An introduction to advanced analytical techniques frequently used by scientists and engineers to study ordinary differential equations and two-point boundary value problems. Topics include: series solution techniques, method of Frobenius, Laplace transforms, Fourier series and boundary value problems.

Fundamentals of probability; discrete & continuous random variables; expected value; variance; joint, marginal, & conditional distributions; conditional expectations; applications; simulation techniques; central limit theorem.

Protocols,network applications in C for UNIX.

Definition of a topology, relative topology, metric topology, quotient topology, and the product topology. Connectedness, local connectedness, components and path components. Compactness and local compactness, countability and separation axioms, the Urysohn Lemma, metrization and compactification.

Lebesgue measure, and the Lebesgue integral of functions of a real variable. General measure and integration theory. Lebesgue-Stieltjes integral and product measures.