# Mechanical and Aerospace Engineering (ENGRMAE)

### Courses

**ENGRMAE 10. Introduction to Engineering Computations. 4 Units. **

Introduction to the solution of engineering problems through the use of the computer. Elementary programming in FORTRAN and Matlab is taught. No previous knowledge of computer programming is assumed.

(Design units: 1)

Corequisite: MATH 2A.

Prerequisite: MATH 2A.

Overlaps with ENGR 10, EECS 10, EECS 12.

Restriction: School of Engineering majors have first consideration for enrollment.

**ENGRMAE 30. Statics. 4 Units. **

Addition and resolution of forces, distributed forces, equivalent system of forces centroids, first moments, moments and products on inertia, equilibrium of rigid bodies, trusses, beams, cables. Course may be offered online.

(Design units: 0)

Corequisite: MATH 2D.

Prerequisite: MATH 2D and PHYSICS 7C.

Same as ENGRCEE 30, ENGR 30.

Restriction: School of Engineering majors have first consideration for enrollment.

**ENGRMAE 52. Computer-Aided Design. 4 Units. **

Develops skills for interpretation and presentation of mechanical design drawings and the use of CAD in engineering design. An integrated approach to drafting based on sketching, manual drawing, and three-dimensional CAD techniques is presented.

(Design units: 0.5)

Restriction: Mechanical Engineering and Materials Science Engineering majors have first consideration for enrollment.

**ENGRMAE 57. Manufacturing Processes in Engineering. 2 Units. **

With laboratory. Machines and processes of mechanical manufacturing. Safety and professional procedures emphasized. Use of measuring instruments, hand tools, lathe, mill, drill press, bandsaw, grinder, welding equipment.

(Design units: 0)

Grading Option: Pass/no pass only.

Restriction: School of Engineering majors have first consideration for enrollment.

**ENGRMAE 60. Electric Circuits. 4 Units. **

Design and analysis of analog circuits based on lumped circuit elements with emphasis on the use of operational amplifiers. Sinusoidal and transient response. Constructional and laboratory testing of analog circuits, and introduction to data acquisition. Materials fee.

(Design units: 2)

Corequisite: MATH 3D.

Prerequisite: PHYSICS 7D and PHYSICS 7LD.

Overlaps with EECS 70A, CSE 70A.

Restriction: Mechanical Engineering and Aerospace Engineering majors have first consideration for enrollment.

**ENGRMAE 80. Dynamics. 4 Units. **

Introduction to the kinetics and dynamics of particles and rigid bodies. The Newton-Euler, Work/Energy, and Impulse/Momentum methods are explored for ascertaining the dynamics of particles and rigid bodies. An engineering design problem using these fundamental principles is also undertaken. Course may be offered online.

(Design units: 0.5)

Prerequisite: MATH 2D and PHYSICS 7C.

Same as ENGRCEE 80, ENGR 80.

Restriction: School of Engineering majors have first consideration for enrollment.

**ENGRMAE 91. Introduction to Thermodynamics. 4 Units. **

Thermodynamic principles; open and closed systems representative of engineering problems. First and second law of thermodynamics with applications to engineering systems and design. Course may be offered online.

(Design units: 0.5)

Prerequisite: PHYSICS 7C and MATH 2D.

Overlaps with CBEMS 45B.

Restriction: Aerospace Engineering, Civil Engineering, Environmental Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 93. Design Project . 1-2 Units. **

Early-stage design/hands-on experience for lower-division students, and allows them to participate along side seniors in the design project.

(Design units: 1)

Repeatability: May be taken for credit 4 times as topics vary.

Restriction: Aerospace Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 106. Mechanical Systems Laboratory. 4 Units. **

Experiments in linear systems, including op-amp circuits, vibrations, and control systems. Emphasis on demonstrating that mathematical models can be useful tools for the analysis and design of electro-mechanical systems. Materials fee.

(Design units: 2)

Prerequisite: ENGRMAE 60 or EECS 70A.

Restriction: Aerospace Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 107. Fluid Thermal Science Laboratory. 4 Units. **

Fluid and thermal engineering laboratory. Experimental analysis of fluid flow, heat transfer, and thermodynamic systems. Probability, statistics, and uncertainly analysis. Report writing is emphasized and a design project is required. Materials fee.

(Design units: 1)

Corequisite: ENGRMAE 120.

Restriction: Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 108. Aerospace Laboratory. 4 Units. **

Analytical and experimental investigation in aerodynamics, fluid dynamics, and heat transfer. Emphasis on study of flow over objects and lift and drag on airfoils. Introduction to basic diagnostic techniques. Report writing is emphasized. Design project is required. Materials fee.

(Design units: 2)

Prerequisite: ENGRMAE 130B.

Restriction: Aerospace Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 110. Combustion and Fuel Cell Systems. 4 Units. **

Fundamentals of gaseous, liquid, and coal-fired combustion and fuel cell systems. Fuels, fuel-air mixing, aerodynamics, and combustion and fuel cell thermodynamics. Operating and design aspects of practical systems including engines, power generators, boilers, furnaces, and incinerators.

(Design units: 2)

Prerequisite: ENGRMAE 115.

Restriction: Chemical Engineering, Environmental Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 112. Propulsion. 4 Units. **

Application of thermodynamics and fluid mechanics to basic flow processes and cycle performance in propulsion systems: gas turbines, ramjets, scramjets, and rockets.

(Design units: 1)

Prerequisite: ENGRMAE 130B.

Restriction: Aerospace Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 113. Electric Propulsion. 4 Units. **

Space propulsion requirements and maneuvers, stressing those best suited to electric propulsion. An introduction to plasma physics. Electrothermal, electromagnetic and electrostatis accelerators, with emphasis in technologies (ion engines, Hall thrusters and colloidal thrusters) belonging to the latter family.

(Design units: 1)

Prerequisite: ENGRMAE 112.

Concurrent with ENGRMAE 213.

**ENGRMAE 114. Fuel Cell Fundamentals and Technology. 4 Units. **

Introduction to electrochemistry and electrocatalysis; nature of fuel-cell electrodes and electrolytes; charge transfer reactions at interfaces; charge transport and mass transport processes; fuel processing reactions; determination of fuel cell efficiency, fuel flexibility, emissions and other characteristics.

(Design units: 0)

Prerequisite: ENGRMAE 115.

Restriction: Aerospace Engineering and Mechanical Engineering majors have first consideration for enrollment. Seniors only.

Concurrent with ENGRMAE 214A

**ENGRMAE 115. Applied Engineering Thermodynamics. 4 Units. **

Application of thermodynamic principles to compressible and incompressible processes representative of practical engineering problems; power cycles, refrigeration cycles, multicomponent mixtures, air conditioning systems, combustion, and compressible flow. Design of a thermodynamic process.

(Design units: 2)

Prerequisite: ENGRMAE 91.

Overlaps with CBEMS 45C.

Restriction: Chemical Engineering, Environmental Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 117. Solar and Renewable Energy Systems. 4 Units. **

Basic principles, design, and operation of solar and other renewable energy systems including solar photo-voltaic, solar thermal, wind, and PEM fuel cell. Includes power generation and storage, and renewable fuels for transportation and stationary power generation.

(Design units: 1)

Prerequisite: ENGRMAE 91.

Restriction: Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 118. Sustainable Energy Systems. 4 Units. **

Basic principles, design, and operation of sustainable energy systems including wind, solar photo-voltaic and thermal, hydroelectric, geothermal, oceanic, biomass combustion, advanced coal, and next generation nuclear. Includes power generation, storage, and transmission for stationary power generation.

(Design units: 1)

Prerequisite: ENGRMAE 115.

Concurrent with ENGRMAE 218.

**ENGRMAE 120. Heat and Mass Transfer. 4 Units. **

Fundamentals of heat and mass transfer. Conduction, heat and mass transfer by convection in laminar and turbulent flows, radiation heat transfer, and combined modes of heat and mass transfer. Practical engineering applications.

(Design units: 0)

Prerequisite: ENGRMAE 130B.

Overlaps with CBEMS 125B.

Restriction: Aerospace Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 130A. Introduction to Fluid Mechanics. 4 Units. **

Fundamental concepts; fluid statics; fluid dynamics; Bernoulli's equation; control-volume analysis; basic flow equations of conservation of mass, momentum, and energy; differential analysis; potential flow; viscous incompressible flow.

(Design units: 0)

Prerequisite: PHYSICS 7C and MATH 2D and MATH 2E and MATH 3D and ENGRMAE 30 and ENGRMAE 80 and ENGRMAE 91. PHYSICS 7C with a grade of C- or better. MATH 2D with a grade of C- or better. MATH 2E with a grade of C- or better. MATH 3D with a grade of C- or better. ENGRMAE 30 with a grade of C- or better. ENGRMAE 80 with a grade of C- or better. ENGRMAE 91 with a grade of C- or better.

Overlaps with CBEMS 125A, ENGRCEE 170.

Restriction: Aerospace Engineering, Civil Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 130B. Introduction to Viscous and Compressible Flows. 4 Units. **

Introduction to the analysis of viscous flows including fully developed laminar and turbulent flow in a pipe, viscous flow over immersed bodies, evaluation of boundary layer characteristics, lift and drag, compressible flow in a duct and normal shock waves.

(Design units: 1)

Prerequisite: ENGRMAE 130A.

**ENGRMAE 132. Computational Fluid Dynamics. 4 Units. **

Introduction to computational fluid dynamics in simple engineering devices. The numerical simulations will be performed via the widely-used software ANSYS-Fluent. While Fluent is the choice of software, all major CFD packages are based on a similar numerical method.

(Design units: 0)

Prerequisite: ENGRMAE 130B. ENGRMAE 130B with a grade of C- or better.

Restriction: Aerospace Engineering and Mechanical Engineering majors have first consideration

**ENGRMAE 135. Compressible Flow. 4 Units. **

Compressibility effects in fluid mechanics. One-dimensional flow with area variation, friction, heat transfer, and shocks. Design of gas supply systems. Two-dimensional flow with oblique shocks and isentropic waves. Supersonic airfoil theory and design, wind tunnel design. Basic diagnostics.

(Design units: 1)

Prerequisite: ENGRMAE 130B.

**ENGRMAE 136. Aerodynamics. 4 Units. **

Analysis of flow over aircraft wings and airfoils, prediction of lift, moment, and drag. Topics: fluid dynamics equations; flow similitude; viscous effects; vorticity, circulation, Kelvin's theorem, potential flow; superposition principle, Kutta-Joukowski theorem; thin airfoil theory; finite wing theory; compressibility.

(Design units: 1)

Prerequisite: ENGRMAE 130B.

**ENGRMAE 140. Introduction to Engineering Analysis. 4 Units. **

Analytical methods of engineering. Nonhomogeneous linear ordinary differential equations. Variable coefficient linear ordinary differential equations. Eigenfunction expansions. Laplace transforms. Introduction to Fourier transforms. Linear partial differential equations.

(Design units: 0)

Prerequisite: MATH 2E and MATH 3D.

Restriction: Aerospace Engineering, Civil Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 145. Theory of Machines and Mechanisms. 4 Units. **

Presents the basic mathematical theory of machines. Focuses on the principles of cam design, gearing and gear train analysis, and the kinematic and dynamic analysis of linkages, together with an introduction to robotics.

(Design units: 2)

Prerequisite: ENGRMAE 52 and ENGRMAE 80 and MATH 3A.

Restriction: Mechanical Engineering and Materials Science Engineering majors have first consideration for enrollment.

**ENGRMAE 146. Astronautics. 4 Units. **

Motion in gravitational force fields, orbit transfers, rocketry, interplanetary trajectories, attitude dynamics and stabilization, navigation, reentry, the space environment.

(Design units: 1)

Prerequisite: ENGRMAE 80.

Restriction: Aerospace Engineering majors have first consideration for enrollment.

**ENGRMAE 147. Vibrations. 4 Units. **

Analysis of structural vibrations of mechanical systems. Modeling for lumped and distributed parameter systems. Topics include single and multi-degree of freedom systems, free and forced vibrations, Fourier series, convolution integral, mass/stiffness matrices, and normal modes with design project.

(Design units: 1)

Prerequisite: (ENGR 80 or ENGRCEE 80 or ENGRMAE 80) and MATH 2E and MATH 3D.

Restriction: Materials Science Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 150. Mechanics of Structures. 4 Units. **

Stresses and strains. Torsion. Bending. Beam deflection. Shear force and moment distributions in beams. Yielding and buckling of columns. Combined loading. Transformation of stresses and strain. Yielding criteria. Finite elements analysis of frames. Dynamic of two-bar truss.

(Design units: 2)

Prerequisite: (ENGRCEE 30 or ENGR 30 or ENGRMAE 30) and MATH 3A.

Same as ENGR 150.

Overlaps with ENGRCEE 150.

Restriction: Aerospace Engineering, Chemical Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 150L. Mechanics of Structures Laboratory. 1 Unit. **

Experimental techniques for the measurement of mechanical properties of materials and structures. Methods for load, displacement, and strain measurements. Tension, bending, compression tests. Determination of strength, stiffness, toughness for metals, polymers, ceramics, and composites. Deformation of structures. Materials fee.

(Design units: 0)

Corequisite: ENGRMAE 150.

Prerequisite: ENGRMAE 30 or ENGR 30 or ENGRCEE 30.

Overlaps with ENGRCEE 150L.

Restriction: Aerospace Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 151. Mechanical Engineering Design. 4 Units. **

A comprehensive group design project experience that involves identifying customer needs, idea generation, reverse engineering, preliminary design, standards, prototype development, testing, analysis, and redesign of a product involving fluid, thermal, and mechanical components. Introduces design for manufacturing and the environment. Materials fee.

(Design units: 3)

Prerequisite: ENGRMAE 120 and ENGRMAE 145 and ENGRMAE 170.

Restriction: Seniors only. Materials Science Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 152. Introduction to Computer-Aided Engineering. 4 Units. **

Elements and principles of computer-aided engineering with modern hardware and software are presented with a design focus. Case studies are used to assist in finite-element method techniques. Not offered every year.

(Design units: 2)

Prerequisite: (ENGRMAE 150 or ENGR 150) and ENGRMAE 120.

Restriction: Materials Science Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 153. Advanced BIOMEMS Manufacturing Techniques. 4 Units. **

Introduction to BIOMEMS. Advanced biotechnology/biomedicine equipment based on MEMS and NEMS. Fundamentals of MEMS/NEMS sensing techniques and the biological and physics principles involved and the preferred MEMS and NEMS manufacturing techniques.

(Design units: 0)

Concurrent with ENGRMAE 253.

**ENGRMAE 155. Composite Materials and Structures. 4 Units. **

Motivation for composite materials. Different classifications according to the nature of the matrix (PMC, MMC, CMC) and the reinforcement topology (fibers, whiskers, particulates). Mechanical properties. Failure mechanisms. Designing with composite materials. Advantages and limitations of homogenization techniques for numerical modeling.

(Design units: 0)

Prerequisite: ENGR 54 and (ENGRMAE 150 or ENGRCEE 150 or ENGR 150).

Restriction: Chemical Engineering, Civil Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

Concurrent with ENGRMAE 255.

**ENGRMAE 156. Mechanical Behavior and Design Principles. 4 Units. **

Principles governing structure and mechanical behavior of materials, relationship relating microstructure and mechanical response with application to elasticity, plasticity, yielding, necking, creep, and fracture of materials. Introduction to experimental techniques to characterize the properties of materials. Design parameters.

(Design units: 2)

Prerequisite: ENGR 54.

Same as CBEMS 155.

Restriction: Chemical Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 157. Lightweight Structures. 4 Units. **

Fundamentals of torsion and bending. Analysis and design of thin-wall and composite beams. Stress analysis of aircraft components. Stiffness, strength, and buckling. Introduction to the Finite Element method and its application to plates and shells.

(Design units: 2)

Prerequisite: ENGR 150 or ENGRCEE 150 or ENGRMAE 150.

Restriction: Aerospace Engineering, Civil Engineering, Materials Science Engineering, and Mechanical Engineering majors have frist consideration for enrollment.

**ENGRMAE 158. Aircraft Performance. 4 Units. **

Flight theory applied to subsonic propeller and jet aircraft. Nature of aerodynamic forces, drag and lift of wing and fuselage, high-lift devices, level-flight performance, climb and glide performance, range, endurance, take-off and landing distances, static and dynamic stability and control.

(Design units: 2)

Prerequisite: ENGRMAE 130A.

**ENGRMAE 159. Aircraft Design. 4 Units. **

Preliminary design of subsonic general aviation and transport aircraft with emphasis on layout, aerodynamic design, propulsion, and performance. Estimation of total weight and weight distribution, design of wings, fuselage, and tail, selection and location of engines, prediction of overall performance.

(Design units: 4)

Prerequisite: ENGRMAE 112 and ENGRMAE 136 and ENGRMAE 158.

**ENGRMAE 164. Air Pollution and Control. 4 Units. **

Sources, dispersion, and effects of air pollutants. Topics include emission factors, emission inventory, air pollution, meteorology, air chemistry, air quality modeling, impact assessment, source and ambient monitoring, regional control strategies.

(Design units: 2)

Prerequisite: ENGRMAE 91 and (ENGRMAE 130A or ENGRCEE 170).

Restriction: Chemical Engineering, Environmental Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 170. Introduction to Control Systems. 4 Units. **

Feedback control systems. Modeling, stability, and systems specifications. Root locus, Nyquist, and Bode methods of analysis and design.

(Design units: 2)

Prerequisite: ENGRMAE 80 and ENGRMAE 106.

Restriction: Aerospace Engineering, Civil Engineering, Materials Science Engineering, and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 171. Digital Control Systems. 4 Units. **

Methods for analysis and design of discrete-time control systems. Z-transforms, difference equations, discrete Fourier transforms. Sampling theorem and applications. Z-plane stability, frequency response. Digital controller design. Introduction to digital filters.

(Design units: 2)

Prerequisite: ENGRMAE 170.

Restriction: Civil Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 172. Design of Computer-Controlled Robots. 4 Units. **

Students design a small robotic device and program it to exhibit sentient behaviors. The basic aspects of mechatronic design are covered, including motor and sensor selection, control strategies, and microcomputer programming for the implementation of control paradigms.

(Design units: 3)

Corequisite: ENGRMAE 60.

Prerequisite: ENGRMAE 170.

Restriction: Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 175. Dynamics and Control of Aerospace Vehicles. 4 Units. **

Equations of motion, linearization, stability derivatives, and longitudinal and lateral modes of motion. Handling qualities, sensors and actuators, and effects of various feedbacks on stability and performance. Stability augmentation. Autopilot design.

(Design units: 3)

Prerequisite: ENGRMAE 106.

**ENGRMAE 183. Computer-Aided Mechanism Design. 4 Units. **

Focuses on design of planar, spherical, and spatial mechanisms using computer algebra and graphics. Topics include exact and approximate analytical design techniques. Students are required to use existing software (or develop new algorithms) to design various mechanisms for new applications.

(Design units: 4)

Prerequisite: MATH 3A.

Restriction: Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 185. Numerical Analysis in Mechanical Engineering. 4 Units. **

Solution of mechanical-engineering equations by means of numerical methods. Errors in numerical analysis. Nonlinear equation and sets of equations. Numerical differentiation and integration. Ordinary differential equations. Boundary-value problems. Partial differential equations.

(Design units: 2)

Prerequisite: ENGRMAE 10 and MATH 3D and MATH 2E.

Overlaps with MATH 105A.

Restriction: Civil Engineering and Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 188. Engineering Design in Industry. 4 Units. **

Principles of engineering design in the context of an industrial application. Local manufacturing firms define an engineering design project to be completed in 10 weeks. Projects include initial brainstorming to final design, with a formal presentation.

(Design units: 4)

Repeatability: May be taken for credit 3 times.

Restriction: Mechanical Engineering majors have first consideration for enrollment.

**ENGRMAE 189. Senior Project - Special Topics. 1-4 Units. **

Group or individual senior project of theoretical or applied nature involving design. Materials fee.

(Design units: 1-4)

Repeatability: May be taken for credit for 12 units as topics vary.

Restriction: Seniors only. Mechanical Engineering majors only.

**ENGRMAE 193. Topics in MAE Design. 1-4 Units. **

Provides early-stage design/hands-on experience for upper-division students, and allows them to participate in senior design projects course ENGRMAE 189.

(Design units: 1)

Repeatability: May be taken for credit for 12 units as topics vary.

**ENGRMAE 195. Seminars in Engineering. 1-4 Units. **

Seminars by individual faculty in major fields of interest. Materials fee.

(Design units: 1-4)

Repeatability: Unlimited as topics vary.

**ENGRMAE 198. Group Study. 1-4 Units. **

Group study of selected topics in Aerospace and Mechanical Engineering.

(Design units: 1-4)

Repeatability: May be repeated for credit unlimited times.

Restriction: Upper-division students only.

**ENGRMAE 199. Individual Study. 1-4 Units. **

For undergraduate Engineering majors in supervised but independent reading, research, or design. Students taking individual study for design credit are to submit a written paper to the instructor and to the Undergraduate Student Affairs Office in the School of Engineering.

(Design units: 1-4)

Repeatability: May be taken for credit for 8 units.

**ENGRMAE 199P. Individual Study. 1-4 Units. **

For undergraduate Engineering majors in supervised but independent reading, research, or design. Students taking individual study for design are to submit a written paper to the instructor and to the Undergraduate Student Affairs Office in the School of Engineering.

(Design units: 1-4)

Grading Option: Pass/no pass only.

Repeatability: May be repeated for credit unlimited times.

**ENGRMAE 200A. Engineering Analysis I. 4 Units. **

Linear algebra, including vector spaces, matrices, linear systems of equations, least squares, and the eigenvalue problem. Ordinary differential equations, including analytical and numerical solution methods, stability, and phase portraits.

Restriction: Graduate students only.

**ENGRMAE 200B. Engineering Analysis II. 4 Units. **

Review of ordinary differential equations, including Bessel and Legendre functions. Partial differential equations, including the diffusion equation, Laplace's equation, and the wave equation. Fourier series, Fourier and Laplace transforms and their applications.

Restriction: Graduate students only.

**ENGRMAE 205. Perturbation Methods in Engineering. 4 Units. **

Asymptotic Expansions of integrals. Regular and singular perturbations. Perturbation methods for ordinary and partial differential equations. Matched asymptotic expansions. Multiple-scale asymptotic expansion schemes. Not offered every year.

Prerequisite: ENGRMAE 200A and ENGRMAE 200B or knowledge of linear differential equations.

Restriction: Graduate students only.

**ENGRMAE 206. Nonlinear Optimization Methods. 4 Units. **

Numerical methods for constrained and unconstrained optimization. Necessary and sufficient conditions for optimimality. Conjugate gradient, variable metric algorithms. Gradient projection, penalty functions, and Lagrange methods. Not offered every year.

Prerequisite: ENGRMAE 200A.

Restriction: Graduate students only.

**ENGRMAE 207. Methods of Computer Modeling in Engineering and the Sciences. 4 Units. **

Unified introduction to finite volume, finite element, field-boundary element, meshless, primal, dual, and mixed methods. Nonlinear problems posed by ordinary as well as partial differential equations. Computer implementations and comparisons of accuracy and convergence.

Restriction: Graduate students only.

**ENGRMAE 210. Advanced Fundamentals of Combustion. 4 Units. **

Premixed, nonpremixed, and heterogenous reactions, with emphasis on kinetics, thermal ignition, turbulent flame propogation, detonations, explosions, flammability limits, diffusion flame, quenching, flame stabilization, and particle and spray combustion. Not offered every year.

Prerequisite: ENGRMAE 224 or ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 212. Engineering Electrochemistry: Fundamentals and Applications. 4 Units. **

Introduction to engineering electrochemistry fundamentals and applications. Examine thermodynamics and transport principles in typical electrochemical systems. Electrochemical sensors, batteries, fuel cells, and supercapacitors. Manufacturing aspects will also be covered.

Restriction: Graduate students only.

**ENGRMAE 213. Electric Propulsion. 4 Units. **

Space propulsion requirements and maneuvers, stressing those best suited to electric propulsion. An introduction to plasma physics. Electrothermal, electromagnetic and electrostatic accelerators, with emphasis in technologies (ion engines, Hall thrusters and colloidal thrusters) belonging to the latter family.

Restriction: Graduate students only.

Concurrent with ENGRMAE 113.

**ENGRMAE 214A. Fuel Cell Fundamentals and Technology. 4 Units. **

Introduction to electrochemistry and electrocatalysis; nature of fuel-cell electrodes and electrolytes; charge transfer reactions at interfaces; charge transport and mass transport processes; fuel processing reactions; determination of fuel cell efficiency, fuel flexibility, emissions and other characteristics.

Restriction: Graduate students only.

Concurrent with ENGRMAE 114

**ENGRMAE 214B. Fuel Cell Systems and Degradation. 4 Units. **

Fuel cell systems design; impacts of operating conditions; experimental and theoretical analysis methods for fuel cells systems; introduction to degradation mechanisms and mitigation techniques; provides broad insight into fuel-cell science, technology, system design and operation. Offered every other year.

Prerequisite: ENGRMAE 214A.

Restriction: Graduate students only.

**ENGRMAE 214C. PEM Fuel Cells . 4 Units. **

An in-depth introduction to the fundamentals of PEM fuel cells, including thermodynamics, kinetics, and transport in electrochemical systems. Topics of specific interest to mechanical engineers will include water/heat management and dynamic responses.

Prerequisite: ENGRMAE 214A.

Restriction: Graduate students only.

**ENGRMAE 215. Advanced Combustion Technology. 4 Units. **

Pollutant formation and experimental methods. Formation of gaseous pollutants and soot; transformation and emission of fuel contaminants in gas, liquid, and solid fuel combustion; methods employed to measure velocity, turbulence intensity, temperature, composition, particle size; methods to visualize reacting flows.

Prerequisite: ENGRMAE 200A and (ENGRMAE 230A or ENGRMAE 270A).

Restriction: Graduate students only.

**ENGRMAE 216. Statistical Thermodynamics. 4 Units. **

Statistics of independent particles, development of quantum mechanical description of atoms and molecules, application of quantum mechanics, evaluation of thermodynamics properties for solids, liquids, and gases, statistical mechanics of dependent particles (ensembles).

Restriction: Graduate students only.

**ENGRMAE 217. Generalized Thermodynamics. 4 Units. **

Generalized thermodynamics develops the laws of continuum thermodynamics from a set of plausible and intuitive postulates. The postulates are motivated qualitatively by a statistical description of matter and are justified by a posterior success for the resulting theory.

Restriction: Graduate students only.

**ENGRMAE 218. Sustainable Energy Systems. 4 Units. **

Basic principles, design and operation of sustainable energy systems including wind, solar photo-voltaic and thermal, hydroelectric, geothermal, oceanic, biomass combustion, advanced coal and next generation nuclear. Includes power generation, storage, and transmission for stationary power generation.

Restriction: Graduate students only.

Concurrent with ENGRMAE 118.

**ENGRMAE 220. Conduction Heat Transfer. 4 Units. **

Steady state and transient conduction heat transfer in one- and multi-dimensional geometries. Analytical methods, exact and approximate. Numerical techniques are also included.

Restriction: Graduate students only.

**ENGRMAE 221. Convective Heat and Mass Transfer. 4 Units. **

Laminar and turbulent convective heat and mass transfer in external and internal flows. Forced and free convection. Exact and approximate solutions. Similarity solutions. Variable properties. Concentration boundary layer theory. Mass transfer conductance.

Prerequisite: ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 222. Radiative Heat Transfer. 4 Units. **

Black body radiation. Radiative transport equations for surfaces separated by non-participating media. Radiant energy transfer through absorbing, emitting, and scattering media. Radiation-conduction interaction. Radiation-convection interaction. Introduction to finite-difference solutions.

Restriction: Graduate students only.

**ENGRMAE 223A. Numerical Methods in Heat, Mass, and Momentum Transport (Laminar Flows) I. 4 Units. **

Introduction to the discretization of various types of partial differential equations (parabolic, elliptic, hyperbolic). Finite-volume discretization for one- and two-dimensional flows. Use of a two-dimensional elliptic procedure to predict sample laminar flows.

Prerequisite: Prerequisite or corequisite: ENGRMAE 230A.

Restriction: Graduate students only.

**ENGRMAE 223B. Numerical Methods in Heat, Mass, and Momentum II. 4 Units. **

Introduction to turbulence. Reynolds-averaging of Navier-Stokes equations. Second-order closure of the average equations. Use of two-dimensional elliptic procedure to predict confined turbulent flows. Not offered every year.

Prerequisite: ENGRMAE 223A.

Restriction: Graduate students only.

**ENGRMAE 224. Advanced Transport Phenomena. 4 Units. **

Fundamentals of transport phenomena in fluid (gas and liquid), solid, and nano systems. Conservation equations, fundamentals of diffusion, ion transport, dispersion in turbulent/laminar flows, absorption, differential/staged distillation, transport in membranes, and nano/microscale transport phenomena. Not offered every year.

Restriction: Graduate students only.

**ENGRMAE 226. Special Topics in Fluid and Thermal Sciences. 1-4 Units. **

Special topics of current interest in fluid mechanics, heat and mass transfer, multiphase flows, or combustion. Emphasis could be placed on theory, computational methods, or experimental techniques.

Repeatability: Unlimited as topics vary.

Restriction: Graduate students only.

**ENGRMAE 230A. Inviscid Incompressible Fluid Mechanics I. 4 Units. **

Equations of motion. Vector notation. Flow kinematics. Potential flow and complex potential. Vorticity and circulation. Bernoulli's theorem. Crocco's theorem. Conformal, Joukowski, and Schwarz-Christoffel transformations.

Restriction: Graduate students only.

**ENGRMAE 230B. Viscous Incompressible Fluid Mechanics II. 4 Units. **

Review of mass, momentum, energy equations. Stress tensor, constitutive relations. Laminar flows. Stokes and Oseen flows. Self-similarity. Boundary layer theory: thin-layer approximation, Falkner-Skan, Blasius solutions, integral methods. Jet, wake, cavity flows. Introduction to turbulence: instability, Reynolds averaging, mixing length.

Restriction: Graduate students only.

**ENGRMAE 230C. Compressible Fluid Dynamics. 4 Units. **

One-dimensional unsteady flow; Riemann invariants, acoustics, shock tube. Two-dimensional flow: shock polars, linear theory, similarity rules, method of characteristics. Three dimensional flow: slender-body theory. Effects of viscosity and conductivity: laminar boundary layer, Crocco-Busemann relations.

Prerequisite: ENGRMAE 230A or ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 230D. Theoretical Foundations of Fluid Mechanics. 4 Units. **

Well-posed problems and boundary, initial, and interface conditions; strong and weak solutions. Similarity, perturbation theory and limit behavior, bifurcations. Dispersive and nondispersive wave propagation, acoustics, ship waves, internal gravity waves, water waves. Vortices: mutual interactions and stability. Jets, wakes, cavities.

Prerequisite: ENGRMAE 230A and ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 231. Fundamentals of Turbulence. 4 Units. **

Phenomenon of turbulence. Reynolds equations. Dynamics of turbulence. Free turbulent shear flows. Wall-bounded turbulent shear flows. Turbulent transport of scalar quantities. Spectral dynamics. Mathematical models of turbulence.

Prerequisite: ENGRMAE 230A and ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 233. Turbulent Free Shear Flows. 4 Units. **

Practical and theoretical aspects of turbulent free shear flows. Instability, global scaling laws, mixing, and noise generation in incompressible and compressible shear layers, jets, and wakes. Kelvin-Helmholtz instability, near- and far-field growth rates, effect of compressibility, aeroacoustics of jets.

Prerequisite: ENGRMAE 200B and ENGRMAE 230A and ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 236. Nonequilibrium Gas Dynamics. 4 Units. **

Molecular description of fluid flow. Boltzmann equation. Chapman-Enskog expansion for flows with translational nonequilibrium. Shock structure. Inviscid flows with chemical and vibrational nonequilibrium. Not offered every year.

Prerequisite: ENGRMAE 230C.

Restriction: Graduate students only.

**ENGRMAE 237. Computational Fluid Dynamics. 4 Units. **

Mathematical, physical, and computational fundamentals of computational fluid dynamics, numerical methods for solving the Euler and Navier-Stokes equations. Topics include: finite-difference and finite-volume discretization, time marching methods, von Neumann analysis, upwinding, flux splitting, TVD, and other high-resolution shock-capturing schemes.

Prerequisite: ENGRMAE 230C.

Restriction: Graduate students only.

**ENGRMAE 238. Experimental Fluid Dynamics. 4 Units. **

Concepts and techniques for measurement of fluid motion. Quantitative and qualitative flow visualization. Flow facilities, shadowgraph, schlieren, interferometer, thermal anemometer. Laser diagnostics, fluorescence, Rayleigh, Raman, Mie scattering. Laser-Doppler, particle-image, and image- correlation velocimetry. Three- and four-dimensional digital imaging.

Prerequisite: ENGRMAE 230A and ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 241. Dynamics. 4 Units. **

Kinematics and dynamics of three-dimensional motions. Lagrange's equations, Newton-Euler equations. Applications include robot systems and spinning satellites.

Restriction: Graduate students only.

**ENGRMAE 242. Robotics. 4 Units. **

Spatial rigid-body transformations. Forward and inverse kinematics. Jacobian of serial and parallel chains. Screw coordinates and transformations. Rate and static analyses using screw theory. Singularity analysis. Trajectory generation. Not offered every year.

Restriction: Graduate students only.

**ENGRMAE 243. Spaceflight Mechanics. 4 Units. **

Accurate force modeling; spacecraft trajectory design problem; two-body dynamics; Lambert problem; orbit perturbations and maintenance; applications to Earth and Moon missions; gravity assists and three-body dynamics; applications to Moon, Mars, interplanetary missions; libration point missions and dynamical system theory methods.

Restriction: Graduate students only.

**ENGRMAE 244. Theoretical Kinematics. 4 Units. **

Spatial rigid body kinematics is presented with applications to robotics. Orthogonal Matrices, Rodrigues' formula, Quaternions, Plucker coordinates, screw theory, and dual numbers are studied using modern projective geometry and multi-linear algebra. Applications include trajectory planning, inverse kinematics, and workspace analysis.

Restriction: Graduate students only.

**ENGRMAE 245. Spatial Mechanism Design. 4 Units. **

Fundamental kinematic theory required for planar, spherical, and spatial mechanism design. The focus is on algebraic methods for the exact solution of constraint equations. Not offered every year.

Restriction: Graduate students only.

**ENGRMAE 247. Micro-System Design. 4 Units. **

Covers the fundamentals of the many disciplines needed for design of Micro-Electro-Mechanical Systems (MEMS): microfabrication technology, structural mechanics on micro-scale, electrostatics, circuit interface, control, computer-aided design, and system integration.

Same as EECS 278.

Restriction: Graduate students only.

**ENGRMAE 249. Micro-Sensors and Actuators. 4 Units. **

Introduction to the technology of Micro-Electro-Mechanical Systems (MEMS). Fundamental principles and applications of important microsensors, actuation principles on microscale. Introduction to the elements of signal processing; processing of materials for micro sensor/actuator fabrication; smart sensors and microsensor/microactuator array devices.

Same as EECS 279.

Restriction: Graduate students only.

**ENGRMAE 250. Biorobotics. 4 Units. **

Sensors, actuators, and neural circuits for biological movement control from an engineering perspective. Current approaches to robotic and mechatronic devices that support and enhance human movement in health and following neurologic injuries like stroke and spinal cord injury.

Restriction: Graduate students only.

**ENGRMAE 252. Fundamentals of Microfabrication. 4 Units. **

Introduces Engineering and Science students to the science of miniaturization. Different options to make very small machines (micro and nano size) are reviewed, materials choices are discussed, scaling laws are analyzed, and many practical applications are listed.

Restriction: Graduate students only.

**ENGRMAE 253. Advanced BIOMEMS Manufacturing Techniques. 4 Units. **

Introduction to BIOMEMS. Advanced biotechnology/biomedicine equipment based on MEMS and NEMS. Fundamentals of MEMS/NEMS sensing techniques and the biological and physics principles involved and the preferred MEMS and NEMS manufacturing techniques.

Restriction: Graduate students only.

Concurrent with ENGRMAE 153.

**ENGRMAE 254. Mechanics of Solids and Structures. 4 Units. **

Finite deformation kinematics; stress and strain measures; invariance in solid mechanics; objective rates; constitutive theory of elastic and inelastic solids; rate formulations; computational approaches; theories of plates and shells; applications to aerospace vehicles.

Restriction: Graduate students only.

**ENGRMAE 255. Composite Materials and Structures. 4 Units. **

Motivation for composite materials. Different classifications according to the nature of the matrix (PMC, MMC, CMC) and the reinforcement topology (fibers, whiskers, particulates). Mechanical properties. Failure mechanisms. Designing with composite materials. Advantages and limitations of homogenization techniques for numerical modeling.

Restriction: Graduate students only.

Concurrent with ENGRMAE 155.

**ENGRMAE 258. Mechanical Behavior of Solids - Continuum Theories. 4 Units. **

Presents a continuum, macroscopic view of deformation and failure of solids. Covers elasticity, plasticity, visco-elasticity, visco-plasticity, fracture and fatigue. Topics include discussions of physical behavior, mathematical formalism and measurement techniques.

Prerequisite: ENGRMAE 254.

Restriction: Graduate students only.

**ENGRMAE 259. Mechanical Behavior of Solids - Atomistic Theories. 4 Units. **

Presents atomistic mechanisms that control mechanical behavior of materials. Covers plasticity, dislocation theory, strengthening mechanisms, high-temperature diffusion and gain boundary sliding, shear localization, void formation, ductile rupture, brittle fracture and fatigue.

Restriction: Graduate students only.

**ENGRMAE 260. Current Issues Related to Tropospheric and Stratospheric Processes. 4 Units. **

Examination of current issues related to the atmosphere, including energy usage; toxicology; effects on humans, forests, plants, and ecosystems; particulate matter (PM10); combustion; modeling and meteorology; airborne toxic chemicals and risk assessment; application of science to development of public policies.

Prerequisite: ENGRMAE 261 or CHEM 245 or EARTHSS 240.

Same as CHEM 241.

Restriction: Graduate students only.

**ENGRMAE 261. Air Quality Modeling. 4 Units. **

Fundamental principles necessary to understand the dynamics of air pollutants. Derivation and description of mathematical techniques for the numerical solution of the atmospheric equation. Formulation and development of air quality models. Not offered every year.

Prerequisite: ENGRMAE 230A and ENGRMAE 230B.

Restriction: Graduate students only.

**ENGRMAE 270A. Linear Systems I. 4 Units. **

Input-output and state-space representations of continuous-time linear systems. State transition matrices, Controllability and observability. Irreducible realizations. State feedback and observer design.

Restriction: Graduate students only.

**ENGRMAE 270B. Linear Systems II. 4 Units. **

Advanced topics in linear systems: bases, linear operator representations, and Jordan forms. Review of dynamical systems, and stability. Time-varying systems, discrete-time representations, and multi-input/multi-output systems. Introduction to continuous and discrete time linear regulator (LQR) problems. Not offered every year.

Prerequisite: ENGRMAE 270A.

Restriction: Graduate students only.

**ENGRMAE 272. Robust Control Theory. 4 Units. **

Methods for control design of systems with uncertainty. Feedback stability and small gain theorem. Multivariable stability margins and multiplier theory. H-infinity-optimal control, linear matrix inequalities. Not offered every year.

Prerequisite: ENGRMAE 270A.

Restriction: Graduate students only.

**ENGRMAE 273. Control of Robot Systems. 4 Units. **

Dynamic analysis and control system design of open- and closed-chained mechanisms. Methods for real time control of nonlinear systems. Lyapunov Stability. Advanced motion planning algorithms. Not offered every year.

Prerequisite: ENGRMAE 270A and ENGRMAE 241.

Restriction: Graduate students only.

**ENGRMAE 274. Optimal Control. 4 Units. **

Principles and methods of optimal control. Topics include: objectives and issues in controlling nonlinear systems; linear variational and adjoint equations; optimality conditions via variational calculus, maximum principle, and dynamic programming; solution methods; applications to control of robots and aerospace vehicles.

Restriction: Graduate students only.

**ENGRMAE 275. Nonlinear Feedback Systems. 4 Units. **

Advanced tools for feedback control system analysis and synthesis. Norms, operators, Lp spaces, contraction mapping theorem, Lyapunov techniques along with their extensions. Circle criterion positivity and passivity. Applications to nonlinear control methods, such as sliding mode or adaptive techniques.

Prerequisite: ENGRMAE 270B.

Restriction: Graduate students only.

**ENGRMAE 276. Geometric Nonlinear Control. 4 Units. **

Using the mathematics of differential geometry, a number of the concepts and results of linear systems theory have been extended to nonlinear systems. Describes these extensions and illustrate their use in nonlinear system analysis and design. Not offered every year.

Prerequisite: ENGRMAE 200A and ENGRMAE 270A.

Restriction: Graduate students only.

**ENGRMAE 277. Introduction To Neural Control Systems. 4 Units. **

Basic models and learning rules of artificial neural networks: perceptrons, multilayer neural networks and backpropagation, support vector machines, radial basis functions networks, CMAC networks. Introduction to Regularization and Statistical learning theory. Neural networks in system identification and control.

Restriction: Graduate students only.

**ENGRMAE 278. Estimation Techniques for Tracking and Navigation. 4 Units. **

Fixed bearing navigation, least squares, uncertainty modeling, minimum variance and maximum likelihood, covariance analysis and filter efficiency, GPS, orbit determination, Gauss-Markov models, inertial navigation, Kalman filters, Fokker-Planck and Kushner equations, nonlinear-filters.

Prerequisite: ENGRMAE 200A and ENGRMAE 270A.

Restriction: Graduate students only.

**ENGRMAE 279. Special Topics in Mechanical Systems. 4 Units. **

Selected topics of current interest in mechanical systems. Topics include robotics, kinematics, control, dynamics, and geometric modeling.

Prerequisite: ENGRMAE 270A and ENGRMAE 241.

Repeatability: Unlimited as topics vary.

Restriction: Graduate students only.

**ENGRMAE 284. Fundamentals of Experimental Design. 4 Units. **

Fundamentals and principles of statistical experimental design and analysis. Emphasis addresses understanding and use of designed experiments, response surfaces, linear regression modeling, process optimization, and development of links between empirical and theoretical models. Not offered every year.

Restriction: Graduate students only.

**ENGRMAE 294. Master of Science Thesis Project. 4 Units. **

Tutorial in which masters-level students taking the comprehensive examination option undertake a masters-level research project.

Repeatability: May be repeated for credit unlimited times.

Restriction: Graduate students only.

**ENGRMAE 295. Special Topics in Mechanical and Aerospace Engineering. 1-4 Units. **

Special topics by individual faculty in major fields of interest.

Repeatability: Unlimited as topics vary.

**ENGRMAE 296. Master of Science Thesis Research. 1-16 Units. **

Individual research or investigation conducted in the pursuit of preparing and completing the thesis required for the M.S. in Engineering.

Repeatability: May be repeated for credit unlimited times.

**ENGRMAE 297. Doctor of Philosophy Dissertation Research. 1-16 Units. **

Individual research or investigation conducted in the pursuit of preparing and completing the dissertation required for the Ph.D. in Engineering.

Repeatability: May be repeated for credit unlimited times.

**ENGRMAE 298. Seminars in Mechanical and Aerospace Engineering. 1 Unit. **

Presentation of advanced topics and reports of current research efforts in mechanical engineering. Required of all graduate students in mechanical engineering.

Grading Option: Satisfactory/unsatisfactory only.

Repeatability: May be repeated for credit unlimited times.

**ENGRMAE 299. Individual Research. 1-16 Units. **

Individual research or investigation under the direction of an individual faculty member.

Repeatability: May be repeated for credit unlimited times.

Restriction: Consent of instructor to enroll