Introduction to Partial Differential Equations [electronic resource] / by David Borthwick.
By: Borthwick, David [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextSeries: Universitext: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Description: XVI, 283 p. 68 illus., 61 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319489360.Subject(s): Differential equations, partial  Partial Differential Equations  Mathematical Applications in the Physical SciencesAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.353 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

EBOOKS 
ISI Library, Kolkata

Available  EB1789 
1. Introduction  2. Preliminaries  3. Conservation Equations and Characteristics  4. The Wave Equation  5. Separation of Variables  6. The Heat Equation  7. Function Spaces  8. Fourier Series  9. Maximum Principles  10. Weak Solutions  11. Variational Methods  12. Distributions  13. The Fourier Transform  A. Appendix: Analysis Foundations  References  Notation Guide  Index.
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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