Introduction to Partial Differential Equations

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Introduction to Partial Differential Equations by David Borthwick, Springer International Publishing
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Author: David Borthwick ISBN: 9783319489360
Publisher: Springer International Publishing Publication: January 12, 2017
Imprint: Springer Language: English
Author: David Borthwick
ISBN: 9783319489360
Publisher: Springer International Publishing
Publication: January 12, 2017
Imprint: Springer
Language: English

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. 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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. 

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