Graduate Texts in Mathematics- Partial Differential Equations An Introduction to Analytical and Numerical Methods
Afbeeldingen
Sla de afbeeldingen overArtikel vergelijken
- Engels
- Hardcover
- 9783031133787
- 02 januari 2023
- 452 pagina's
Samenvatting
This textbook introduces the study of partial differential equations using both analytical and numerical methods. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains.
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 Maple™ 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.
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 onfinite difference and finite element methods. Computer-aided calculation with Maple™ 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.
Productspecificaties
Inhoud
- Taal
- en
- Bindwijze
- Hardcover
- Oorspronkelijke releasedatum
- 02 januari 2023
- Aantal pagina's
- 452
Betrokkenen
- Hoofdauteur
- Wolfgang Arendt
- Tweede Auteur
- Karsten Urban
- Hoofduitgeverij
- Springer International Publishing Ag
Vertaling
- Eerste Vertaler
- James B. Kennedy
Overige kenmerken
- Editie
- 1st ed. 2023
- Product breedte
- 155 mm
- Product lengte
- 235 mm
- Studieboek
- Nee
- Verpakking breedte
- 155 mm
- Verpakking hoogte
- 235 mm
- Verpakking lengte
- 235 mm
- Verpakkingsgewicht
- 875 g
EAN
- EAN
- 9783031133787
Je vindt dit artikel in
- Categorieën
- Studieboek of algemeen
- Studieboeken
- Beschikbaarheid
- Leverbaar
- Taal
- Engels
- Boek, ebook of luisterboek?
- Boek
Kies gewenste uitvoering
Prijsinformatie en bestellen
De prijs van dit product is 70 euro en 22 cent.- Prijs inclusief verzendkosten, verstuurd door bol
- Ophalen bij een bol afhaalpunt mogelijk
- 30 dagen bedenktijd en gratis retourneren
- Dag en nacht klantenservice
Rapporteer dit artikel
Je wilt melding doen van illegale inhoud over dit artikel:
- Ik wil melding doen als klant
- Ik wil melding doen als autoriteit of trusted flagger
- Ik wil melding doen als partner
- Ik wil melding doen als merkhouder
Geen klant, autoriteit, trusted flagger, merkhouder of partner? Gebruik dan onderstaande link om melding te doen.