0.1 Review of Separation of Variables and Eigenfunction Expansions

1.1 Incompressible and Inviscid Fluid Equation. Theory and Homework

1.4 (Haberman) Equilibrium Temperature Distribution

1.5 (Haberman) Derivation of the Heat Equation 3-D

1.2.2 Well-posedeness of a Drichelt BVP for the Heat Equation

1.3.3 (Section 2.5 Haberman) Well-posedeness of BVPs for Laplace and Poisson Equations

9.3 (Section 9.3.1, 9.3.4 and 9.3.5 Haberman) Green's Functions of BVP for Ordinary Differential Equations

9.3.3 Method of Eigenfunction Expansion for Green's Function

5.3 Sturm-Liouville Eigenvalue Problems

9.4 Fredholm Alternative: BVPs and Algebraic Systems

Vibrating Rectangular Membrane

Existence and Uniqueness for Poisson's Equation BVP.

Green's Functions for PDE's

Green's Functions for PDE's Part II

Method of Characteristics. First Order Equations

Method of Characteristics. Infinite line

Method of Characteristics: Semi-infinite line

Method of Characteristics: Finite Line

Shock Waves (Flaherty Notes)

Shock Waves in More Details

Definition of Fourier Transform

Heat Conduction for Infinite Domain. Convolution Theorem

Transform of Derivatives. Application to heat Conduction

Laplace's' Equation in a Half-Plane

Fourier Sine and Cosine Transforms

Two-Dimensional Fourier Transforms