1.2 Derivation of the Heat Equation 1-D

1.4 Equilibrium Temperature Distribution

1.5 Derivation of the Heat Equation 3-D

2.4.2 Method of Separation of Variables. Heat Conduction in a Thin Insulated Circular Ring

1.5 Derivation of a Vertically Vibrating String

Waves I

Method of Characteristics. First Order Equations

Method of Characteristics. Infinite line

Method of Characteristics: Semi-infinite line

Method of Characteristics: Finite Line

Method of Separation of Variables: Laplace Equation

Laplace Equation for a Circular Disk

Qualitative Properties of Laplace's equation. Well Posedness and Solvability Condition

Fourier Series I

More Details on Fourier Series

Fourier Series of f(x)=exp(x)

Differentiation of Fourier Series

Integration of Fourier Series

Complex Representation of Fourier Series

Sturm-Liouville Eigenvalue Problems

Sturm-Liouville Eigenvalue Problems II

Vibrating Rectangular Membrane

Two-Dimensional Sturm-Liouville EVP

Green's Formula. Multidimensional EVP and Rayleigh Quotient

Vibrating Circular Membrane

Vibrating Circular Membrane (Summary)

Vibrating Circular Membrane. Circularly Symmetric Case

Sections 8.2 and 8.3: Nonhomogeneous Problems. Via Equilibrium Solution. Method of Eigenfunction Expansion

Section 8.4 and 8.5 Nonhomogeneous Problems. Method of Eigenfunction Expansion and Green's Formula

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