Introduction to Partial Differential Equations
Borthwick, David.
creator
author.
aut
http://id.loc.gov/vocabulary/relators/aut
SpringerLink (Online service)
text
gw
2016
monographic
eng
access
XVI, 283 p. 68 illus., 61 illus. in color. online resource.
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.
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.
by David Borthwick.
Differential equations, partial
Partial Differential Equations
Mathematical Applications in the Physical Sciences
QA370-380
515.353
Springer eBooks
Universitext
9783319489360
https://doi.org/10.1007/978-3-319-48936-0
https://doi.org/10.1007/978-3-319-48936-0
ISI Library, Kolkata
170112
20181204134236.0
978-3-319-48936-0