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Título : Mathematical Analysis I Tipo de documento: documento electrónico Autores: Canuto, Claudio ; SpringerLink (Online service) ; Tabacco, Anita Editorial: Milano : Springer Milan Fecha de publicación: 2008 Colección: Universitext Número de páginas: XII, 433 p Il.: online resource ISBN/ISSN/DL: 978-88-470-0876-2 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Integral equations transforms Operational calculus Differential Partial differential Equations Transforms, Calculus Ordinary Clasificación: 51 Matemáticas Resumen: The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level consists of links to online material, which enable the strongly motivated reader to explore further into the subject. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution Nota de contenido: Basic notions -- Functions -- Limits and continuity I -- Limits and continuity II -- Local comparison of functions. Numerical sequences and series -- Differential calculus -- Taylor expansions and applications -- Geometry in the plane and in space -- Integral calculus I -- Integral calculus II -- Ordinary differential equations En línea: http://dx.doi.org/10.1007/978-88-470-0876-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34445 Mathematical Analysis I [documento electrónico] / Canuto, Claudio ; SpringerLink (Online service) ; Tabacco, Anita . - Milano : Springer Milan, 2008 . - XII, 433 p : online resource. - (Universitext) .
ISBN : 978-88-470-0876-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Integral equations transforms Operational calculus Differential Partial differential Equations Transforms, Calculus Ordinary Clasificación: 51 Matemáticas Resumen: The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level consists of links to online material, which enable the strongly motivated reader to explore further into the subject. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution Nota de contenido: Basic notions -- Functions -- Limits and continuity I -- Limits and continuity II -- Local comparison of functions. Numerical sequences and series -- Differential calculus -- Taylor expansions and applications -- Geometry in the plane and in space -- Integral calculus I -- Integral calculus II -- Ordinary differential equations En línea: http://dx.doi.org/10.1007/978-88-470-0876-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34445 Ejemplares
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Título : Mathematical Analysis II Tipo de documento: documento electrónico Autores: Canuto, Claudio ; SpringerLink (Online service) ; Tabacco, Anita Editorial: Milano : Springer Milan Fecha de publicación: 2010 Colección: Universitext Número de páginas: X, 543 p Il.: online resource ISBN/ISSN/DL: 978-88-470-1784-9 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Differential equations Partial differential Mathematics, general Ordinary Equations Clasificación: 51 Matemáticas Resumen: The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined Nota de contenido: Numerical series -- Series of functions and power series -- Fourier series -- Functions between Euclidean spaces -- Differential calculus for scalar functions -- Differential calculus for vector-valued functions -- Applying differential calculus -- Integral calculus in several variables -- Integral calculus on curves and surfaces -- Ordinary differential equations En línea: http://dx.doi.org/10.1007/978-88-470-1784-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33807 Mathematical Analysis II [documento electrónico] / Canuto, Claudio ; SpringerLink (Online service) ; Tabacco, Anita . - Milano : Springer Milan, 2010 . - X, 543 p : online resource. - (Universitext) .
ISBN : 978-88-470-1784-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Differential equations Partial differential Mathematics, general Ordinary Equations Clasificación: 51 Matemáticas Resumen: The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined Nota de contenido: Numerical series -- Series of functions and power series -- Fourier series -- Functions between Euclidean spaces -- Differential calculus for scalar functions -- Differential calculus for vector-valued functions -- Applying differential calculus -- Integral calculus in several variables -- Integral calculus on curves and surfaces -- Ordinary differential equations En línea: http://dx.doi.org/10.1007/978-88-470-1784-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33807 Ejemplares
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Título : Partial Differential Equations in Action : From Modelling to Theory Tipo de documento: documento electrónico Autores: Salsa, Sandro ; SpringerLink (Online service) Editorial: Milano : Springer Milan Fecha de publicación: 2009 Colección: Universitext Número de páginas: XV, 556 p Il.: online resource ISBN/ISSN/DL: 978-88-470-0752-9 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first one has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas and connections with concrete aspects are emphasized whenever possible, in order to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, the repeated use of the method of separation of variables assumes some basic results from the theory of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods for the variational formulation and analysis of linear boundary and initial-boundary value problems\emph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various concepts and results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix. At the end of each chapter, a number of exercises at different level of complexity is included. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising the comprehension and to facilitate a selection of topics for a one or two semester course Nota de contenido: Diffusion -- The Laplace Equation -- Scalar Conservation Laws and First Order Equations -- Waves and Vibrations -- Elements of Functional Analysis -- Distributions and Sobolev Spaces -- Variational Formulation of Elliptic Problems -- Weak Formulation of Evolution Problems En línea: http://dx.doi.org/10.1007/978-88-470-0752-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34120 Partial Differential Equations in Action : From Modelling to Theory [documento electrónico] / Salsa, Sandro ; SpringerLink (Online service) . - Milano : Springer Milan, 2009 . - XV, 556 p : online resource. - (Universitext) .
ISBN : 978-88-470-0752-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first one has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas and connections with concrete aspects are emphasized whenever possible, in order to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, the repeated use of the method of separation of variables assumes some basic results from the theory of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods for the variational formulation and analysis of linear boundary and initial-boundary value problems\emph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various concepts and results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix. At the end of each chapter, a number of exercises at different level of complexity is included. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising the comprehension and to facilitate a selection of topics for a one or two semester course Nota de contenido: Diffusion -- The Laplace Equation -- Scalar Conservation Laws and First Order Equations -- Waves and Vibrations -- Elements of Functional Analysis -- Distributions and Sobolev Spaces -- Variational Formulation of Elliptic Problems -- Weak Formulation of Evolution Problems En línea: http://dx.doi.org/10.1007/978-88-470-0752-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34120 Ejemplares
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