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This textbook offers a high-level introduction to multi-variable differential calculus. Differential forms are introduced incrementally in the narrative, eventually leading to a unified treatment of Green's, Stokes' and Gauss' theorems. Furthermore, the presentation offers a natural route to differential geometry. Contents:Calculus of Vector FunctionsTangent Spaces and 1-formsLine IntegralsDifferential Calculus of MappingsApplications of Differential CalculusDouble and Triple IntegralsWedge Products and Exterior DerivativesIntegration of FormsStokes' Theorem and Applications

Differential calculus. --- Mathematical analysis. --- Stokes' theorem. --- Integrals --- Vector valued functions --- 517.1 Mathematical analysis --- Mathematical analysis --- Calculus, Differential --- Calculus

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The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

Metric spaces. --- Topological spaces. --- Vector valued functions. --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Spaces, Topological --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology

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Measure theory. Mathematical integration --- Mesure, Théorie de la --- Calcul intégral --- Fonctions vectorielles. --- Vector valued functions --- Calculus, Integral --- Measure theory --- Integrals, Bochner. --- Integrals, Bochner --- Bochner integrals --- Banach spaces --- Convergence --- Integrals, Generalized --- 517.518.1 --- 517.518.1 Measure. Integration. Differentiation --- Measure. Integration. Differentiation

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This book contains nine well-organized survey articles by leading researchers in positivity, with a strong emphasis on functional analysis. It provides insight into the structure of classical spaces of continuous functions, f-algebras, and integral operators, but also contains contributions to modern topics like vector measures, operator spaces, ordered tensor products, non-commutative Banach function spaces, and frames. Contributors: B. Banerjee, D.P. Blecher, K. Boulabiar, Q. Bu, G. Buskes, G.P. Curbera, M. Henriksen, A.G. Kusraev, J. Mart??-nez, B. de Pagter, W.J. Ricker, A.R. Schep, A. Tri

Ordered algebraic structures. --- Vector valued functions. --- Functional analysis. --- Positive operators. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Operators, Positive --- Linear operators --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Global analysis (Mathematics). --- Algebra. --- Operator theory. --- Cell aggregation --- Economics. --- Analysis. --- Order, Lattices, Ordered Algebraic Structures. --- Functional Analysis. --- Operator Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Economics, general. --- Mathematics. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematics --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Manifolds (Mathematics). --- Complex manifolds. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- 517.1 Mathematical analysis

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V-INVEX FUNCTIONS AND VECTOR OPTIMIZATION summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past several decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. V-invex functions are areas in which there has been much interest because it allows researchers and practitioners to address and provide better solutions to problems that are nonlinear, multi-objective, fractional, and continuous in nature. Hence, V-invex functions have permitted work on a whole new class of vector optimization applications. There has been considerable work on vector optimization by some highly distinguished researchers including Kuhn, Tucker, Geoffrion, Mangasarian, Von Neuman, Schaiible, Ziemba, etc. The authors have integrated this related research into their book and demonstrate the wide context from which the area has grown and continues to grow. The result is a well-synthesized, accessible, and usable treatment for students, researchers, and practitioners in the areas of OR, optimization, applied mathematics, engineering, and their work relating to a wide range of problems which include financial institutions, logistics, transportation, traffic management, etc.

Convex functions. --- Vector valued functions. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Functions, Convex --- Mathematics. --- Operations research. --- Management. --- Optimization. --- Applications of Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Operations Research/Decision Theory. --- Operations Research, Management Science. --- Innovation/Technology Management. --- Administration --- Industrial relations --- Organization --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Calculus of variations. --- Decision making. --- Management science. --- Industrial management. --- Business administration --- Business enterprises --- Business management --- Corporate management --- Corporations --- Industrial administration --- Management, Industrial --- Rationalization of industry --- Scientific management --- Management --- Business --- Industrial organization --- Quantitative business analysis --- Problem solving --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Isoperimetrical problems --- Variations, Calculus of --- Engineering --- Engineering analysis --- Decision making --- Mathematics