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Density Functional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contained in this book allow for a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green’s function or response functions - are introduced step by step, rather than just used. The same applies to some basic notions of solid state theory, as, for instance, the Fermi surface. Also, the language of second quantization is introduced systematically in an Appendix for readers without a formal theoretical physics background.

Density functionals. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Density functional methods --- Density functional theory --- Functional methods, Density --- Functionals, Density --- Functional analysis --- Density functionals --- Mathematical physics --- Fonctionnelles densité --- Physique mathématique --- Chemistry. --- Materials. --- Atomic, Molecular, Optical and Plasma Physics. --- Theoretical and Computational Chemistry. --- Numerical and Computational Physics, Simulation. --- Condensed Matter Physics. --- Materials Science, general. --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Physical sciences --- Materials --- Fonctionnelles densité. --- Physique mathématique. --- Atoms. --- Physics. --- Chemistry, Physical and theoretical. --- Condensed matter. --- Materials science. --- Material science --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Natural philosophy --- Philosophy, Natural --- Dynamics --- Chemistry, Physical and theoretical --- Stereochemistry --- Constitution

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After an introduction to basic concepts of mechanics more advanced topics build the major part of this book. Interspersed is a discussion of selected problems of motion. This is followed by a concise treatment of the Lagrangian and the Hamiltonian formulation of mechanics, as well as a brief excursion on chaotic motion. The last chapter deals with applications of the Lagrangian formulation to specific systems (coupled oscillators, rotating coordinate systems, rigid bodies). The level of this textbook is advanced undergraduate. The authors combine teaching experience of more than 40 years in all fields of Theoretical Physics and related mathematical disciplines and thorough knowledge in creating advanced eLearning content. The text is accompanied by an extensive collection of online material, in which the possibilities of the electronic medium are fully exploited, e.g. in the form of applets, 2D- and 3D-animations. - A collection of 74 problems with detailed step-by-step guidance towards the solutions. - A collection of comments and additional mathematical details in support of the main text. - A complete presentation of all the mathematical tools needed.

Mechanics, Analytic. --- Physics. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Analytical mechanics --- Kinetics --- Mechanics, applied. --- Classical Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory

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