Introduction to Partial Differential Equations

David Borthwick

ISBN 10: 3319840517 / ISBN 13: 9783319840512

Editore: Springer International Publishing AG, CH, 2018

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions: What is the scientific problem we are trying to understand?How do we model that with PDE?What techniques can we use to analyze the PDE?How do those techniques apply to this equation?What information or insight did we obtain by developing and analyzing the PDE?The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspirationfor the development of methods. Softcover reprint of the original 1st ed. 2016. Codice articolo LU-9783319840512

Riassunto:

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. 

Within each section the author creates a narrative that answers the five questions: 

1. What is the scientific problem we are trying to understand?
   
2. How do we model that with PDE?
3. What techniques can we use to analyze the PDE?
4. How do those techniques apply to this equation?
5. What information or insight did we obtain by developing and analyzing the PDE?

The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspirationfor the development of methods. 

Informazioni sull?autore: David Borthwick, Department of Mathematics and Computer Science, Emory University,  Atlanta, GA 30322

Dati bibliografici

Titolo: Introduction to Partial Differential ...
Casa editrice: Springer International Publishing AG, CH
Data di pubblicazione: 2018
Legatura: Paperback
Condizione: New