Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Questo testo trae la sua origine da miei vecchi appunti, preparati per il corso di Metodi Matematici della Fisica e via via sistemati, raffinati e aggiornati nel corso di molti anni di insegnamento. L'obiettivo è stato sempre quello di fornire una presentazione per quanto possibile semplice e diretta dei metodi matematici rilevanti per la Fisica: serie di Fourier, spazi di Hilbert, operatori lineari, funzioni di variabile complessa, trasformata di Fourier e di Laplace, distribuzioni. Oltre a questi argomenti di base, viene presentata, in Appendice, una breve introduzione alle prime nozioni di teoria dei gruppi, delle algebre di Lie e delle simmetrie in vista delle loro applicazioni alla Fisica. Anche allo scopo di mantenere il libro nei limiti ragionevoli di un manuale di dimensioni contenute e di agevole consultazione, sono stati spesso tralasciati i dettagli tecnici delle dimostrazioni matematiche (o anzi le dimostrazioni per intero) e tutti i formalismi eccessivi che spesso nascondono la vera natura del problema e del metodo necessario per affrontarlo. Al contrario, si è cercato di chiarire le "idee sottostanti" ai diversi procedimenti; anche le applicazioni proposte sono quelle che meglio e piu' direttamente illustrano i procedimenti stessi, tralasciando altre applicazioni (Meccanica Quantistica, Elettromagnetismo, Equazioni alle Derivate Parziali, Funzioni Speciali, tanto per fare qualche esempio) che sconfinano in differenti discipline. Riassumendo, lo scopo principale e' quello di mettere in condizione chi legge questo libro di acquisire le conoscenze di base che gli permettano di affrontare senza difficoltà anche testi ben più avanzati e impegnativi.

Mathematical physics. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics --- Functional analysis. --- Functions of complex variables. --- Fourier analysis. --- Group theory. --- Mathematical Methods in Physics. --- Functional Analysis. --- Functions of a Complex Variable. --- Fourier Analysis. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Analysis, Fourier --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value. .

Physics. --- Group theory. --- Fourier analysis. --- Functions of complex variables. --- Integral transforms. --- Operational calculus. --- Operator theory. --- Mathematical Methods in Physics. --- Fourier Analysis. --- Operator Theory. --- Functions of a Complex Variable. --- Integral Transforms, Operational Calculus. --- Group Theory and Generalizations. --- Mathematical physics. --- Integral Transforms. --- Physical mathematics --- Physics --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Functional analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Analysis, Fourier --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematics --- Operational calculus --- Differential equations --- Electric circuits --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value. .

Group theory --- Algebra --- Algebraic geometry --- Operator theory --- Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical physics --- Fourieranalyse --- algebra --- analyse (wiskunde) --- complexe veranderlijken --- wiskunde --- fysica

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is the second edition, whose original mission was to offer a new approach for students wishing to better understand the mathematical tenets that underlie the study of physics. This mission is retained in this book. The structure of the book is one that keeps pedagogical principles in mind at every level. Not only are the chapters sequenced in such a way as to guide the reader down a clear path that stretches throughout the book, but all individual sections and subsections are also laid out so that the material they address becomes progressively more complex along with the reader's ability to comprehend it. This book not only improves upon the first in many details, but it also fills in some gaps that were left open by this and other books on similar topics. The 350 problems presented here are accompanied by answers which now include a greater amount of detail and additional guidance for arriving at the solutions. In this way, the mathematical underpinnings of the relevant physics topics are made as easy to absorb as possible. .

Group theory --- Algebraic geometry --- Operator theory --- Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Physics --- Fourieranalyse --- analyse (wiskunde) --- complexe veranderlijken --- wiskunde --- fysica

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Group theory --- Algebraic geometry --- Operator theory --- Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Physics --- Fourieranalyse --- analyse (wiskunde) --- complexe veranderlijken --- wiskunde --- fysica