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Partial Differential Equations in Action: From Modelling to Theory (Universitext) [Paperback]

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Item description for Partial Differential Equations in Action: From Modelling to Theory (Universitext) by Sandro Salsa...

This book is designed as an advanced undergraduate or a first-year graduate

course for students from various disciplines like applied mathematics,

physics, engineering.

The main purpose is on the one hand to train the students to appreciate the

interplay between theory and modelling in problems arising in the applied

sciences; on the other hand to give them a solid theoretical background for

numerical methods, such as finite elements.

Accordingly, this textbook is divided into two parts.

The first one has a rather elementary character with the goal of

developing and studying basic problems from the macro-areas of diffusion,

propagation and transport, waves and vibrations. Ideas and connections with

concrete aspects are emphasized whenever possible, in order to provide

intuition and feeling for the subject.

For this part, a knowledge of advanced calculus and ordinary differential

equations is required. Also, the repeated use of the method of separation of

variables assumes some basic results from the theory of Fourier series,

which are summarized in an appendix.

The main topic of the second part is the

development of Hilbert space methods for the variational formulation and

analysis of linear boundary and initial-boundary value problems\emph{. }%

Given the abstract nature of these chapters, an effort has been made to

provide intuition and motivation for the various concepts and results.

The understanding of these topics requires some basic knowledge of Lebesgue

measure and integration, summarized in another appendix.

At the end of each chapter, a number of exercises at different level of

complexity is included. The most demanding problems are supplied with

answers or hints.

The exposition if flexible enough to allow substantial changes without

compromising the comprehension and to facilitate a selection of topics for a

one or two semester course.

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Item Specifications...

Pages   556
Est. Packaging Dimensions:   Length: 1.25" Width: 6" Height: 9"
Weight:   2.4 lbs.
Binding  Softcover
Release Date   Feb 13, 2008
Publisher   Springer
ISBN  8847007518  
ISBN13  9788847007512  

Availability  131 units.
Availability accurate as of Oct 24, 2016 11:43.
Usually ships within one to two business days from La Vergne, TN.
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More About Sandro Salsa

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Product Categories

1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Differential Equations
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Calculus
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Functional Analysis
4Books > Subjects > Science > General
5Books > Subjects > Science > Mathematics > Applied > Differential Equations
6Books > Subjects > Science > Mathematics > General
7Books > Subjects > Science > Mathematics > Pure Mathematics > Calculus
8Books > Subjects > Science > Mathematics > Pure Mathematics > Functional Analysis

Reviews - What do customers think about Partial Differential Equations in Action: From Modelling to Theory (Universitext)?

a valuable new addition for students and Professionals  Jun 14, 2008
Sandro Salsa's book: "Partial Differential Equations in Action: From modelling to Theory" is true to it's title. It guides the reader
from the modeling stage to the theory, i.e. it is written from
the point of view of an applied mathematician who wishes
to understand the phenomenon that gives rise the PDE but who also
seeks to gain an analytical understanding of the PDE before proceeding
to it's numerical implementation. The book is written at a level
suitable for both an advanced undergraduate or first year graduate
school class at most American Institutions.
Salsa's light but incisive touch in writing about PDE's is reminiscent,
for those familiar with Gilbert Strang's books,
with Strang's way of entertaining while at the same
time challenging the reader. The book is unique
in many ways. For instance the use of Fourier series in treating
the diffusion equation is, in of itself standard, but Salsa's
use of the energy method to show that the Fourier series
solution is the unique solution is a nice illustration
of how the book alternates between the practical and
the more qualitative or technical aspects of the subject.
For students of mathematical finance and mathematical
biology, as well as for students of mathematical physics
the treatment of random walks and their relations to
Brownian motion and to the diffusion equation is the
best I've ever seen. For students of mathematical
finance there is a nice section on the Black-Scholes equation
and a use of the maximum principle to show that
call option prices are increasing with increasing
volatility. For student in applied physics the
sections on the wave equation and on hyperbolic
problems are some of the best I've found available.

In later Chapters more advanced material introducing the
student to the use of Sobolev spaces in solving Elliptic
equations and evolution equations is carried out
in a highly efficient and very clear fashion.

In summary, I highly recommend this book.
Indeed, I think it is destined to become a classic.

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