Book Description:
This new, completely revised edition of a classic text introduces all elements necessary for understanding The Proof (Title of a PBS series dedicated to the proof of Fermat's Last Theorem) as well as new development and unsolved problems. Written by two distinguished mathematicians, Ian Stewart and David Tall, this book weaves together the historical development of the subject with a presentation of mathematical techniques. The result is a solid introduction to one of the most active research areas of mathematics for serious math buffs and a textbook accessible to undergraduates

Book Description:

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry.

This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years

This book is very rigorous and detailed. This book covers what usually is covered in 2 semesters of Linear Algebra, it covers introductory and advanced Linear ALgebra. I would not recommend it for someone who has not ever seen Linear Algebra because of the lack of concrete examples although I would highly recommend it for someone who has had Linear Algebra. This book is all the Linear Algebra you need up to a Master's degree in Mathematics. For Linear Algebra beginners I would recommend the following 2 books because no one book is good enough : "Elementary Linear Algebra" by Robert S. Johnson; and "Linear Algebra 3rd edition" by Fraleigh. Please see also "Linear Algebra, an applied first course 8th edition" page 447 for those of you intersted in Differential Equations

Book Description:

This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. Jürgen Jost is Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Postmodern Analysis (1998), Compact Riemann Surfaces (1997) and Riemannian Geometry and Geometric Analysis (1995). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998).

This quote helps demonstrate the *******, scope, and nature of this encyclopedia. The rich ******* covers the gamut from Abacus to Zero. Coverage is given to figures in mathematical history and development such as Galileo, Grace Hopper, and Pythagoras. Careers that rely on mathematics, like air traffic controller, insurance agent, radio disc jockey, and stonemason, have one-half to one-page articles describing how mathematics and a knowledge of it are essential to the profession. Standard mathematical and arithmetical topics are covered as well. The numerous contributors include college and university professors, K-12 teachers, and curriculum specialists

All there is to know about functional analysis, integral equations and calculus of variations in a single volume.
This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations.
After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory

Intended as a companion for textbooks in mathematical methods for science and engineering, this book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica(R). The accompanying CD contains Mathematica Notebooks for illustrating most of the topics in the text and for solving problems in mathematical physics. Although it is primarily designed for use with the author's "Mathematical Methods: For Students of Physics and Related Fields," the discussions in the book sufficiently self-contained that the book can be used as a supplement to any of the standard textbooks in mathematical methods for undergraduate students of physical sciences or engineering

In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text is on how to find and use the symmetries; this is supported by many examples and more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduat

Book Description:

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The five main parts of the book encompass the fundamentals of linear algebra; combinatorial and numerical linear algebra; applications of linear algebra to various mathematical and nonmathematical disciplines, such as quantum computing, control theory, signal processing, and computational biology; and software packages for linear algebra computations, including MATLAB®, Maple™, and Mathematica®