Solution to 9 notable problems and expansion of the theory of highly nonlinear functions

We extend the Theory of Differentially $\delta$-Uniform Functions in its various confines, now its influence is multiplied; we provide a special collection of $K$-Algebras. This solves hot challenges, e.g.: 1). We generalize for the second time Dillon's switching method in the (general) differentially uniform context. 2). With a singular style, we develop the analysis of Differential Equations exclusively for Galois fields (Section 9.4: an in-depth discussion, plus questions that require immediate action); on which there is hardly any research done and in a completely different sense, where the investigated functions have co-domain that is never the structure $\mathbb{F}_{p^n}$. Besides, we generalize the elegant BDC of Steinbach-Posthoff, and construct fascinating Chain Complexes. We introduce the $\bbF_{p^{n}}$-{\it Schr"odinger equation} (and the newest {\it Black-Scholes}). 3). We obtain the novel Fundamental Theorem of Calculus associated with a derivative order type other than the famous Fractional. Further, we conduct the corresponding Algebraic Attack on the functions that currently offer the best resistance, and identify the survivors.