Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.

Mathematical analysis --- Functions of real variables --- Real variables --- Functions of complex variables --- 517.1 Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Operator theory --- 517.98 --- Functional analysis and operator theory --- 517.98 Functional analysis and operator theory --- Function spaces. --- Linear operators. --- Functions of complex variables. --- Hypergeometric functions. --- Functions of complex variables --- Function spaces --- Hypergeometric functions --- Linear operators --- Linear maps --- Maps, Linear --- Operators, Linear --- Functions, Hypergeometric --- Transcendental functions --- Hypergeometric series --- Spaces, Function --- Functional analysis --- Complex variables --- Elliptic functions --- Functions of real variables

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties). This introduction to the subject can be regarded as a textbook on "Modern Algebraic Topology'', which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology). The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements. Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.

Sheaf theory --- 515.14 --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- 515.14 Algebraic topology --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Algebraic topology. --- Algebraic geometry. --- Functions of complex variables. --- Algebraic Topology. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Algebraic geometry --- Topology --- Topologie algébrique --- Faisceaux, Théorie des --- Faisceaux --- Geometrie algebrique --- Topologie algebrique --- Cohomologie --- Homologie et cohomologie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

“Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics. Gives comprehensive details on how to recognize convex optimization problems in a wide variety of settings ; Provides a broad range of practical algorithms for solving real problems ; Contains hundreds of worked examples and homework exercises”

Operational research. Game theory --- Convex functions --- Mathematical optimization --- 519.6 --- 519.8 --- 681.3*G16 --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 519.8 Operational research --- Operational research --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functions, Convex --- Functions of real variables --- Convex functions. --- Mathematical optimization. --- Optimisation mathématique --- Fonctions convexes --- Optimisation mathématique. --- Fonctions convexes.