152 / FIELDS OF INSTRUCTION


 Prerequisite: EGC 630. Application of spectral theory of linear operators to
 differential equations, eigenfunction expansion, Green's function techniques, method
 of separation of variables, and integral transform techniques.
 EGC 632-ANALYTICAL TECHNIQUES FOR ENGINEERS AND SCIENTISTS 3.
 3 credits
 Prerequisite: EGC 631. Application of spectral theory of linear operators to
 integral equations, asymptotic solutions and evaluation of integrals, perturbation
 methods, WKB method, variational methods, and Wiener-Hopf technique.
 EGC 633-PRINCIPLES OF ENGINEERING ANALYSIS 1. 3 credits
 Prerequisite: MS 501. Solution of ordinary differential equations with variable
 coefficients. Method of Frobenius, classification of singularities, integral representa-
 tions of solutions. Treatment of classical equations of Bessel, Legendre, Hermite
 and Mathieu. Asymptotic solutions using the WBK method and saddle-point
 technique.
 EGC 634-PRINCIPLES OF ENGINEERING ANALYSIS 2. 3 credits
 Prerequisite: MS 501. General methods for solving partial differential equations
 of first and second order. Classification into hyperbolic, elliptic, and parabolic types.
 Reduction to canonical form. Equations of wave propagation, heat conduction, and
 Laplace. Treatment of initial and boundary value problems.
 EGC 635-PRINCIPLES OF ENGINEERING ANALYSIS 3. 3 credits
 Prerequisite: EGC 634. Dirichlet and Neumann boundary value problems.
 Green's function for Laplace's equation, conformal mapping, spherical harmonics.
 Solution of the Helmholtz, Poisson, and biharmonic equations. Application to in-
 viscid hydrodynamics, optical diffraction and gravitational potential theory.
 EGC 636-PRINCIPLES OF ENGINEERING ANALYSIS 4. 3 credits
 Prerequisite: MS 501. Solution of Volterra and Fredholm integral equations of
 the first and second kind. Inversion of self-adjoint operators via Green's function,
 properties of symmetric kernels, Hilbert-Schmidt theory, and the bilinear formula.
 Treatment of the singular integral equations of Abel and Carleman. Iteration and
 approximation techniques.
 EGC 637-PRINCIPLES OF ENGINEERING ANALYSIS 5. 3 credits
 Prerequisite: EGC 633. Solution techniques for nonlinear differential and in-
tegral equations. The equations of Riccati, van der Pol, and Hammerstein. Elliptic
functions and Painlev6 transcendents. Phase plane, singular points, limit cycles and
stability of autonomous systems. Similarity transforms and singular perturbation
theory applied to nonlinear partial differential equations arising in hydrodynamics.
EGC 638-APPROXIMATION TECHNIQUES IN ENGINEERING AND SCIENCE 1.
 3 credits
 Prerequisite: EGC 632. Asymptotic solutions of differential and integral equa-
tions, geometrical theory of diffraction, regular and singular perturbations, WBK
method, and variational methods.
EGC 639-APPROXIMATION TECHNIQUES IN ENGINEERING AND SCIENCE 2.
 2 credits
 Prerequisite: EGC 632. Krylov-Bogoliubov-Whitham's averaging technique for
nonlinear differential equations. Chapman-Enskog's and Grad's approximate solu-
tion of Boltzmann equation; other approximation techniques.
EGC 671-INTRODUCTION TO PLASMAS. 3 credits
 Prerequisites: PS 300, MS 505. Nomenclature, materials, and plasma devices,
fundamentals of plasma kinetic theory, low and high pressure discharges, technical
applications.