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Mathematical physics --- Problems, exercises, etc. --- Mathematical physics - Problems, exercises, etc.

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Il testo richiama i principali concetti, definizioni e teoremi relativi agli spazi vettoriali, agli sviluppi in serie di Fourier, alle equazioni alle derivate parziali, alle trasformate integrali di Laplace e di Fourier, ad alcune classi di equazioni integrali (con specifico riferimento alla funzione di Green). Si danno altresi' cenni di funzioni di variabile complessa, di teoria dei gruppi, e di spazi funzionali. Di ciascun argomento vengono ampiamente discusse le motivazioni e le applicazioni nel campo della fisica e, talora, di altre discipline scientifiche. Tali argomenti vengono approfonditi da esercizi (perlopiu' svolti, o con soluzione), spesso tratti da effettivi temi d'esame del corso di Metodi matematici per la fisica del corso di laurea in Fisica (Catania).

Boundary value problems. --- Engineering mathematics. --- Mathematical physics -- Methodology. --- Mathematical physics -- Problems, exercises, etc. --- Mathematical physics. --- Physics --- Physical Sciences & Mathematics --- Physics - General --- Differential equations --- Engineering mathematics --- Numerical solutions --- 517.91 Differential equations --- Physics. --- Applied mathematics. --- Mathematical Methods in Physics. --- Appl.Mathematics/Computational Methods of Engineering. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previous edition: "The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities." --Physics Today "Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done." --Zentralblatt MATH.

Mathematical physics -- Problems, exercises, etc. --- Mathematical physics -- Study and teaching. --- Mathematical physics. --- Mathematical physics --- Applied Physics --- Physics - General --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Study and teaching. --- Physical mathematics --- Mathematics --- Fréchet spaces. --- Fréchet spaces --- Espaces nucléaires (Analyse fonctionnelle) --- 515.142.2 --- General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- Physics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Mathematical Methods in Physics. --- Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 512.58 --- 512.58 Categories. Category theory --- Categories. Category theory --- Analytical spaces --- Algebraic topology --- Categories (Mathematics) --- Topology --- Congresses. --- Linear operators. --- Nuclear spaces (Functional analysis). --- Nuclear spaces (Functional analysis) --- Linear operators --- Opérateurs linéaires --- Global analysis (Mathematics). --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Fréchet, Espaces de. --- Fréchet spaces. --- Topologie --- Catégories (mathématiques) --- 517.1 Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Espaces nucléaires (analyse fonctionnelle) --- Fréchet, Espaces de. --- Espaces nucléaires (analyse fonctionnelle) --- Topology. --- Catégories (mathématiques) --- Topologie generale --- Analyse fonctionnelle --- Espaces particuliers --- Espaces de suites