Derivation of the Heat Equation (Updated Jan 12, 2005)

Equilibrium Temperature Distribution

Three-dimensional Heat Equation

Method of Separation of Variables

Method of Separation of Variables II

Method of Separation of Variables III

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) (Feb 2010)

Differentiation of Fourier Series

Integration of Fourier Series

Complex Representation of Fourier Series

Waves I

Method of Characteristics. First Order Equations (Modified Feb 24, 2010)

Method of Characteristics. Infinite line (Updated March 8, 2005)

Method of Characteristics. Semi-infinite line (Updated March 8, 2005)

Method of Characteristics. Semi-infinite Dirichlet and Neumann Problems. Finite line (Feb 2010)

Sturm-Liouville Eigenvalue Problems (Updated Sat MArch 19, 2005)

Sturm-Liouville Eigenvalue Problems II (March 24, 2005)

Vibrating Rectangular Membrane

Two-Dimensional Sturm-Liouville EVP

Green's Formula. Multidimensional EVP and Rayleigh Quotient

Vibrating Circular Membrane (Updated April 6, 2005)

Vibrating Circular Membrane. Circularly Symmetric Case

Nonhomogeneous Problems and Eigenfunctions Expansion