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6 produkter
6 produkter
Del 47 - Springer Series in Computational Mathematics
Numerical Methods for Nonlinear Partial Differential Equations
Inbunden, Engelska, 2015
1 512 kr
Skickas inom 10-15 vardagar
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Del 64 - Texts in Applied Mathematics
Numerical Approximation of Partial Differential Equations
Inbunden, Engelska, 2016
631 kr
Skickas inom 5-8 vardagar
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.
Del 47 - Springer Series in Computational Mathematics
Numerical Methods for Nonlinear Partial Differential Equations
Häftad, Engelska, 2016
1 512 kr
Skickas inom 10-15 vardagar
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Del 64 - Texts in Applied Mathematics
Numerical Approximation of Partial Differential Equations
Häftad, Engelska, 2018
442 kr
Skickas inom 5-8 vardagar
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.
Häftad, Tyska, 2023
388 kr
Skickas inom 10-15 vardagar
Dieses Buch bietet eine Einführung in Methoden zur praktischen Lösung mathematischer Probleme, wie der Lösung von Gleichungssystemen, der Bestimmung von Eigenwerten, der Approximation und Integration von Funktionen, der Lösung nichtlinearer Gleichungen und der näherungsweisen Lösung gewöhnlicher Differenzialgleichungen. Es ist in drei Teile gegliedert: Lineare Gleichungssysteme, Eigenwertaufgaben und Optimierung Interpolation, Quadratur und nichtlineare Gleichungen Anfangswertprobleme und Hamiltonsche SystemeJeder dieser Teile ist in neun kurze Kapitel unterteilt und entspricht etwa dem Umfang einer zweistündigen Vorlesung. Vorausgesetzt werden Grundkenntnisse aus der linearen Algebra und Analysis sowie elementare Programmiererfahrungen.Resultate der Analysis werden nur im zweiten und dritten Teil des Buchs verwendet. Lernziele, Tests zur Selbstüberprüfung und Anwendungsaufgaben am Ende jedesKapitels sollen das Verständnis des dargestellten Materials vertiefen. Im Anhang des Buchs finden sich umfangreiche Aufgabensammlungen, detaillierte Beschreibungen für Programmierprojekte, Einführungen in die Programmiersprachen MATLAB, C++ und Python, Zusammenstellungen der wichtigsten Resultate aus der linearen Algebra und Analysis, einige Beispielprogramme, eine Liste weiterführender Themen sowie ausführliche Literaturhinweise. Das Buch richtet sich an Bachelor- und Lehramtsstudenten der Mathematik sowie der Ingenieurs- und Naturwissenschaften.
Del 160 - UNITEXT
Numerical Mathematics 3x9
Three subject areas in 27 short chapters
Häftad, Engelska, 2025
651 kr
Skickas inom 10-15 vardagar
This book provides an introduction to methods for practically solving mathematical problems, such as solving systems of linear equations, determining eigenvalues, approximating and integrating functions, solving nonlinear equations, and the approximate solution of ordinary differential equations.It consists of three parts:• Systems of linear equations, eigenvalue problems and optimisation• Interpolation, quadrature and nonlinear equations• Initial value problems and Hamiltonian systemsEach of these parts is divided into nine short chapters and corresponds approximately to the scope of a two-hour lecture over one semester. Basic knowledge of linear algebra and analysis as well as elementary programming experience are assumed. Results of analysis are only used in the second and third part of the book. Learning objectives, self-assessment tests and exemplary applications at the end of each chapter are intended to deepen the understanding of the presented material. The last chapters of the book contain extensive collections of exercises, detailed descriptions for programming projects, introductions to the programming languages MATLAB, C++ and Python, compilations of the most important results from linear algebra and analysis, some example programs, a list of further topics as well as detailed literature references. The book is aimed at undergraduate students of mathematics as well as engineering and natural sciences. The translation of this book was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.