An Introduction to Partial Differential Equations
by Per Kristen Jakobsen
Publisher: arXiv.org 2019
Number of pages: 226
These lecture notes view the subject through the lens of applied mathematics. From this point of view, the physical context for basic equations like the heat equation, the wave equation and the Laplace equation are introduced early on, and the focus of the lecture notes are on methods, rather than precise mathematical definitions and proofs. With respect to methods, both analytical and numerical approaches are discussed.
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by John Douglas Moore - UCSB
The author develops the most basic ideas from the theory of partial differential equations, and apply them to the simplest models arising from physics. He presents some of the mathematics that can be used to describe the vibrating circular membrane.
by Erich Miersemann - Leipzig University
These lecture notes are intended as an introduction to linear second order elliptic partial differential equations. From the table of contents: Potential theory; Perron's method; Maximum principles; A discrete maximum principle.
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The reason for my choosing the partial differential equations as the subject for these lectures is my wish to inspire in my audience a love for Mathematics. I give a brief historical account of the application of Mathematics to natural phenomena.
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