200. Professional Seminar
(1) McMeeking, Milstein, Odette
Prerequisite: graduate standing.
A series of weekly lectures given by university staff and outside experts in all fields of echanical and environmental engineering.

200P. Master of Science Project
(3) Staff
Prerequisite: graduate standing.
A ten-week research project on an advanced topic in Mechanical Engineering.

201. Advanced Dynamics
(3) Mezic
Newton’s laws and symmetries, Newton, Laplace and principle of determinism, qualitative analysis of Newton’s equations of motion, Hamiltonian mechanics, one degree of freedom (DOF) systems, two DOF systems, motion in central fields, application to molecular dynamics, control of classical dynamical systems, Lagrangian mechanics, chaos and ergodic theory, rigid body motion.

202. Advanced Dynamics
(3) Mezic
Prerequisite: ME 201; graduate standing.
Differentiable manifolds in dynamical systems theory, differential forms, Hamiltonian phase flow, Lie algebras of vector fields, canonical formalism, integrable systems, introduction to perturbation theory, averaging, chaos in Hamiltonian systems, theory of invariant measures in dynamical systems, ergodic partition, dissipative dynamical systems, limit cycles,
Lyapunov exponents, strange attractors.

203. Special Topics in Dynamical Systems
(3) Mezic
Prerequisite: ME 201.
Geometric mechanics, volume-preserving dynamical systems, molecular dynamics; Infinite dimensional dynamics and finite dimensional approximations including incompressible Euler equations and point vortex theory, transport and fluid mixing, control of measure-preserving systems, equilibrium and nonequilibrium statistical mechanics methods for vortex
gases.

207. Faculty Research Seminar
(1) Khamash
A series of bi-weekly presentations given by ladder faculty members to familiarize graduate students with current department research projects. This course is required to be taken by all graduate students within the first year of arrival.

210A. Matrix Analysis and Computation
(4) Staff
Prerequisite: consent of instructor.
Same course as Computer Science 211A, ECE 210A, Mathematics 206A, Chemical Engineering 211A, and Geology 251A.
Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. Graduate level-matrix theory with introduction to matrix computations. SVD’s, pseudoinverses, variational characterization of eigenvalues, perturbation theory, direct and iterative methods for matrix computations.

210B. Numerical Simulation
(4) Petzold
Prerequisite: consent of instructor.
Same course as Computer Science 211B, ECE 210B, Mathematics 206B, and Chemical Engineering 211B and Geology 251B.
Students should be proficient in basic numerical methods, linear algebra, mathematically
rigorous proofs, and some programming language. Linear multistep methods and Runge-Kutta methods for ordinary differential equations: stability, order and convergence. Stiffness. Differential algebraic equations. Numerical solution of boundary value problems.

210C. Numerical Solution of Partial
Differential Equations—Finite Difference Methods
(4) Staff
Prerequisite: consent of instructor.
Same course as Computer Science 211C, ECE 210C, Mathematics 206C, Chemical Engineering 211C, and Geolgy 251C.
Students should be proficient in basic numerical methods, linear algebra, mathematically
rigorous proofs, and some programming language. Finite difference methods for hyperbolic, parabolic and elliptic PDEs, with application to problems in science and engineering. Convergence, consistency, order and stability of finite difference methods. Dissipation and dispersion. Finite volume methods. Software design and adaptivity.

210D. Numerical Solution of Partial Differential Equations—Finite Element Methods
(4) Staff
Prerequisite: consent of instructor.
Same course as Computer Science 211D, ECE 210D, Mathematics 206D, Chemical Engineering 211D, and Geology 251D.
Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. Weighted residual and finite element methods for the solution of hyperbolic, parabolic and elliptical partial differential equations, with application to problems in science and engineering. Error estimates. Standard and discontinuous Galerkin methods.

212. Risk Assessment and Management
(3) Theofanous
Prerequisites: consent of instructor.
Same course as Chemical Engineering 212
Conceptual foundations of risk and its utility for decision making. Determinism, statistical inference, and uncertainty. Formulation of safety goals and approaches to risk management. Generalized methodology and tools for assessing risks in the industrial, ecological, and public health context.

215A. Applied Dynamical Systems I
(3) Moehlis
Prerequisite: graduate standing.
Phase-plane methods, non-linear oscillators, stability of fixed pints and periodic orbits, invariant
manifolds, structural stability, normal form theory, local bifurcations for vector fields and maps, applications from engineering, physics, chemistry, and biology.

215B. Applied Dynamical Systems II
(3) Moehlis
Prerequisites: ME 215A; graduate standing.
Local codimension two bifurcations, global bifurcations, chaos for vector fields and maps, Smale horseshoe, symbolic dynamics, strange attractors, universality, bifyrcation with symmetry, perturbation theory and averaging, Melnikov’s methods, canards, applications from engineering, physics, chemistry, and biology.

216. Level Set Methods
(4) Gibou
Prerequisite: Computer Science 211C, or Chemical Engineering 211C, or ECE 210C, or ME 210C.
Same course as Chemical Engineering 226, ECE 226, and Computer Science 216.
Mathematical description of the level set method and design of the numerical methods used in its implementations (ENO-WENO, Godunov, Lax-Friedrich, etc.). Introduction to the Ghost Fluid Method. Applications in CFD, Materials Sciences, Computer Vision and Computer Graphics.

218. Introduction to Multiphase Flows
(3) Theofanous
Prerequisite: consent of instructor.
Same course as Chemical Engineering 218.
Development from basic concepts and techniques of fluid mechanics and heat transfer, to local behavior in multiphase flows. Key multiphase phenomena, related physics. Extension of local conservation principles to usable formulations in multiphase flows. Modelling approaches. Practical examples. Computer simulations.

219. Mechanics of Materials
(3) McMeeking
Same course as Materials 207.
Matrices and tensors, stress deformation and flow, compatibility conditions, constitutive equations, field equations and boundary conditions in fluids and solids, applications in solid and fluid mechanics.

220A-B. Fundamentals of Fluid Mechanics
(3-3) Bennett, Homsy, Meinhart
Prerequisites: ME 151A-B and 152A-B.
Introductory course in fluid mechanics. Basic equations of motion (continuity, momentum, energy, vorticity), coordinate transformations, “potential” flow, thin airfoil theory, conformal mapping, vortex dynamics, boundary layers, stability theory, laminar/turbulent transition, turbulence. Inviscid/viscid, irrotational/rotational, incompressible/compressible flow examples.

221. Advanced Viscous Flow
(3) Homsy
Prerequisite: ME 220A.
Review the Navier-Stokes equations in velocity, pressure, and vorticity variables. Analyze details of important low and moderate Reynolds number flow applications and then high Reynolds number flows with boundary layer phenomena. Compare exact, approximate, numerical, and experimental solution methods.

223. Turbulent Flow
(3) Staff
Prerequisites: ME 220A-B or Chemical Engineering 220A-B.
Same course as Chemical Engineering 221.
Nature and origin of turbulence, boundary layer mechanics law of the wall, wakes, and jets, transport of properties, statistical description of turbulence, measurement problems, stratification effects. Application of principles to practical problems is stressed.

225AA-ZZ. Special Topics in Mechanical Engineering
(3) Staff
Prerequisite: consent of instructor.
Specialized courses dealing with advanced topics and recent developments in one or more of the following areas: dynamic systems, control and robotics, fluid mechanics, materials science and engineering, ocean engineering, solid mechanics and structures, thermal sciences.

230. Elasticity
(3) Beltz, McMeeking
Prerequisite: ME 219 or Materials 207; consent of instructor.
Same course as Materials 230.
Review of the field equations of elasticity. Energy principles and uniqueness theorems. Elementary problems in one and two dimensions. Stress functions, complex variable methods and three-dimensional potential functions. Fundamental solutions in two and three dimensions. Approximate methods.

232. Plasticity
(3) McMeeking, Milstein
Prerequisite: ME 219.
Same course as Materials 232.
Plastic, creep, and relaxation behavior of solids. Mechanics of inelastically strained bodies; plastic stress-strain laws; flow potentials. Torsion and bending of prismatic bars, expansion of thick shells, plane plastic flow, slip line theory. Variational formulations, approximate methods.

233A. Design of Composite Structures
(3) Kedward
Prerequisite: ME 230 or 275A.
Emphasis is placed on the differences of design with composites vis-à-vis the design of conventional metallic structures. The content is directed at the class of polymer-matrix composites.

234A. Structural Dynamics
(3) Bruch
Formulation of the equations of motion for free and forced response of single and multi-degree
of freedom systems and for distributed-parameter systems. Modal analysis. Approximate solution techniques. Numerical algorithms. Damping.

236. Nonlinear Control Systems
(4) Kokotovic, Teel
Same course as ECE 236.
Recommended preparation: ECE 230A.
Analysis and design of nonlinear control systems. Focus on Lyapunov stability theory, with sufficient time devoted to contrasts between linear and nonlinear systems, input-output stability and the describing function method.

237. Nonlinear Control Design
(4) Kokotovic
Prerequisite: ECE 236 or ME 236.
Same course as ECE 237.
Stabilizability by linearization and by geometric methods. State feedback design and input/output linearization. Observability and output feedback design. Singular perturbations and composite control. Backstepping design of robust controllers for systems with uncertain nonlinearities. Adaptive nonlinear control.

239. Conduction Heat Transfer
(3) Staff
Prerequisite: undergraduate course in heat transfer.
Development of mathematical representation of conduction heat transfer and techniques available for analytical, analog, and numerical solutions.

241. Radiative Energy Transfer
(3) Staff
Prerequisite: undergraduate course in heat transfer.
The physical nature of radiation and of its interaction with matter, conservation principles in radiative transfer and their relation to molecular and convective processes, and thermodynamic equilibrium with consideration of nondimensional parameters is considered. Applications to astrophysics, combustion, and plasma technology are discussed.

243A-B. Linear Systems I, II
(4-4) Kokotovic, Bamieh
Prerequisites: ME 210A (for 243A): ECE 140; and, ECE 230A or ME 243A; and ME 210A.
Same courses as ECE 230A-B.
Internal and external descriptions. Solution of state equations. Controllability and observability realizations. Pole assignment, observers; modern compensator design. Disturbance localization and decoupling. Leastsquares control. Least-squares estimation; Kalman filters; smoothing. The separation theorem; LQG compensator design. Computational considerations.
Selected additional topics.

244A. Advanced Theoretical Methods in Engineering
(4) Fredrickson, Chmelka, Leal
Prerequisite: consent of instructor.
Same course as Chemical Engineering 230A.
Methods of solution of partial differential equations and boundary value problems. Linear vector and function spaces, generalized Fourier analysis, Sturm- Liouville theory, calculus of variations, and conformal mapping techniques.

244B. Advanced Theoretical Methods in Engineering
(3) Fredrickson
Prerequisites: ME 244A and consent of instructor.
Same course as Chemical Engineering 230B.
Advanced mathematical methods for engineers and scientists. Complex analysis, integral equations and Green’s functions. Asymptotic analysis of integrals and sums. Boundary layer methods and WKB theory.

250. Advanced Thermodynamics
(3) Milstein
Prerequisites: ME 151A-B.
An extended treatment of the fundamentals of
classical thermodynamics, including availability and reversibility, the chemical potential, properties of matter, thermochemistry, chemical equilibrium of real gases and gas mixtures.

251. Statistical Thermodynamics
(3) Milstein
Prerequisites: ME 151A-B.
An extended treatment of the fundamentals of statistical thermodynamics, equilibrium distributions, properties of gases, liquids, and solids.

252A. Computational Fluid Dynamics
(3) Meiburg
Prerequisites: ME 210C or Computer Science 211C or ECE 210C or Mathematics 206C or Chemical Engineering 211C.
Numerical simulation of fluid flows. Basic discretization techniques for parabolic, elliptical, and hyperbolic conservation laws. Stability and accuracy. Diffusion equation, linear convection equation.

252B. Computational Fluid Dynamics
(3) Meiburg
Prerequisites: ME 210C or Computer Science 211C or ECE 210C or Mathematics 206C or Chemical Engineering 211C.
Discussion of appropriate boundary conditions. Nonlinear convection dominated problems, curvilinear coordinates, basics of grid generation. Inviscid flow, boundary layer flow, incompressible Navier-Stokes flows.

252C. Computational Fluid Dynamics
(3) Meiburg
Prerequisites: ME 210C or Computer Science 211C or ECE 210C or Mathematics 206C or Chemical Engineering 211C.
Compressible inviscid flows. Compressible viscous flows. Boundary element methods. Lagrangian and vortex methods.

ME 254. Optimal Control
(3) Bamieh
Prerequisites: ME 163B, 155A, or equivalent
Introduction to the classical calculus of variations. Optimization problems for dynamic systems with terminal and path constraints. Necessary and sufficient conditions. Neighboring extremal paths and the second variation.Singular solutions. Numerical solutions of optimal control problems. Applications to engineering systems.

256. Introductory Robust Control with Applications
(4) Smith, Khamash
Prerequisites: ECE 230A or ME 255A; and ECE 230B or ME 243B (may be taken concurrently).
Same course as ECE 232.
Robust Control theory; uncertainty modeling; stability of systems in the presence of norm-bounded perturbations; induced norm performance problems; structured singular value analysis; H-infinity control theory; model reduction; computer simulation based design project involving practical problems.

260A. Materials Structures and Bonding
(3) Milstein
Prerequisite: consent of instructor.
Crystal structures (Miller indices, Bravais lattices, symmetry operations). Modeling of atomic bonding, determination and applications of interatomic potentials, atomic basis for elastic moduli. Crystal anisotrophy. Lattice statics and molecular dynamics computations.

262. Thermodynamics and Phase Equilibria
(3) Odette, Clarke, Zok
Prerequisite: consent of instructor.
Same course as Materials 201.
Advanced thermodynamics with emphasis on phase equilibria, properties of solutions, and multicomponent systems.

264. Mechanical Behavior of Materials
(3) Staff
Prerequisite: consent of instructor.
Same course as Materials 220.
Concepts of stress and strain. Deformation of metals, polymers, and ceramics. Elasticity, viscoelasticity, plastic flow, and creep. Linear elastic fracture mechanics. Mechanisms of ductile and brittle fracture.

265. Composite Materials
(3) Odette, Clarke, Zok
Prerequisite: consent of instructor.
Same course as Materials 261.
Stress and strain relations in composites. Residual stresses. The fracture resistance of organic and inorganic matrix composites. Statistical aspects of fiber failure. Composite laminates and delamination cracks. Cumulative damage concepts. Interface properties. Design criteria.

271. Finite Element Structural Analysis
(3) McMeeking
Prerequisite: ME 219.
Same course as Materials 240.
Definitions and basic element operations. Displacement approach in linear elasticity. Element formulation: direct methods and variational methods. Global analysis procedures: assemblage and solution. Plane stress and plane strain. Solids of revolution and general solids. Isoparametric representation and numerical integration. Computer implementation.

273. Dislocation Mechanics
(3) Beltz
Prerequisite: ME 230; concurrent enrollment in ME 275.
A rigorous review of classical dislocation theory with the intention of understanding its behavior in real materials (as it affects mechanical and electrical properties) as well as how it is used to construct solutions to elastic boundary value problems.

275. Fracture Mechanics
(3) Odette, McMeeking
Prerequisite: ME 219.
Same course as Materials 234.
Analytic solutions of a stationary crack under static loading. Elastic and elastoplastic analysis. The J integral. Energy balance and crack growth. Criteria for crack initiation and growth. Dynamic crack progagation. Fatigue. The micromechanics of fracture.

285. Geophysical Fluid Dynamics
(3) McLean
Prerequisite: ME 152A.
The ocean-atmosphere system. Air-sea interaction. Governing equations for rotating system: conservation of mass, momentum and energy. Ocean surface waves: generation, spectral characteristics. Internal waves. Geostrophic motion. Rotating boundary layers: Ekman dynamics. Tides. Kelvin waves.

291A. Physics of Transducers
(3) Soh
Prerequisite: graduate standing.
Recommended preparation: ECE 220A (may be taken concurrently).
The use of concepts in electromagnetic theory and solid state physics to describe capacitive, pierzoresistive, piezoelectric and tunneling transduction mechanisms and analyze their applications in microsystems technology.

292. Design of Transducers
(3) Turner
Prerequisites: ME 291A and ECE 220A; graduate standing.
Design issues associated with microscale transduction. Electrodynamics, linear and nonlinear mechanical behavior, sensing methods, MEMS-specific fabrication design rules, and layout are all covered. Modeling techniques for electromechanical systems are also discussed.

501. Teaching Assistant Practicum
(1-4) Staff
Normally required of students serving as teaching assistants. No unit credit allowed towards advanced degree. Practical experience in the various activities associated with teaching, including lecturing, supervision of laboratories and discussion sections, preparation and
grading of homework and exams.

503. Research Assistant Practicum
(1-4) Staff
Will not count as unit credit towards M.S. or Ph.D. degree in mechanical engineering.
Practical experience in the various activities associated with research, including experimental work, theoretical work and analyses, and assisting department faculty and other professional researchers in their duties.

596. Directed Research
(1-12) Staff
Prerequisite: consent of instructor.
Not applicable to course requirement for M.S. and Ph.D. degree. S/U grading.
Experimental or theoretical research undertaken under the direction of a faculty member for graduate students who have not yet advanced to candidacy.

597. Individual Study for Ph.D. Qualifying Examination
(1-12) Staff
Prerequisite: graduate standing.
No unit credit allowed toward advanced degree. Maximum of 12 units per quarter; enrollment limited to 24 units per examination. Instructor is normally student’s major advisor. S/U grading.
Individual studies for Ph.D. qualifying examination.

598. Master’s Thesis Research and Preparation
(1-12) Staff
Prerequisite: consent of thesis advisor.
No unit credit allowed toward advanced degree. For research underlying the thesis and writing of
the thesis.

599. Ph.D. Dissertation Research and Preparation
(1-12) Staff
Prerequisite: consent of dissertation advisor.
No unit credit allowed toward advanced degree. For research and preparation of the dissertation.