Fluid Flow Past a Circular Cylinder (updated Fall 2010) (Leal's notes and [H]: 2.5.3)

Vector Calculus. Suffix Notation

Vector Identities

PDE Basic Concepts (Logan 6.1)

Conservation Laws ([DL]: 4.2)

Conservation Laws. Mass Conservation and Diffusion Equation ([H]: 1.2-1.3 [DL]:4.2)

Conservation Laws and Navier-Stokes Equations.

Heat Equation ([H]: 1.2-1.3 [DL]:4.2)

Equilibrium Equations (updated Sep 19, 2005) ([DL: 4.3 [H]: 1.4)

Two-Dimensional Sturm-Liouville EVP and Fredholm Alternative ([H]: 7.4-7.5)

Green's Functions for ODEs. Delta Function ([H]: 9.3)

Green's Functions for ODEs. Eigenfunction Expansions ([H]: 9.3)

Generalized Green's Functions for ODEs. Eigenfunction Expansions ([H]: 9.4)

Existence and Uniqueness for Poisson's Equation BVP.

Green's Functions for PDE's

Green's Functions for PDE's Part II

Fourier Transform. Definition and Application to Heat Conduction on infinite domain. (Updated Nov 21, 2005)

Transform of Derivatives. Convolution Theorem

Application to Wave Equation. Fourier Sine and Cosine Transform II

Two-dimensional Fourier Transform

Linear Volterra Integral Equations. Motivation. Definition. Relationship with 2nd order Linear ODE

IVP for a Linear First Order ODE as a Nonlinear Volterra Integral Equation

Linear Volterra Integral Equations. Existence and Uniqueness of Solutions Theorem

Fredholm Integral Equations with Separable Kernels

Fredholm Integral Equations with Symmetric Kernels

Numerical Solutions of Fredholm Integral Equations