ENGINEERING SCIENCES / 77 Method of averaging. Application to one degree of freedom autonomous and nonautonomous systems. Nonlinear reso- nance. Stability of solutions. Parametrically excited systems. Method of perturbations. EGM 6245-Random Vibrations (3) Prereq: EGM 6215. Statistical analysis, response of discrete single and multiple degree of freedom dynamical systems to stationary random forces and parametric excitation. Extension to continuous systems and nonstationary excitation. Applications to engineer- ing problems. EGM 6250-Theoretical Acoustics (3) Prereq: basic course in vibrations and some background with partial differential equa- tions. Fundamentals of wave phenomena in vibrating solid and fluid media. Analytical methods of attacking acoustical problems. EGM 6321-Principles of Engineering Analysis I (3) Prereq: EGM 4313 orMAP4305. Solution of linear and nonlinear ordi- nary differential equations. Method of Frobenius, classification of singularities. Integral representation of solutions. Treatment of the Bessel, Hermite, Legendre, hypergeometric and Mathieu equations. Asymptotic methods including the WBK and saddle point techniques. Treatment of nonlinear autonomous equa- tions. Phase plane trajectories and limit cycles. Thomas-Fermi, Emden and van der Pol equations. EGM 6322-Principles of Engineering Analysis 11 (3) Prereq: EGM 4313 orMAP4341. General analytic methods for solving partial differential equations of first and second order. Treat- ment of elliptic, parabolic and hyperbolic equations including reduction to canonical form. Detailed discussion of the equa- tions of wave propagation, heat conduction and potential theory. Application of similarity transforms for reduction to ordinary dif- ferential equations. Solution of certain nonlinear partial differen- tial equations arising in hydrodynamics via use of perturbation expansions. EGM 6323-Principles of Engineering Analysis III (3) Prereq: EGM 6322 or equivalent. Dirichlet and Neumann boundary value problems. Green's function for Laplace's equation in two and three dimensions. Conformal mapping techniques and spherical harmonics. Treatment of the Helmholtz, Poisson, and Schroedinger equations. Use of integral transform techniques to solve certain equations arising in applied physics, hydro- dynamics, and electromagnetic theory. EGM 6324-Principles of Engineering Analysis IV (2) Prereq: EGM 4313 or MAP4305. Solution of Volterra and Fredholm in- tegral 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. Treat- ment of the singular integral equations of Abel and Carleman. Iteration and approximation techniques. EGM 6341-Numerical Methods of Engineering Analysis I (3) Prereq: EGM 4313 or equivalent. Finite-difference calculus; in- terpolation and extrapolation; roots of equations; solution of algebraic equations; eigenvalue problems; least-squares method; quadrature formulas; numerical solution of ordinary differen- tial equations; methods of weighted residuals. Use of digital computer. EGM 6342-Numerical Methods of Engineering Analysis II (3) Prereq: EGM 6341 or consent of instructor. Finite-difference methods for parabolic, elliptic, and hyperbolic partial differen- tial equations. Application to heat conduction, solid and fluid mechanics problems. EGM 6351-Finite Element Methods (3) Prereq: EGM 6341 and 6611, or consent of instructor. Displacement method formula- tion; generalization by means of variational principles and methods of weighted residuals; element shape functions. Appli- cation to heat conduction, solid and fluid mechanics problems. Use of general purpose computer codes. EGM 6422-Modern Techniques of Structural Dynamics II (2) Prereq: EGM 5421 and 6215. Modeling of complex structural systems occurring in aeronautical, mechanical, and structural engineering. Response of such systems to impulse, shock and random excitations, emphasizing computer techniques. EGM 6444-Advanced Dynamics I (3) Prereq: EGM 5430. Dynamics of particles and rigid bodies applied to advanced engineering problems utilizing variational and transformation principles. EGM 6445-Advanced Dynamics II (3) Prereq: EGM 6444. Theory and application of Lagrangian equations to engineer- ing problems. Hamilton-Jacobi theory and its applications. EGM 6460-Stability of Dynamical Systems (3) Prereq: EGM 4200 or 5430. Basic concepts of stability, stability and asymp- totic behavior of motion. Forced oscillations of systems with nonlinear characteristics. Floquet theory, Mathieu and Hill equa- tions. Liapunov's direct method, criteria of Routh-Hurwitz, Popov and others. EGM 6476-Inertial Guidance and Control (3) Prereq: EEL 6614. Modern navigational and vehicle guidance and control techniques based on use of inertial reference. EGM 6478-Nonlinear Control Systems (3) Prereq: EEL 5182. Stability of nonlinear systems using Liapunov's second method, the Popov and other frequency domain criteria. EGM 6551-Introduction to Theory of Thermal Stresses (2) Prereq: EGM 5550. Theory of thermal distortion and induced thermal stresses: Strain energy principles. Two- and three- dimensional problems. Creep. Thermal instability. EGM 6584-Principles of Mechanics in Biomedical Engineer- ing (3) Rheological behavior of biological materials subject to steady-state and dynamic loading. Mathematical models and analytical techniques used in the biosciences. Experimental techniques for material property investigation of representative body tissues. EGM 6611-Continuum Mechanics I (3) Prereq: EGM 3520. Foundations of continuum mechanics. Analysis of motion and deformation. Conservation laws; tensor properties of stress and strain. Constitutive theory. Therfnodynamics of continuous media. EGM 6612-Continuum Mechanics II (3) Prereq: EGM 6611. Specific constitutive classes of continuous media; elastic solids, Newtonian and non-Newtonian fluids. Materials which exhibit plastic and viscoelastic behavior. Formulation of specific prob- lems. EGM 6613-Advanced Continuum Mechanics (2),Prereq: EGM 6612. Comprehensive, unified treatment of mathematical theories of solid and fluid mechanics, including gases. EGM 6652-Introduction to Elasticity (3) Prereq: EGM 3520. Analysis of stress. Analysis of strain. Stress-strain relations of elasticity. Compatibility equations. Plane elasticity in Cartesian and polar coordinates. Solution of two-dimensional problems by means of complex variable methods. EGM 6653-Theory of Elasticity (3) Prereq: EGM 6652. Three- dimensional problems including torsion, bending, stress con- centration. Thermal stress and stress wave propagation. Energy principles and variational methods. EGM 6670-Introduction to Inelastic Behavior of Materials (3) Prereq: EGM 3520. Metal plasticity theory: emphasis on ideal plasticity with applications; slip-line fields; limit analysis. Linear viscoelasticity; analysis of creep, relaxation and alternating load response; application to initial-boundary value problems. EGM 6671-Theory of the Inelastic Continuum (3) Prereq: EGM 6611, 6670. Constitutive theories of work-hardening metal plasticity and viscoplasticity; formulation of theories for analytical and numerical problem solution; selected applications. EGM 6682-Theory of Viscoelasticity (2) Prereq: EGM 6611, 6670. Theories of solid and fluid materials which exhibit history dependence. Development from Boltzmann linear viscoelasticity to general thermodynamic theories of materials with memory. EGM 6683-Dynamic Plasticity (2) Prereq: EGM 6611, 6670. Analysis of propagation of impact induced transient loading and unloading waves of uniaxial stress or strain in inelastic solids. Rate-dependent and rate-independent constitutive assumptions. Experimental verifications. Combined stress waves. EGM 6684-Special Topics in Dynamic Plasticity (1-3; max: 6) Prereq: EGM 6683. EGM 6716-Theory of Plates (3) Prereq: EGM 3520. Funda- mental equations for the bending and stretching of thin plates. Small deformation. Various loading and boundary conditions. Large deformation and nonlinar considerations. Transverse shear effects. Thermal stresses. Energy methods. Vibration of plates. Anisotropy and plasticity. EGM 6717-Theory of Shells I (3) Prereq: EGM 6716. Curvi- linear coordinates. Surface of shells. General theory of thin, elastic shells. Shallow shells. Membrane shells of revolution. Bending of shells. Static and dynamic analysis of linear equa- tions for elastic shells. EGM 6718-Theory of Shells II (3) Prereq: EGM 6717. Ortho- tropic and anisotropic shells. Transverse shear and normal stress effects. Nonlinear geometric theory. Plastic shells. Interaction