Book Description
An unabridged printing, to include all figures - ... Read more

Book Description
This book concludes the outstanding series of historical studies of the mathematics in the nineteenth century. Previous volumes have studied logic, algebra, number theory, probability, geometry, and analytic functions. The third volume encompasses: an essay on the development of Chebyshev's theory of approximation of functions, later called "Constructive function theory", a systematic analysis of the history of the theory of ordinary differential equations from Chauchy and certain of his predecessors up to Poincaré and A.M. Lyapunov, an essay of the development of the calculus of variations, and a study of the history of finite differences, in whose development Soviet mathematicians have played a prominent role. This book will be a valuable source of understanding the development of these areas. It provides the general reader, as well as historians of science, not only with the descriptive history but also with a good understanding of the outer and inner motivations and the results and effects of the presented concepts and methods. ... Read more

Customer Reviews (1)

Long shadow.
(It is now in paperback!) I like this book because it highlights
how several of the central questions and ideas in mathematics from the 19th century still cast a long shadow into the present. It is as true for the pioneering work of Abel and Galois, from the early part of the period which is covered, as it is for the discoveries of Chebychev, Markov, and Kolmogorov toward the end. The period starts roughly at the time of the Napoleon wars, and extends up to the Second World War. The articles in this well written book go into mathematical detail (for example, Kummer's theory and work on Fermat's Last Theorem, Dedekin's ideal theory, and cuts,...)and they represent a well chosen treat of papers, written by major players. ... Read more

Book Description
The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science. ... Read more

Customer Reviews (1)

Introductory and readable, yet rigorous
I had read/studied most of this book when I was a graduate student in chemical engineering at Syracuse University (in 1987-88). I also took two courses on the subject from Professor Troutman. I strongly recommend thisbook to any "newcomer" to the subject. The author is amathematician, and a large fraction of the book consists of theorems,lemmas, propositions, corollaries (and their rigorous proofs). The bookalso contains, however, a good number of illustrative examples andexercises which make it useful to engineers and scientists as well as tostudents of mathematics who want to learn more about applications ofmathematics to physical sciences. ... Read more

Book Description
This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades. ... Read more

Book Description

These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research.

Customer Reviews (1)

very bad book
This books contains lecture notes for a course of Moser published after his death in 1999. It is a good example
that this practise is not very advisable since certainly Moser
would not have been happy with the outcome (the book
has been edited by a student of his).

The book is riddled with a very high number of misprints
and inaccuracies which leaves the impression
that no one has read the book prior to publication.
Many results are misstated and hard to understand
(for instance the basic theorem 1.4.4. should be
... Assume F_pp\ge 0 on \Omega. Then \gamma^star
can be embedded in an extremal field. ...)

The publisher would be well advised to offtake the book
immediately and publish a carefully corrected version
at a later time. ... Read more

Book Description

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them.

Customer Reviews (1)

It is my bible!
This book not only includes the state-of-art image processig techniques using math methods, but also provides very good numerical schemes for these methods. This book is written by mathematicians, but engineers still can easily implemente many commonly used image processing algorithm, just follow the detailed numerical difference schemes provided in the appendix. ... Read more

Book Description
Designed for the Calculus I-II-III sequence, the seventh edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The new edition retains the strengths of earlier editions--its trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level--while incorporating new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors. For the first time, the Seventh Edition is available in both Late Transcendentals and Early Transcendentals versions. ... Read more

Customer Reviews (1)

Simply Excellent!
What can I say, I think the reviewers before me have said it all.This book explains the most difficult concepts in the most simple ways I have seen so far.And illustrates the most abstract concepts with the most delightful examples and applications.You certainly won't go wrong with this book. ... Read more

Book Description
This is a book for those who want to understand the main ideas in thetheory of optimal problems. ... Read more

Product Description
This Elibron Classics book is a facsimile reprint of a 1871 edition by Macmillan and Co., London and Cambridge. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more