1st Edition
by John J. Shynk (Author)
Extensive coverage of
mathematical techniques used in engineering with an emphasis on
applications in linear circuits and systems
Mathematical Foundations for Linear Circuits and Systems in Engineering provides
an integrated approach to learning the necessary mathematics
specifically used to describe and analyze linear circuits and systems.
The chapters develop and examine several mathematical models consisting
of one or more equations used in engineering to represent various
physical systems. The techniques are discussed in-depth so that the
reader has a better understanding of how and why these methods work.
Specific topics covered include complex variables, linear equations and
matrices, various types of signals, solutions of differential equations,
convolution, filter designs, and the widely used Laplace and Fourier
transforms. The book also presents a discussion of some mechanical
systems that mathematically exhibit the same dynamic properties as
electrical circuits. Extensive summaries of important functions and
their transforms, set theory, series expansions, various identities, and
the Lambert W-function are provided in the appendices.
The book has the following features:
- Compares
linear circuits and mechanical systems that are modeled by similar
ordinary differential equations, in order to provide an intuitive
understanding of different types of linear time-invariant systems.
- Introduces
the theory of generalized functions, which are defined by their
behavior under an integral, and describes several properties including
derivatives and their Laplace and Fourier transforms.
- Contains
numerous tables and figures that summarize useful mathematical
expressions and example results for specific circuits and systems, which
reinforce the material and illustrate subtle points.
- Provides access to a companion website that includes a solutions manual with MATLAB code for the end-of-chapter problems.
Mathematical Foundations for Linear Circuits and Systems in Engineering is
written for upper undergraduate and first-year graduate students in the
fields of electrical and mechanical engineering. This book is also a
reference for electrical, mechanical, and computer engineers as well as
applied mathematicians.
John J. Shynk, PhD, is
Professor of Electrical and Computer Engineering at the University of
California, Santa Barbara. He was a Member of Technical Staff at Bell
Laboratories, and received degrees in systems engineering, electrical
engineering, and statistics from Boston University and Stanford
University.