The open access book covers a large class of nonlinear systems with many practical engineering
applications. The approach is based on the extension of linear systems theory using the
Volterra series. In contrast to the few existing treatments our approach highlights the
algebraic structure underlying such systems and is based on Schwartz's distributions (rather
than functions). The use of distributions leads naturally to the convolution algebras of linear
time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple
extensions to higher order distributions without having to resort to ad hoc operators. The
result is a much-simplified notation free of multiple integrals a conceptual simplification
and the ability to solve the associated nonlinear differential equations in a purely algebraic
way. The representation based on distributions not only becomes manifestly power series alike
but it includes power series as the description of the subclass of memory-less time-invariant
weakly nonlinear systems. With this connection many results from the theory of power series
can be extended to the larger class of weakly nonlinear systems with memory. As a specific
application the theory is specialised to weakly nonlinear electric networks. The authors show
how they can be described by a set of linear equivalent circuits which can be manipulated in
the usual way. The authors include many real-world examples that occur in the design of RF and
mmW analogue integrated circuits for telecommunications. The examples show how the theory can
elucidate many nonlinear phenomena and suggest solutions that an approach entirely based on
numerical simulations can hardly suggest. The theory is extended to weakly nonlinear
time-varying systems and the authors show examples of how time-varying electric networks allow
implementing functions unfeasible with time-invariant ones. The book is primarily intended for
engineering students in upper semesters and in particular for electrical engineers. Practising
engineers wanting to deepen their understanding of nonlinear systems should also find it
useful. The book also serves as an introduction to distributions for undergraduate students of
mathematics.
