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Author: Carlo Presilla Publisher: Springer Science & Business Media ISBN: 8847055016 Category : Mathematics Languages : it Pages : 369
Book Description
Questo testo, giunto alla seconda edizione, è adatto per una prima esposizione della teoria delle funzioni di singola variabile complessa e si rivolge a studenti di Fisica, Matematica e Ingegneria che abbiano acquisito le nozioni fondamentali dell’Analisi Matematica reale. L’esigenza di una nuova pubblicazione nasce dall’idea di effettuare una selezione di argomenti, ritenuti fondamentali, la cui esposizione risulti sistematica e autoconsistente in circa 60 ore di lezione mantenendo, al tempo stesso, il rigore matematico volto a favorire la maturazione scientifica dello studente e prepararlo alla lettura di testi avanzati. A corredo della trattazione teorica vengono proposti circa 250 esercizi, raccolti tra le prove scritte assegnate per il superamento del corso, tutti forniti di soluzione dettagliata. Il loro svolgimento costituisce una parte imprescindibile per l’acquisizione della materia.
Author: Carlo Presilla Publisher: Springer Science & Business Media ISBN: 8847055016 Category : Mathematics Languages : it Pages : 369
Book Description
Questo testo, giunto alla seconda edizione, è adatto per una prima esposizione della teoria delle funzioni di singola variabile complessa e si rivolge a studenti di Fisica, Matematica e Ingegneria che abbiano acquisito le nozioni fondamentali dell’Analisi Matematica reale. L’esigenza di una nuova pubblicazione nasce dall’idea di effettuare una selezione di argomenti, ritenuti fondamentali, la cui esposizione risulti sistematica e autoconsistente in circa 60 ore di lezione mantenendo, al tempo stesso, il rigore matematico volto a favorire la maturazione scientifica dello studente e prepararlo alla lettura di testi avanzati. A corredo della trattazione teorica vengono proposti circa 250 esercizi, raccolti tra le prove scritte assegnate per il superamento del corso, tutti forniti di soluzione dettagliata. Il loro svolgimento costituisce una parte imprescindibile per l’acquisizione della materia.
Author: Claudio Canuto Publisher: Springer ISBN: 3319127721 Category : Mathematics Languages : en Pages : 495
Book Description
The purpose of the volume is to provide a support for a first course in Mathematics. 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 requires the additional study of the material contained in the appendices, 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. This new edition features additional material with the aim of matching the widest range of educational choices for a first course of Mathematics.
Author: Shair Ahmad Publisher: Springer ISBN: 3319164082 Category : Mathematics Languages : en Pages : 337
Book Description
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
Author: Sandro Salsa Publisher: Springer ISBN: 3319154168 Category : Mathematics Languages : en Pages : 433
Book Description
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.
Author: Sandro Salsa Publisher: Springer Science & Business Media ISBN: 8847028620 Category : Mathematics Languages : en Pages : 494
Book Description
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.
Author: Valter Moretti Publisher: Springer Science & Business Media ISBN: 8847028353 Category : Mathematics Languages : en Pages : 742
Book Description
This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.
Author: M. Abate Publisher: Springer Science & Business Media ISBN: 8847019419 Category : Mathematics Languages : en Pages : 407
Book Description
The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.
Author: Carlo Presilla
Author: Carlo Presilla
Author: Filippo Gazzola
Author: Franco Tomarelli
Author: Claudio Canuto
Author: Aldo Andreotti
Author: Shair Ahmad
Author: Sandro Salsa
Author: Sandro Salsa
Author: Valter Moretti
Author: M. Abate