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Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics. This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in chapter 10, and the necessary tools from functional analysis are developed within the coarse. The book can be used to teach a variety of different courses. This new edition features new problems throughout, and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.

Partial differential equations --- Differential equations, Partial. --- Equations aux dérivées partielles --- Differential equations, Partial --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- 517.95 --- 517.95 Partial differential equations --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Partial Differential Equations. --- Applications of Mathematics. --- Mathematical Methods in Physics. --- Appl.Mathematics/Computational Methods of Engineering. --- Differential equations, partial. --- Mathematical physics. --- Mathematical and Computational Engineering. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Engineering --- Engineering analysis --- Mathematical analysis --- Differential equations. --- Differential Equations. --- Mathematical and Computational Engineering Applications. --- Data processing.

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The Vehicle Routing Problem (VRP) has been an especially active and fertile area of research. Over the past five to seven years, there have been numerous technological advances and exciting challenges that are of considerable interest to students, teachers, and researchers. The Vehicle Routing Problem: Latest Advances and New Challenges will focus on a host of significant technical advances that have evolved over the past few years for modeling and solving vehicle routing problems and variants. New approaches for solving VRPs have been developed from important methodological advances. These developments have resulted in faster solution algorithms, more accurate techniques, and an improvement in the ability to solve large-scale, complex problems. The book will systematically examine these recent developments in the VRP and provide the following in a unified and carefully developed presentation: Present novel problems that have arisen in the vehicle routing domain and highlight new challenges for the field; Present significant methodological advances or new approaches for solving existing vehicle routing problems; Summarize the most significant research results for the vehicle routing problem and its variants from 2000 to the present. .

Vehicle routing problem. --- Transportation problems (Programming) --- Delivery of goods --- Mathematical models. --- Store delivery services --- Transportation --- Parcel post --- Shipment of goods --- VRP (Vehicle routing problem) --- Combinatorial optimization --- Traveling salesman problem --- Transport problems (Programming) --- Linear programming --- Road traffic --- Operational research. Game theory --- 519.8 --- 681.3*G22 --- 519.8 Operational research --- Operational research --- 681.3*G22 Graph theory: graph algorithms; network problems; path and tree problems; trees--See also {681.3*F22} --- Graph theory: graph algorithms; network problems; path and tree problems; trees--See also {681.3*F22} --- Operations research. --- Engineering mathematics. --- Mathematics. --- Engineering economy. --- Production management. --- Operations Research/Decision Theory. --- Mathematical and Computational Engineering. --- Applications of Mathematics. --- Operations Research, Management Science. --- Engineering Economics, Organization, Logistics, Marketing. --- Operations Management. --- Manufacturing management --- Industrial management --- Economy, Engineering --- Engineering economics --- Industrial engineering --- Math --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Operational analysis --- Management science --- Research --- System theory --- Mathematics --- Decision making. --- Applied mathematics. --- Management science. --- Engineering economics. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Decision making --- Engineering—Data processing. --- Industrial Management. --- Operations Research and Decision Theory. --- Mathematical and Computational Engineering Applications. --- Operations Research, Management Science . --- Business administration --- Business enterprises --- Business management --- Corporate management --- Corporations --- Industrial administration --- Management, Industrial --- Rationalization of industry --- Scientific management --- Business --- Industrial organization