The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has 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 in 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 turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.The third edition contains a few text and formulas revisions and new exercises.
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 of OCPs 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.
Excerpt from: Lorenzo Peccati, Sandro Salsa, Annamaria Squellati Mathematics for Economics and Business 2016, Bocconi University Press 978-88-999-0210-0 Sandro Salsa, Annamaria Squellati Dynamical Systems and Optimal Control 2018, Bocconi University Press 978-88-999-0211-7
Viquito, el querido hermano de Santiago y líder de la pandilla, ha muerto, dejándole como herencia, sólo, una extraña conversación en la playa y una tarjeta con un número telefónico. Al llamar descubrirá, por medio de Filósofo, el mensaje que le dejó su hermano: tenía que hacerse con el liderazgo de la banda. Está en la peor situación posible porque su propio hermano lo mantuvo alejado del grupo, no sabe casi nada del negocio y, mucho menos, está apto para enfrentarse a esos hampones despiadados que sólo lo respetaban por ser el hermano del jefe. ¿Puede un muchacho de los bajos fondos aplicar métodos empresariales al mundo del hampa? la respuesta de "Portvs Imperator" es SI
A cookbook based on science and inspired by a love of good food. Like many Australian doctors worried about soaring rates of obesity, diabetes and heart disease, Dr Sandro Demaio, star of the ABC's Ask the Doctor, knows that the single most effective thing we can do to improve our health is to improve our diet. He also knows that many of us are confused by what this means. His first book, The Doctor's Diet, cuts through the noise of conflicting dietary information and presents a simple, affordable and delicious way of eating that is accessible to every Australian. Drawing on his Italian heritage, his medical training and knowledge as an international expert on obesity, he explains that the best diet is one based on unprocessed ingredients, simply and easily prepared. The book features 110 recipes plus clever tips for making sure that preparing and eating good food is the most pleasurable way possible of getting well and staying healthy. This is a specially formatted fixed-layout ebook that retains the look and feel of the print book.
Are you a good first date? Are you worried about being girlfriend or boyfriend material? Do you just worry there are no more good options left in the world? Where HAVE all the good people gone? We all do. And the solution is establishing a standard we can all live by and date by. Sandro D’Abruzzo shares insights into the quantifiable methods to dating success and helps define a “standard” we should all strive towards in efforts to improve our love lives. He shares his experiences dating in big cities around the world, including jaw-dropping anecdotes about his personal journey, and explaining what happened, what went wrong and what the next move ought to be. From quirky to nightmarish, So You Think You Can Date takes us on a tour of different dating archetypes and offers advice for creating a healthy, realistic dating mentality in the 21st century.
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has 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 in 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 turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.The third edition contains a few text and formulas revisions and new exercises.
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.
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.
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 of OCPs 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.
Excerpt from: Lorenzo Peccati, Sandro Salsa, Annamaria Squellati Mathematics for Economics and Business 2016, Bocconi University Press 978-88-999-0210-0 Sandro Salsa, Annamaria Squellati Dynamical Systems and Optimal Control 2018, Bocconi University Press 978-88-999-0211-7
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