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The edition introduces a new class of invariantderivatives and shows their relationships with otherderivatives, such as the Sobolev generalized derivative and thegeneralized derivative of the distribution theory. This is a newdirection in mathematics.
i-Smooth analysis is the branch of functional analysisthat considers the theory and applications of the invariantderivatives of functions and functionals. The important directionof i-smooth analysis is the investigation of the relation ofinvariant derivatives with the Sobolev generalized derivative andthe generalized derivative of distribution theory.
Until now, i-smooth analysis has been developed mainly toapply to the theory of functional differential equations, and thegoal of this book is to present i-smooth analysis as a branch offunctional analysis. The notion of the invariant derivative(i-derivative) of nonlinear functionals has been introduced inmathematics, and this in turn developed the correspondingi-smooth calculus of functionals and showed that for linearcontinuous functionals the invariant derivative coincides with thegeneralized derivative of the distribution theory. This bookintends to introduce this theory to the general mathematics,engineering, and physicist communities.