Franco Tomarelli's Books

Analytic Functions Integral Transforms Differential Equations

By: Franco Tomarelli,Filippo Gazzola,Maurizio Zanotti

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Analytic Functions Integral Transforms Differential Equations

By: Franco Tomarelli,Filippo Gazzola,Maurizio Zanotti

Differential equations play a relevant role in many disciplines and provide powerful tools for analysis and modeling in applied sciences. The book contains several classical and modern methods for the study of ordinary and partial differential equations. A broad space is reserved to Fourier and Laplace transforms together with their applications to the solution of boundary value and/or initial value problems for differential equations. Basic prerequisites concerning analytic functions of complex variable and Lp spaces are synthetically presented in the first two chapters. Techniques based on integral transforms and Fourier series are presented in specific chapters, first in the easier framework of integrable functions and later in the general framework of distributions. The less elementary distributional context allows to deal also with differential equations with highly irregular data and pulse signals. The theory is introduced offhandedly and learning of miscellaneous methods is achieved step-by-step through the proposal of many exercises of increasing difficulty. Additional recap exercises are collected in dedicated sections. Several tables for easy reference of main formulas are available at the end of the book. The presentation is oriented mainly to students of Schools in Engineering, Sciences and Economy. The partition of various topics in several self-contained and independent sections allows an easy splitting in at least two didactic modules: one at undergraduate level, the other at graduate level. This text is the English translation of the Second Edition of the Italian book “Analisi Complessa, Trasformate, Equazioni Differenziali" published by Esculapio in 2013.

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Page Count

392

Publisher

Società Editrice Esculapio

Published Date

ISBN 10

8874886608

ISBN 13

9788874886609

Discrete Dynamical Models

By: Ernesto Salinelli,Franco Tomarelli

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Discrete Dynamical Models

By: Ernesto Salinelli,Franco Tomarelli

This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations. The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty; in the last chapter the detailed solution is given for most of them.

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398

Publisher

Springer

Published Date

ISBN 10

3319022911

ISBN 13

9783319022918

Mathematical Analysis Tools for Engineering

By: franco tomarelli

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Mathematical Analysis Tools for Engineering

By: franco tomarelli

This book is an introduction to the study of ordinary differential equations and partial differential equations, ranging from elementary techniques to advanced tools. The presentation focusses on initial value problems, boundary value problems, equations with delayed argument and analysis of periodic solutions: main goals are the analysis of diffusion equation, wave equation, Laplace equation and signals. The study of relevant examples of differential models highlights the notion of well-posed problem. An expanded tutorial chapter collects the topics from basic undergraduate calculus that are used in subsequent chapters. A wide exposition concerning classical methods for solving problems related to differential equations is available: mainly separation of variables and Fourier series, with basic worked exercises. A whole chapter deals with the analytic functions of complex variable. An introduction to function spaces, distributions and basic notions of functional analysis is present. Several chapters are devoted to Fourier and Laplace transforms methods to solve boundary value problems and initial value problems for differential equations. Tools for the analysis appear gradually: first in function spaces, then in the more general framework of distributions, where a powerful arsenal of techniques allows dealing with impulsive signals and singularities in both data and solutions of differential problems. This Second Edition contains additional exercises and a new chapter concerning signals and filters analysis in connection to integral transforms.

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528

Publisher

Società Editrice Esculapio

Published Date

ISBN 13

9791220841580

Analytic Functions Integral Transforms Differential Equations

By: Filippo Gazzola,Franco Tomarelli,Maurizio Zanotti

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Analytic Functions Integral Transforms Differential Equations

By: Filippo Gazzola,Franco Tomarelli,Maurizio Zanotti

Differential equations play a relevant role in many disciplines and provide powerful tools for analysis and modeling in applied sciences. The book contains several classical and modern methods for the study of ordinary and partial differential equations. A broad space is reserved to Fourier and Laplace transforms together with their applications to the solution of boundary value and/or initial value problems for differential equations. Basic prerequisites concerning analytic functions of complex variable and Lp spaces are synthetically presented in the first two chapters. Techniques based on integral transforms and Fourier series are presented in specific chapters, first in the easier framework of integrable functions and later in the general framework of distributions. The less elementary distributional context allows to deal also with differential equations with highly irregular data and pulse signals. The theory is introduced concisely, while learning of miscellaneous methods is achieved step-by-step through the proposal of many exercises of increasing difficulty. Additional recap exercises are collected in dedicated sections. Several tables for easy reference of main formulas are available at the end of the book. The presentation is oriented mainly to students of Schools in Engineering, Sciences and Economy. The partition of various topics in several self-contained and independent sections allows an easy splitting in at least two didactic modules: one at undergraduate level, the other at graduate level. This text is the English translation of the Third Edition of the Italian book “Analisi Complessa, Trasformate, Equazioni Differenziali" published by Esculapio in 2015.

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Page Count

522

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Società Editrice Esculapio

Published Date

ISBN 10

887488561X

ISBN 13

9788874885619

Variational Methods for Discontinuous Structures

International Workshop at Villa Erba (Cernobbio), Italy, July 2001

By: Gianni Dal Maso

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Variational Methods for Discontinuous Structures

International Workshop at Villa Erba (Cernobbio), Italy, July 2001

By: Gianni Dal Maso

This volume contains the Proceedings of the International Workshop "Variational Methods For Discontinuous Structures", held at Villa Erba Antica (Cernobbio) on the Lago di Como, July 4-6, 2001. The workshop was jointly organized by the Dipartimento di Matematica Francesco Brioschi of Milano Politecnico and the International School for Advanced Studies (SISSA) of Trieste. In past years the calculus of variations faced mainly the study of continuous structures, particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities. In many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, variational description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes. In most cases theoretical and numerical analysis of these models were provided. Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport problems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework. This volume contains contributions by 12 of the 16 speakers invited to deliver lectures in the workshop. Most of the contributions present original results in fields which are rapidly evolving at present.

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208

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764369132

ISBN 13

9783764369132

Shape Reconstruction from Apparent Contours

Theory and Algorithms

By: Giovanni Bellettini,Valentina Beorchia,Maurizio Paolini,Franco Pasquarelli

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Shape Reconstruction from Apparent Contours

Theory and Algorithms

By: Giovanni Bellettini,Valentina Beorchia,Maurizio Paolini,Franco Pasquarelli

Motivated by a variational model concerning the depth of the objects in a picture and the problem of hidden and illusory contours, this book investigates one of the central problems of computer vision: the topological and algorithmic reconstruction of a smooth three dimensional scene starting from the visible part of an apparent contour. The authors focus their attention on the manipulation of apparent contours using a finite set of elementary moves, which correspond to diffeomorphic deformations of three dimensional scenes. A large part of the book is devoted to the algorithmic part, with implementations, experiments, and computed examples. The book is intended also as a user's guide to the software code appcontour, written for the manipulation of apparent contours and their invariants. This book is addressed to theoretical and applied scientists working in the field of mathematical models of image segmentation.

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385

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Springer

Published Date

ISBN 10

3662451913

ISBN 13

9783662451915

Discrete Dynamical Models

By: Ernesto Salinelli,Franco Tomarelli

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Discrete Dynamical Models

By: Ernesto Salinelli,Franco Tomarelli

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398

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Springer

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ISBN 10

3319022911

ISBN 13

9783319022918

Variational Problems in Materials Science

By: Gianni Dal Maso,Antonio de Simone,Franco Tomarelli

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Variational Problems in Materials Science

By: Gianni Dal Maso,Antonio de Simone,Franco Tomarelli

This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.

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162

Publisher

Birkhäuser

Published Date

ISBN 10

3764375647

ISBN 13

9783764375645

Variational Methods for Discontinuous Structures

International Workshop at Villa Erba (Cernobbio), Italy, July 2001

By: Gianni Dal Maso

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Variational Methods for Discontinuous Structures

International Workshop at Villa Erba (Cernobbio), Italy, July 2001

By: Gianni Dal Maso

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Page Count

208

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Springer Science & Business Media

Published Date

ISBN 10

3764369132

ISBN 13

9783764369132

Variational Methods for Discontinuous Structures

By: Raul Serapioni,Franco Tomarelli

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Variational Methods for Discontinuous Structures

By: Raul Serapioni,Franco Tomarelli

In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.

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212

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Springer Science & Business Media

Published Date

ISBN 10

3764352736

ISBN 13

9783764352738

Analytic Functions Integral Transforms Differential Equations

By: Filippo Gazzola,Franco Tomarelli,Maurizio Zanotti

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Analytic Functions Integral Transforms Differential Equations

By: Filippo Gazzola,Franco Tomarelli,Maurizio Zanotti

Differential equations play a relevant role in many disciplines and provide powerful tools for analysis and modeling in applied sciences. The book contains several classical and modern methods for the study of ordinary and partial differential equations. A broad space is reserved to Fourier and Laplace transforms together with their applications to the solution of boundary value and/or initial value problems for differential equations. Basic prerequisites concerning analytic functions of complex variable and Lp spaces are synthetically presented in the first two chapters. Techniques based on integral transforms and Fourier series are presented in specific chapters, first in the easier framework of integrable functions and later in the general framework of distributions. The less elementary distributional context allows to deal also with differential equations with highly irregular data and pulse signals. The theory is introduced concisely, while learning of miscellaneous methods is achieved step-by-step through the proposal of many exercises of increasing difficulty. Additional recap exercises are collected in dedicated sections. Several tables for easy reference of main formulas are available at the end of the book. The presentation is oriented mainly to students of Schools in Engineering, Sciences and Economy. The partition of various topics in several self-contained and independent sections allows an easy splitting in at least two didactic modules: one at undergraduate level, the other at graduate level. This text is the English translation of the Third Edition of the Italian book “Analisi Complessa, Trasformate, Equazioni Differenziali" published by Esculapio in 2015.

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Solve jigsaw puzzle

Age

Page Count

522

Publisher

Società Editrice Esculapio

Published Date

ISBN 10

887488561X

ISBN 13

9788874885619

Book's by Franco Tomarelli

Analytic Functions Integral Transforms Differential Equations

Analytic Functions Integral Transforms Differential Equations

Discrete Dynamical Models

Discrete Dynamical Models

Mathematical Analysis Tools for Engineering

Mathematical Analysis Tools for Engineering

Analytic Functions Integral Transforms Differential Equations

Analytic Functions Integral Transforms Differential Equations

Variational Methods for Discontinuous Structures

Variational Methods for Discontinuous Structures

Shape Reconstruction from Apparent Contours

Shape Reconstruction from Apparent Contours

Discrete Dynamical Models

Discrete Dynamical Models

Variational Problems in Materials Science

Variational Problems in Materials Science

Variational Methods for Discontinuous Structures

Variational Methods for Discontinuous Structures

Variational Methods for Discontinuous Structures

Variational Methods for Discontinuous Structures

Analytic Functions Integral Transforms Differential Equations

Analytic Functions Integral Transforms Differential Equations

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