The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.

Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.

Investigations in Algebra departs from a preoccupation with calculus as the ultimate goal of and the universal introduction to advanced mathematics by using Logo to explore combinatorics, number theory, the study of discrete functions, and other topics that are not on the traditional path to calculus. This approach encourages students to participate actively in exciting mathematics, developing in them a facility for abstraction and an appreciation for the power of mathematical methods. Most of the projects in the first two parts of the book have been worked through by students at Woburn High School, often without assistance from a teacher. In three parts, Investigations in Algebra emphasizes the treatment of functions as concrete objects modeled as Logo procedures, applies the techniques of induction and recursion to combinatorial problems, and takes up topics in number theory (including unique factorization congruence, and multiplicative functions). Integral to the presentation are numerous carefully constructed problems routine exercises, long term projects, and open ended experiments - developed in twenty years of classroom use. Investigations in Algebra is included in the series Exploring with Logo, edited by E. Paul Goldenberg.

The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.

A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association An attractive text...written in [a] lean and precise style...eminently readable. Especially pleasant are the care and attention devoted to details... A very fine book. —Mathematical Reviews

The Wiley Classics Library consists of selected books that havebecome recognized classics in their respective fields. With thesenew unabridged and inexpensive editions, Wiley hopes to extend thelife of these important works by making them available to futuregenerations of mathematicians and scientists. Currently availablein the Series: T. W. Anderson Statistical Analysis of Time SeriesT. S. Arthanari & Yadolah Dodge Mathematical Programming inStatistics Emil Artin Geometric Algebra Norman T. J. Bailey TheElements of Stochastic Processes with Applications to the NaturalSciences George E. P. Box & George C. Tiao Bayesian Inferencein Statistical Analysis R. W. Carter Simple Groups of Lie TypeWilliam G. Cochran & Gertrude M. Cox Experimental Designs,Second Edition Richard Courant Differential and Integral Calculus,Volume I Richard Courant Differential and Integral Calculus, VolumeII Richard Courant & D. Hilbert Methods of MathematicalPhysics, Volume I Richard Courant & D. Hilbert Methods ofMathematical Physics, Volume II D. R. Cox Planning of ExperimentsHarold M. S. Coxeter Introduction to Modern Geometry, SecondEdition Charles W. Curtis & Irving Reiner Representation Theoryof Finite Groups and Associative Algebras Charles W. Curtis &Irving Reiner Methods of Representation Theory with Applications toFinite Groups and Orders, Volume I Charles W. Curtis & IrvingReiner Methods of Representation Theory with Applications to FiniteGroups and Orders, Volume II Bruno de Finetti Theory ofProbability, Volume 1 Bruno de Finetti Theory of Probability,Volume 2 W. Edwards Deming Sample Design in Business Research Amosde Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume1 --Nuclear Structure J. L. Doob Stochastic Processes NelsonDunford & Jacob T. Schwartz Linear Operators, Part One, GeneralTheory Nelson Dunford & Jacob T. Schwartz Linear Operators,Part Two, Spectral Theory--Self Adjoint Operators in Hilbert SpaceNelson Dunford & Jacob T. Schwartz Linear Operators, PartThree, Spectral Operators Herman Fsehbach Theoretical NuclearPhysics: Nuclear Reactions Bernard Friedman Lectures onApplications-Oriented Mathematics Gerald d. Hahn & Samuel S.Shapiro Statistical Models in Engineering Morris H. Hansen, WilliamN. Hurwitz & William G. Madow Sample Survey Methods and Theory,Volume I--Methods and Applications Morris H. Hansen, William N.Hurwitz & William G. Madow Sample Survey Methods and Theory,Volume II--Theory Peter Henrici Applied and Computational ComplexAnalysis, Volume 1--Power Series--lntegration--ConformalMapping--Location of Zeros Peter Henrici Applied and ComputationalComplex Analysis, Volume 2--Special Functions--IntegralTransforms--Asymptotics--Continued Fractions Peter Henrici Appliedand Computational Complex Analysis, Volume 3--Discrete FourierAnalysis--Cauchy Integrals--Construction of ConformalMaps--Univalent Functions Peter Hilton & Yel-Chiang Wu A Coursein Modern Algebra Harry Hochetadt Integral Equations Erwin O.Kreyezig Introductory Functional Analysis with Applications WilliamH. Louisell Quantum Statistical Properties of Radiation All HasanNayfeh Introduction to Perturbation Techniques Emanuel ParzenModern Probability Theory and Its Applications P.M. Prenter Splinesand Variational Methods Walter Rudin Fourier Analysis on Groups C.L. Siegel Topics in Complex Function Theory, Volume I--EllipticFunctions and Uniformization Theory C. L. Siegel Topics in ComplexFunction Theory, Volume II--Automorphic and Abelian integrals C. LSiegel Topics in Complex Function Theory, Volume III--AbelianFunctions & Modular Functions of Several Variables J. J. StokerDifferential Geometry J. J. Stoker Water Waves: The MathematicalTheory with Applications J. J. Stoker Nonlinear Vibrations inMechanical and Electrical Systems

Linear Network Optimization presents a thorough treatment of classical approaches to network problems such as shortest path, max-flow, assignment, transportation, and minimum cost flow problems.