Series: Applied Mathematical Sciences, Vol. 127
2005, XII, 262 p., Hardcover
ISBN: 0-387-25364-5
About this book
A comprehensive description of the current theoretical and
numerical aspects of inverse problems in partial differential
equations. Applications include recovery of inclusions from
anomalies of their gravity fields, reconstruction of the interior
of the human body from exterior electrical, ultrasonic, and
magnetic measurement. By presenting the data in a readable and
informative manner, the book introduces both scientific and
engineering researchers as well as graduate students to the
significant work done in this area in recent years, relating it
to broader themes in mathematical analysis.
Table of contents
Preface.- Inverse problems.- Ill-Posed Problems and
Regularization.- Uniqueness and Stability in the Cauchy Problem.-
Elliptic Equations: Single Boundary Measurements.- Elliptic
Equations: Many Boundary Measurements.- Scattering Problems.-
Integral Geometry and Tomography.- Hyperbolic Equations.-
Parabolic Equations.- Some Numerical Methods.- Appendix.-
References.- Index.
2005, Approx. 680 p., Hardcover
ISBN: 3-540-26169-9
About this book
The book contains a selection of 43 scientific papers of the
great mathematician Ennio De Giorgi. All papers are written in
English and 17 of them appear also in their original Italian
version. The editors provide also a short biography of Ennio De
Giorgi and a detailed account of his scientific achievements,
ranging from his seminal paper on the solution of Hilbertfs 19th
problem to the theory of perimeter and minimal surfaces, the
theory of G-convergence and the Foundations of Mathematics.
Table of contents
Preface.- Biography.- Prizes and academic awards.- Teaching and
academic commitment.- The activities out of Pisa.- Civil,
religious and political commitment.- The scientific work of Ennio
De Giorgi.- From the juvenile papers to Plateaufs problem and
the solution of Hilbertfs19th problem.- Partial differential
equations and the foundations of G-convergence.- Asymptotic
problems in the Calculus of Variations.- The most recent
developments in the Calculus of Variations.- The work on
Foundations of Mathematics.- De Giorgifs contribution to the
regularity theory for elliptic partial differential equations, by
Luis Caffarelli.- Remarks on some of the analytical work of Ennio
De Giorgi, by Louis Nirenberg.- Complete list of De Giorgifs
scientific publications.- Selected papers.
Series: Universitext
2006, Approx. 400 p., Softcover
ISBN: 3-540-25484-6
About this textbook
The book consists of two parts. The first part concerns the
classical probability theory. It contains a detailed analysis of
Markov chains, Limit theorems, their relation to Renormalization
Group theory. It also describes several applications of
probability theory, which are not discussed in most other text-books.
The second part includes the theory of stationary random
processes, martingales, stochastic integrals and stochastic
differential equations. One section is devoted to the theory of
Gibbs random fields. The book contains essential material for an
undergraduate or a graduate course in Probability theory and the
theory of Random Processes. It may also serve as a reference for
scientists who use modern probability theory in their research.
Table of contents
Spaces of Elementary Outcomes. Random Variables and their
Distributions: Spaces of Elementary Outcomes.- Expectations,
Variances and Moments of Random Variables.- Probability of the
Union of Events.- Equivalent formulations of $\sigma $-additivity.
Borel $\sigma $-algebras.- Distribution Functions and Densities.-
Problems. Sequences of Independent Trials: Sequences of
Independent Trials and the Law of Large Numbers.- De Moivre-Laplace
Limit Theorem.- Poisson Limit Theorem. Conditional Probabilities.
Formula of Total Probability. Independence of Events, $\sigma $-algebras,
Partitions, and Random Variables. Gambler Ruin Problem:
Conditional Probabilities.
Series: Springer Monographs in Mathematics
2005, Approx. 445 p., Hardcover
ISBN: 1-85233-993-4
About this book
This book is devoted predominantly to one particular way of
looking at the evolution of the system in which we describe time
changes as transitions from one state to another. This leads in a
natural way to the semigroup theory that has been developed in
the last fifty years.
There are many applications coming from kinetic theory,
fragmentation theory, mathematical biology and many other fields,
where the assumptions of standard perturbation theory are not
satisfied. In this book the authors concentrate on perturbation
results that take advantage of the fact that in many applications
the operators involved are positive (as only nonnegative data and
solutions make sense) and dissipative.
The main part of the book is devoted to linking the properties of
the generator with the properties of the semigroup, that are
important in applications. In the final part of the book the
authors discuss applications of the developed theory to a variety
of problems ranging from the classical birth-and-death type
problems of population dynamics, through fragmentation models in
both conservative and mass loss regimes, to kinetic models. The
authors also discuss a few miscellaneous applications that do not
fit into their theory exactly but nevertheless their treatment
draws substantially from it.
Table of contents
Introduction;-Basic Facts from Functional Analysis and Banach
Lattices;-An Overview of Semigroup Theory;-Some Classical
Perturbation Results;-Positive Perturbations of Positive
Semigroups;-Substochastic Semigroups and Generator
Characterization;-Applications to Birth-and-Death Problems;-Applications
to Pure Fragmentation Problems;-Fragmentation with Growth and
Decay;-Applications of Kinetic Theory;-Singularly Perturbed
Inelastic Collision Models;-Index;-References
Series: Undergraduate Texts in Mathematics
2006, Approx. 260 p. 55 illus., Softcover
ISBN: 0-387-25964-3
About this textbook
While the standard sophomore course on elementary differential
equations is typically one semester in length, most of the texts
currently being used for these courses have evolved into calculus-like
presentations that include a large collection of methods and
applications, packaged with state-of-the-art color graphics,
student solution manuals, the latest fonts, marginal notes, and
web-based supplements. All of this adds up to several hundred
pages of text and can be very expensive. Many students do not
have the time or desire to read voluminous texts and explore
internet supplements. Thats what makes the format of this
differential equations book unique. It is a one-semester, brief
treatment of the basic ideas, models, and solution methods. Its
limited coverage places it somewhere between an outline and a
detailed textbook. The author writes concisely, to the point, and
in plain language. Many worked examples and exercises are
included. A student who works through this primer will have the
tools to go to the next level in applying ODEs to problems in
engineering, science, and applied mathematics. It will also give
instructors, who want more concise coverage, an alternative to
existing texts.
This text also encourages students to use a computer algebra
system to solve problems numerically. It can be stated with
certainty that the numerical solution of differential equations
is a central activity in science and engineering, and it is
absolutely necessary to teach students scientific computation as
early as possible. Templates of MATLAB programs that solve
differential equations are given in an appendix. Maple commands
are given as well. The author taught this material on several
ocassions to students who have had a standard three-semester
calculus sequence. It has been well received by many students who
appreciated having a small, definitive parcel of material to
learn. Moreover, this text gives students the opportunity to
start reading mathematics at a slightly higher level than
experienced in pre-calculus and calculus; not every small detail
is included. Therefore the book can be a bridge in their progress
to study more advanced material at the junior-senior level, where
books leave a lot to the reader and are not packaged with
elementary formats.
J. David Logan is Professor of Mathematics at the University of
Nebraska, Lincoln. He is the author of another recent
undergraduate textbook, Applied Partial Differential Equations, 2nd
Edition (Springer 2004).
Table of contents
Preface.- Differential Equations and Models.- Analytic Solutions
and Approximations.-Second-Order Differential Equations.- Laplace
Transforms.- Linear Systems.- Nonlinear Systems.- Appendix A:
References.- Appendix B: A Brief on MATLAB.- Appendix C: Maple
Commands.- Appendix D: Sample Examinations.- Appendix E:
Solutions to Selected Exercises.