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The book is designed chiefly for the use of students and teachers. The research worker will perhaps find some helpful suggestions, as well. The student reading this book is presumed to have a thorough knowledge of differential and integral calculus. In some sections also an acquaintance with the most elementary theorems of the theory of analytic functions and of the theory of linear differential equations is desirable. The text offers a short introduction to vector analysis and a presentation of the Fredholm theory of integral equations. The theory of spherical harmonics is also briefly explained. Consistent use of vector analysis is a characteristic feature of the book. The authors hope that the present text fills a gap, by leading the student reader from the elements of potential theory to the solutions of boundary value problems in a simple and easily understandable way.
Potential theory (Mathematics) --- Spherical harmonics. --- Fisica Matematica.
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Geometry, Differential. --- Differential geometry --- Geometria diferencial --- Generació espontània --- Física matemàtica
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The book collects relevant contributions presented at a conference, organized in honour of Carlo Cercignani, that took place at Politecnico di Milano on May 24–28, 2021. Different research areas characterizing the scientific work of Carlo Cercignani have been considered with a particular focus on: mathematical and numerical methods for kinetic equations; kinetic modelling of gas mixtures and polyatomic gases; applications of the Boltzmann equation to electron transport, social phenomena and epidemic spread; turbulence modelling; the Einstein Classical Program; Dynamical Systems Theory.
Differential equations --- Mathematical physics --- differentiaalvergelijkingen --- wiskunde --- fysica --- Física matemàtica
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This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.
Operator theory. --- Operator Theory. --- Functional analysis --- Mathematical physics --- Operator theory --- Teoria d'operadors --- Física matemàtica
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This book is the second volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to quantum field theory and open quantum systems.
Mathematical physics. --- Quantum physics. --- Mathematical Physics. --- Quantum Physics. --- Física matemàtica --- Teoria quàntica --- Descobriments científics
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This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.
Celestial mechanics. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Mecànica celeste --- Relativitat general (Física) --- Astrometria --- Física matemàtica --- Celestial mechanics
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This book is intended for students taking an honours course in mathematics (Master's degree), but the arrangement of the material is suitable for the pass degree candidate. Several of the theorems in pure mathematics specially required for the subject are brought together in Chapter 1; the more difficult chapters on Green's theorem, harmonic functions and the attraction of ellipsoids come at the end. Examples are grouped according to difficulty. --Back cover.
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Mathematical physics. --- Mathematical physics --- Physique mathématique --- Periodicals. --- Périodiques --- Physical mathematics --- Physics --- Mathematics --- theoretical physics --- experimental physics --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Física. --- Física --- Física matemàtica
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This concise volume presents an overview of equations of mathematical physics and generalized functions. While intended for advanced readers, the accessible introduction and text structure allows beginners to study at their own pace as the material gradually increases in difficulty. The text introduces the concept of generalized Sobolev functions and L. Schwartz distributions briefly in the opening section, gradually approaching a more in-depth study of the “generalized” differential equation (also known as integral equality). In contrast to the traditional presentation of generalized Sobolev functions and L. Schwartz distributions, this volume derives the topology from two natural requirements (which are equivalent to it). The text applies the same approach to the theory of the canonical Maslov operator. It also features illustrative drawings and helpful supplementary reading in the footnotes concerning historical and bibliographic information related to the subject of the book. Additionally, the book devotes a special chapter to the application of the theory of pseudodifferential operators and Sobolev spaces to the inverse magneto/electroencephalography problem. Explicit numerically realizable formulas related to the Cauchy problem for elliptic equations (including quasilinear ones) and also to the Poincaré--Steklov operators are presented. The book is completed by three additions, which were written by famous mathematicians Yu. V. Egorov, A. B. Antonevich, and S. N. Samborski.
Functional analysis. --- Mathematical physics. --- Functional Analysis. --- Mathematical Physics. --- Physical mathematics --- Physics --- Mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Física matemàtica
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Mathematical physics --- Physics --- Physique mathématique --- Physique --- Philosophy --- Philosophie --- Mathematical physics. --- Natuurkunde. --- Wetenschapsfilosofie. --- Física matemática. --- Física --- Methodologie. --- Physik. --- Physique mathématique. --- Philosophy. --- Collections. --- Filosofía. --- Philosophie. --- 530.1 --- Basic principles of physics --- 530.1 Basic principles of physics --- Physique mathématique
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