Abstract
Partial differential equations arise frequently in the formulation of fundamental laws of nature and in the mathematical analysis of a wide variety of problems in applied mathematics, mathematical physics, and engineering science. This subject plays a central role in modern mathematical sciences, especially in physics, geometry, and analysis. Many problems of physical interest are described by partial differential equations with appropriate initial and/or boundary conditions. These problems are usually formulated as initial-value problems, boundary-value problems, or initial boundary-value problems. In order to prepare the reader for study and research in nonlinear partial differential equations, a broad coverage of the essential standard material on linear partial differential equations and their applications is required.
Keywords
- Wave Equation
- Linear Partial Differential Equation
- Free Surface Elevation
- Telegraph Equation
- Fractional Diffusion Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
However varied may be the imagination of man, nature is still a thousand times richer, …. Each of the theories of physics … presents (partial differential) equations under a new aspect … without these theories, we should not know partial differential equations.
Henri Poincaré
Since a general solution must be judged impossible from want of analysis, we must be content with the knowledge of some special cases, and that all the more, since the development of various cases seems to be the only way to bringing us at last to a more perfect knowledge.
Leonard Euler
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Debnath, L. (2012). Linear Partial Differential Equations. In: Nonlinear Partial Differential Equations for Scientists and Engineers. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8265-1_1
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