Partial Differential Equations : An Introduction to Analytical and Numerical Methods /

This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics com...

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Main Authors: Arendt, Wolfgang, 1950-, author 298021, Urban, Karsten, author 651726, Kennedy, J. B., translator 259344, SpringerLink (Online service)
Format: software, multimedia
Language:eng
Published: Cham : Springer, 2023
Subjects:
Online Access:https://www.ebooks.com
https://drive.google.com/file/d/15hIT3r62bdxZ-JLFoM8MVXJJJ_l0GfpM/view?usp=drive_link
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author Arendt, Wolfgang, 1950-, author 298021
Urban, Karsten, author 651726
Kennedy, J. B., translator 259344
SpringerLink (Online service)
author_facet Arendt, Wolfgang, 1950-, author 298021
Urban, Karsten, author 651726
Kennedy, J. B., translator 259344
SpringerLink (Online service)
author_sort Arendt, Wolfgang, 1950-, author 298021
collection OCEAN
description This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
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spelling KOHA-OAI-TEST:6073192024-11-16T01:00:06ZPartial Differential Equations : An Introduction to Analytical and Numerical Methods / Arendt, Wolfgang, 1950-, author 298021 Urban, Karsten, author 651726 Kennedy, J. B., translator 259344 SpringerLink (Online service) software, multimedia Electronic books 631902 Cham : Springer,2023engThis textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.Includes bibliographical references and index1. Modeling, or where do differential equations come from -- 2. Classification and characteristics -- 3. Elementary methods -- 4. Hilbert spaces -- 5. Sobolev spaces and boundary value problems in dimension one -- 6. Hilbert space methods for elliptic equations -- 7. Neumann and Robin boundary conditions -- 8.Spectral decomposition and evolution equations -- 9. Numerical methods -- 10. Maple, or why computers can sometimes help.This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.Differential EquationsFunctional AnalysisNumerical Analysishttps://www.ebooks.comhttps://drive.google.com/file/d/15hIT3r62bdxZ-JLFoM8MVXJJJ_l0GfpM/view?usp=drive_linkURN:ISBN:9783031133794
spellingShingle Differential Equations
Functional Analysis
Numerical Analysis
Arendt, Wolfgang, 1950-, author 298021
Urban, Karsten, author 651726
Kennedy, J. B., translator 259344
SpringerLink (Online service)
Partial Differential Equations : An Introduction to Analytical and Numerical Methods /
title Partial Differential Equations : An Introduction to Analytical and Numerical Methods /
title_full Partial Differential Equations : An Introduction to Analytical and Numerical Methods /
title_fullStr Partial Differential Equations : An Introduction to Analytical and Numerical Methods /
title_full_unstemmed Partial Differential Equations : An Introduction to Analytical and Numerical Methods /
title_short Partial Differential Equations : An Introduction to Analytical and Numerical Methods /
title_sort partial differential equations an introduction to analytical and numerical methods
topic Differential Equations
Functional Analysis
Numerical Analysis
url https://www.ebooks.com
https://drive.google.com/file/d/15hIT3r62bdxZ-JLFoM8MVXJJJ_l0GfpM/view?usp=drive_link
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