Distributions in the Physical and Engineering Sciences is a
comprehensive exposition on analytic methods for solving science and
engineering problems. It is written from the unifying viewpoint of
distribution theory and enriched with many modern topics which are
important for practitioners and researchers. The goal of the books is to
give the reader, specialist and non-specialist, useable and modern
mathematical tools in their research and analysis.
Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues
the multivolume project which endeavors to show how the theory of
distributions, also called the theory of generalized functions, can be
used by graduate students and researchers in applied mathematics,
physical sciences, and engineering. It contains an analysis of the three
basic types of linear partial differential equations--elliptic,
parabolic, and hyperbolic--as well as chapters on first-order nonlinear
partial differential equations and conservation laws, and generalized
solutions of first-order nonlinear PDEs. Nonlinear wave, growing
interface, and Burger's equations, KdV equations, and the equations of
gas dynamics and porous media are also covered.
The careful explanations, accessible writing style, many
illustrations/examples and solutions also make it suitable for use as a
self-study reference by anyone seeking greater understanding and
proficiency in the problem solving methods presented. The book is ideal
for a general scientific and engineering audience, yet it is
mathematically precise.
Features
- Application oriented exposition of distributional (Dirac delta)
methods in the theory of partial differential equations. Abstract
formalism is keep to a minimum.
- Careful and rich selection of examples and problems arising in
real-life situations. Complete solutions to all exercises appear at the
end of the book.
- Clear explanations, motivations, and illustration of all necessary
mathematical concepts.
