generalized derivative and the generalized derivative of the
distribution theory.
i-smooth analysis is the branch of functional analysis that considers
the theory and applications of the invariant derivatives of functions
and functionals. The important direction of i-smooth analysis is the
investigation of the relation of invariant derivatives with the Sobolev
generalized derivative and the generalized derivative of distribution
theory.
Until now, i-smooth analysis has been developed mainly to apply to the
theory of functional differential equations, and the goal of this book
is to present i-smooth analysis as a branch of functional analysis.
The notion of the invariant derivative (i-derivative) of nonlinear
functionals has been introduced in mathematics, and this in turn
developed the corresponding i-smooth calculus of functionals and
showed that for linear continuous functionals the invariant derivative
coincides with the generalized derivative of the distribution theory.
This book intends to introduce this theory to the general mathematics,
engineering, and physicist communities.
i-Smooth Analysis: Theory and Applications
- Introduces a new class of derivatives of functions and functionals, a
revolutionary new approach
- Establishes a relationship with the generalized Sobolev derivative and
the generalized derivative of the distribution theory
- Presents the complete theory of i-smooth analysis
- Contains the theory of FDE numerical method, based on i-smooth
analysis
- Explores a new direction of i-smooth analysis, the theory of the
invariant derivative of functions
- Is of interest to all mathematicians, engineers studying processes
with delays, and physicists who study hereditary phenomena in nature.
AUDIENCE
Mathematicians, applied mathematicians, engineers, physicists, students
in mathematics
