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Sandro Salsa

Kirjat ja teokset yhdessä paikassa: 11 kirjaa, julkaisuja vuosilta 2005-2022, suosituimpien joukossa Mathematics for Economics and Business. Vertaile teosten hintoja ja tarkista saatavuus suomalaisista kirjakaupoista.

11 kirjaa

Kirjojen julkaisuhaarukka 2005-2022.

Optimal Control of Partial Differential Equations

Optimal Control of Partial Differential Equations

Andrea Manzoni; Alfio Quarteroni; Sandro Salsa

Springer Nature Switzerland AG
2022
nidottu
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance.The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes ofOCPs that stand behind the advanced applications mentioned above.Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text.The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Partial Differential Equations in Action

Partial Differential Equations in Action

Sandro Salsa; Gianmaria Verzini

Springer International Publishing AG
2022
nidottu
This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.
Optimal Control of Partial Differential Equations

Optimal Control of Partial Differential Equations

Andrea Manzoni; Alfio Quarteroni; Sandro Salsa

Springer Nature Switzerland AG
2021
sidottu
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance.The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes ofOCPs that stand behind the advanced applications mentioned above.Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text.The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Mathematics for Economics and Business

Mathematics for Economics and Business

Lorenzo Peccati; Sandro Salsa; Annamaria Squellati

Bocconi University Press
2017
nidottu
This textbook is tailored for those educational programs, such as Economics and Management, that include an introductory (and frequently the only) course in Mathematics. The volume focuses on a number of selected, fundamental topics: the knowledge of Calculus, for functions of one and two variables; the use of Calculus in optimization; the notion of integral for functions of one variable; the language and the elementary techniques of Linear Algebra; the basics of Financial Calculus. Several preliminary examples from applied sciences (mainly from Economics) introduce the theoretical aspects. An excessive formalism is avoided, in order to quickly reach the fundamental concepts. Mybook contains the solutions to the end-of-chapter exercises.
Equazioni a derivate parziali

Equazioni a derivate parziali

Sandro Salsa

Springer Verlag
2016
nidottu
Il testo costituisce una introduzione alla teoria delle equazioni a derivate parziali, strutturata in modo da abituare il lettore ad una sinergia tra modellistica e aspetti teorici. La prima parte riguarda le più note equazioni della fisica-matematica, idealmente raggruppate nelle tre macro-aree diffusione, propagazione e trasporto, onde e vibrazioni. Nella seconda parte si presenta la formulazione variazionale dei principali problemi iniziali e/o al bordo e la loro analisi con i metodi dell'Analisi Funzionale negli spazi di Hilbert.
Partial Differential Equations in Action

Partial Differential Equations in Action

Sandro Salsa; Gianmaria Verzini

Springer International Publishing AG
2015
nidottu
This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.
A Primer on PDEs

A Primer on PDEs

Sandro Salsa; Federico Vegni; Anna Zaretti; Paolo Zunino

Springer Verlag
2013
nidottu
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.
Regularity Estimates for Nonlinear Elliptic and Parabolic Problems

Regularity Estimates for Nonlinear Elliptic and Parabolic Problems

John Lewis; Peter Lindqvist; Juan J. Manfredi; Sandro Salsa

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2012
nidottu
The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.
Partial Differential Equations in Action

Partial Differential Equations in Action

Sandro Salsa

Springer Verlag
2009
nidottu
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines. The main purpose is on the one hand to train students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods. At the end of each chapter, a number of exercises at different level of complexity is included
Invito alle equazioni a derivate parziali

Invito alle equazioni a derivate parziali

Sandro Salsa; Federico Vegni; Anna Zaretti; Paolo Zunino

Springer Verlag
2009
nidottu
Il testo è rivolto a studenti di ingegneria, matematica applicata e fisica ed è disegnato per corsi alle fine del triennio o all'inizio del biennio magistrale. obiettivo didattico è duplice: da un lato presentare ed analizzare alcuni classici modelli differenziali della Meccanica dei Continui, completati da esercizi svolti e da simulazioni numeriche, illustrate usando il metodo delle differenze finite; dall'altro introdurre la formulazione variazionale dei più importanti problemi iniziali/al bordo, accompagnate da simulazioni numeriche effettuate utilizzando il metodo degli elementi finiti. In ultima analisi, il percorso didattico è caratterizzato da una costante sinergia tra modello-teoria-simulazione numerica.
Geometric Approach to Free Boundary Problems

Geometric Approach to Free Boundary Problems

Luis Caffarelli; Sandro Salsa

AMERICAN MATHEMATICAL SOCIETY
2005
sidottu
Describes the properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity. This book is suitable for graduate students and researchers interested in partial differential equations.