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In this introductory text, physics concepts are introduced as a means of understanding experimental observations, not as a sequential list of facts to be memorized. The book is structured around the key scientific discoveries that led to much of our current understanding of the universe. Numerous exercises are provided that utilize Mathematica software to help students explore how the language of mathematics is used to describe physical phenomena. Topics requiring quantum mechanics for a more complete explanation are identified but not pursued. In a departure from the traditional methodology and subject matter used in introductory physics texts, this is organized in a manner that will facilitate a guided discovery style of instruction. Students will obtain much more detailed information about fewer topics and will also gain proficiency with Mathematica, a powerful tool with many potential uses in subsequent courses.

Physics. --- Classical Continuum Physics. --- Mathematical Methods in Physics. --- Numerical and Computational Physics. --- Mathematical Applications in the Physical Sciences. --- Mathematical physics. --- Physique --- Physique mathématique --- Physics --- Physical Sciences & Mathematics --- Physics - General --- Continuum physics. --- Classical and Continuum Physics. --- Numerical and Computational Physics, Simulation. --- Physical mathematics --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Classical field theory --- Continuum physics --- Continuum mechanics

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Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors, and theoretical computer scientists.

Mathematics. --- Commutative Rings and Algebras. --- Field Theory and Polynomials. --- Linear and Multilinear Algebras, Matrix Theory. --- Symbolic and Algebraic Manipulation. --- Algebra --- Algebra. --- Field theory (Physics). --- Matrix theory. --- Mathématiques --- Algèbre --- Champs, Théorie des (Physique) --- Data processing. --- Informatique --- Commutative algebra. --- Mathematics --- Physical Sciences & Mathematics --- Computer science --- Commutative rings. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematical analysis --- Computer science—Mathematics. --- Rings (Algebra) --- Field theory (Physics)

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This book addresses a fascinating set of questions in theoretical physics which will both entertain and enlighten all students, teachers and researchers and other physics aficionados. These range from Newtonian mechanics to quantum field theory and cover several puzzling issues that do not appear in standard textbooks. Some topics cover conceptual conundrums, the solutions to which lead to surprising insights; some correct popular misconceptions in the textbook discussion of certain topics; others illustrate deep connections between apparently unconnected domains of theoretical physics; and a few provide remarkably simple derivations of results which are not often appreciated. The connoisseur of theoretical physics will enjoy a feast of pleasant surprises skilfully prepared by an internationally acclaimed theoretical physicist. Each topic is introduced with proper background discussion and special effort is taken to make the discussion self-contained, clear and comprehensible to anyone with an undergraduate education in physics.

Physics. --- Theoretical, Mathematical and Computational Physics. --- Classical Continuum Physics. --- Astronomy, Astrophysics and Cosmology. --- Statistical Physics, Dynamical Systems and Complexity. --- Astronomy. --- Physique --- Astronomie --- Engineering & Applied Sciences --- Applied Physics --- Continuum physics. --- Astrophysics. --- Cosmology. --- Statistical physics. --- Dynamical systems. --- Classical and Continuum Physics. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Statistical methods --- Field theory (Physics) --- Classical field theory --- Continuum physics --- Continuum mechanics --- Mathematical physics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Astronomical physics --- Astronomy --- Cosmic physics --- Physical mathematics

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This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

Engineering. --- Continuum Mechanics and Mechanics of Materials. --- Classical Continuum Physics. --- Structural Mechanics. --- Materials. --- Mechanical engineering. --- Ingénierie --- Matériaux --- Génie mécanique --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Materials Science --- Applied Mathematics --- Girders. --- Continuum mechanics. --- Mechanics of continua --- Beams --- Continuum physics. --- Structural mechanics. --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Bars (Engineering) --- Structural frames --- Graphic statics --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Classical and Continuum Physics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Classical field theory --- Continuum physics --- Continuum mechanics

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Sebastian Uhlig presents the first experimental investigation of self-organized surface structures (LIPSS) generated by ablation from different (semiconductor and metallic) targets with an ultrafast white-light continuum (WLC) spreading in wavelength from 400-750 nm. The main goal is to study the possibility of LIPSS formation upon irradiation with an incoherent and polychromatic light source (e.g. the WLC) in order to discriminate between the two debated formation scenarios. The generation of a suitable WLC in terms of sufficient white-light pulse energy, broad spectral bandwidth, and low spatial coherence for the LIPSS generation, as well as the characterization of this WLC are additional important objectives of this work. Contents Introduction to Laser Induced Periodic Surface Structures (LIPSS) Introduction to White-Light Continuum Generation Characterization of White-Light Supercontinuum Self-Organized Pattern Formation with Ultrafast White-Light Target Groups Lecturers, researchers and students in the fields of Material Science, Microsystems, Engineering The Author Sebastian Uhlig studied physics at Brandenburg University of Technology Cottbus-Senftenberg and wrote his Master Thesis at the Chair of Experimental Physics II, under the supervision of Prof. Dr. Jürgen Reif. Currently, he is employed at the Fraunhofer Institute for Photonic Microsystems in Dresden, where he works on integrated sensors for a new class of electrostatic actuators.

Physics. --- Classical Continuum Physics. --- Laser Technology, Photonics. --- Physique --- Physics --- Physical Sciences & Mathematics --- Physics - General --- Laser ablation. --- Femtosecond lasers. --- Surfaces (Physics) --- Ablation, Laser --- Laser-induced ablation --- Continuum physics. --- Lasers. --- Photonics. --- Surface chemistry --- Surfaces (Technology) --- Lasers --- Manufacturing processes --- Industrial applications --- Classical and Continuum Physics. --- Optics, Lasers, Photonics, Optical Devices. --- New optics --- Optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Classical field theory --- Continuum physics --- Continuum mechanics