# Partial differential equations

January 27, 2021 — July 23, 2022

algebra

functional analysis

linear algebra

PDEs

Placeholder.

## 1 Classic PDE systems

Andrew Gibiansky, Fluid Dynamics: The Navier-Stokes Equations is a great and compact introduction.

## 2 Green’s functions

Cole’s list of Green’s Functions.

TBD. Operator adjoints.

## 3 Basis function methods

## 4 Laplacian methods

## 5 Eulerian methods

## 6 for fluids specifically

See CFD.

## 7 References

Bluman. 1983. “On Mapping Linear Partial Differential Equations to Constant Coefficient Equations.”

*SIAM Journal on Applied Mathematics*.
Borthwick. 2016.

*Introduction to Partial Differential Equations*. Universitext.
Borzì, and Schulz. 2012.

*Computational Optimization of Systems Governed by Partial Differential Equations*. Computational Science and Engineering Series.
Brezis. 2010.

*Functional Analysis, Sobolev Spaces and Partial Differential Equations*.
Dynkin. 2004.

*Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations*. University Lecture Series, v. 34.
Evans. 1998.

*Partial Differential Equations*.
Kovacic. 1986. “An Algorithm for Solving Second Order Linear Homogeneous Differential Equations.”

*Journal of Symbolic Computation*.
Kuzmin. 2010.

*A Guide to Numerical Methods for Transport Equations*.
Reid. 2015.

*Advanced Analytic 18.305 Methods in Science and Engineering*.