Introduction to Partial Differential Equations (Universitext) - Hardcover

Borthwick, David

Hardcover

ISBN 10: 3319489348 ISBN 13: 9783319489346

Verlag: Springer International Publishing AG, 2017

Inhaltsangabe

<DIV><DIV><DIV>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.&NBSP;</DIV><DIV><BR></DIV><DIV>WITHIN EACH SECTION THE AUTHOR CREATES A NARRATIVE THAT ANSWERS THE FIVE QUESTIONS:&NBSP;</DIV></DIV><OL><LI>WHAT IS THE SCIENTIFIC PROBLEM WE ARE TRYING TO UNDERSTAND?<BR></LI><LI>HOW DO WE MODEL THAT WITH PDE?</LI><LI>WHAT TECHNIQUES CAN WE USE TO ANALYZE THE PDE?</LI><LI>HOW DO THOSE TECHNIQUES APPLY TO THIS EQUATION?</LI><LI>WHAT INFORMATION OR INSIGHT DID WE OBTAIN BY DEVELOPING AND ANALYZING THE PDE?</LI></OL></DIV><DIV>THE TEXT STRESSES THE INTERPLAY BETWEEN MODELING AND MATHEMATICAL ANALYSIS, PROVIDING A THOROUGH SOURCE OF PROBLEMS AND AN INSPIRATION FOR THE DEVELOPMENT OF METHODS.&NBSP;</DIV><BR>

Über diesen Titel

Críticas

“The book under review is intended for an introductory course for students. The author gives a balanced presentation that includes modern methods, without requiring prerequisites beyond vector calculus and linear algebra. Concepts and definitions from analysis are introduced only as they are needed in the text.” (Dian K. Palagachev, zbMATH 1364.35001, 2017)

Reseña del editor

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 inspiration for the development of methods. 

Details zur Ausgabe

• Verlag: Springer International Publishing AG
• Erscheinungsdatum: 2017
• ISBN 10: 3319489348
• ISBN 13: 9783319489346
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 283