Ph.D. Qualifying Written Exam

Ph.D. Qualifying Written Exam

Regulations and Subject Areas

Format of the Exam:

The student must obtain a passing grade in 4 subject areas. A separate exam will be administered for each selected subject

The student must obtain a passing grade in 3 subject areas in the first 4 categories. Each of these subjects must belong to a different category.

The 4th subject may belong to any of the 5 categories. At most one subject from the "Advanced Topics" category may be counted toward the fulfillment of the Ph.D. Qualifying Written Exam requirements.

The exams will be given by at least three different faculty members.


Subject Areas:
Category 1): Mechanical Systems:

Mechanical Systems: Stress and strain; Axial loading, bending, torsion, combined loading; Static Failure, Dynamic Failure, Fatigue and Endurance, Machine Elements, fasteners, Bearings, Gears, Shafts, keys, Couplings, Flexible Machine Elements, Gears, Friction, Wear, Lubrication.


  • “Machine Design an Integrated Approach”, R.L. Norton, Prentice Hall, New Jersey, USA, 2006.
  • “Mechanical Engineering Design”, J Shigley, C Mischke, R Budynas,, 7th Edition, McGraw-Hill, 2003; ISBN: 0072921935
  • “Mechanical Engineering Design”, J Shigley, C Mischke, R Budynas,, 7th Edition, McGraw-Hill, 2003; ISBN: 0072921935

Kinematics and Dynamics: Kinematics and Dynamics of rigid and elastic bodies, Momentum principles for rigid bodies, Variational formulation, Modal analysis and matrix formulation of vibration problems.


  • "Dynamics: Theory and Applications", Kane and Levison, McGraw Hill, 1985."Principles of Dynamics", Greenwood, Second Edition, Prentice Hall, 1987.
  • "Fundamentals of Applied Dynamics", William, John Wiley and Sons, 1996
  • “Dynamics of Mechanical and Electromechanical Systems”, S.H. Crandall, D.C. Karnopp, E.F. Kurtz, Jr., and D.C. Pridmore-Brown, , Krieger, 1982
  • "Mechanical Vibration", Rao, W, Prentice Hall
  • "Dynamics of Structures", Clough and Penzien, ISBN 0-07-011392-0
  • "Mechanism Design", Erdman. Sandor and Kota, Prentice Hall. ISBN 0-13-040872-7
  • “Kinematics and Dynamics of Machinery”, Wilson and Sadler, ISBN-0-201-35099-8

Fluid Mechanics: Fluid Mechanics, Fluid statics, fluid kinematics, elementary fluid dynamics, conservation laws, potential flows, simple solutions of Navier-Stokes equations, drag and lift forces, compressible flows and turbomachinery.


  • “Fundamentals of Fluid Mechanics”, Munson, B.R., Young, D.F., Okiishi, T.H., Huebsch, W.W., 6e, Wiley, 2009.
  • “Fluid Mechanics”, White, F., 7th ed., McGraw Hill, 2010.

Heat and Mass Transfer: Transient and steady heat conduction in single and multi-dimensions, forced and natural convection, heat exchangers, boiling and condensation, radiation and mass transfer.


  • “Fundamentals of Heat and Mass Transfer”, Incropera, F.P, DeWitt, D.P., Bergman T.L. and Lavine, A.S., 6th edition, Wiley, 2006.
  • “Basic Heat and Mass Transfer”, Mills, A.F., 2nd ed. Prentice-Hall, 2006.

Solid Mechanics: Statics: moment and force resultants, equilibrium; Mechanics of deformable bodies: stress/strain; Generalized Hooke's law (3D); Stress and strain; Axial loading, bending, torsion, combined loading; Analysis of strain and compatibility; Analysis of stress: Cauchy stress, traction; Transformation of stress and strain; Constitutive relations, energy density; St. Venant's principle, displacement equations; Plane stress / plane strain concepts; Analysis and design of beams; Deflection of beams; Energy Methods: Castigliano's theorems, Rayleigh-Ritz methods; Linear Elasticity: Equilibrium and Compatibility 2D and 3D Problems.


  • Mechanics of Materials, Beer, F.P., E.R. Johnston, DeWolf J. T., McGraw Hill, 2006.
  • Statics and Mechanics of Materials, Hibbeler, R.C., Prentice-Hall, 2004.
  • Materials Selection in Design, Ashby, M.F., Pergamon, 1992.
  • Engineering Mechanics of Solids, Popov, E. P., Prentice Hall, 1990.
  • Elastic and inelastic stress analysis, Shames, I.H., Cozzarelli F.A., Prentice-Hall, 1991.
  • Strength of Materials, Timoshenko S., Krieger Publishing Company, 1976.
  • Elements of Strength of Materials, Timoshenko, S.P., Young D.H., D. Van Nostrand Company, 1968.
  • Elasticity in Engineering Mechanics, Boresi A. P., Chong K.P., Wiley, 1987.
  • Theory of Elasticity, Timoshenko S. , Goodier and J.N., Mc-Graw Hill, 1970.
  • Solid Mechanics: An Introduction (Solid Mechanics and Its Applications), Ward, J. P., Springer, 1992.

Mechanical System Design: Design of mechanical systems, computer-aided design, geometric design, design optimization, risk and reliability-based optimization, design sensitivity analysis, system design integration, ergonomic and aesthetic considerations, design of direct contact systems, including cams, gears and power transmission systems; design of energy, fluid, and power handing systems; mechanisms and machine theory; machine component, and machine system design; design theory and methodology, including creativity in design, decision analysis, design cognition, and design synthesis.


  • Principles of optimal design: modeling and computation”, Panos Y. Papalambros, and Douglass J. Wilde, Cambridge University Press, ISBN-13: 9780521627276
  • "Mechanical System Design”, S P Patil, Jaico Publishing House, ISBN: 8179923150

Category 2): Electronics and Computing:
Subject Areas:

Circuits: Kirchhoff's voltage and current laws, circuit elements, node voltage and mesh current analysis, Thevenin and Norton circuits, RC and RL circuits, RLC circuits, steady-state analysis, sinusoidal analysis, phasors, frequency response, first order filters, high pass filters, Bode plots, resonance circuits, amplifier basics, operational amplifiers, diodes, bipolar junction transistors.


  • “Electrical Engineering Principles & Applications”, Allan R. Hambley, 4th Ed.

Power Electronics: Switching matrix, topologies of switching power converters, dc-to-dc, dc-to-ac, ac-to-dc conversion, CCM and DCM, switching converter control.


  • “Fundamentals of Power Electronics”, R. W. Erickson and D. Maksimovic: Kluwer Academic Publishers, 2001 (second edition) ISBN 0-7923-7270-0
  • “POWER ELECTRONICS, Circuits, Devices, and Applications”, Muhammad H. Rashid: (Third Edition), Prentice Hall, ISBN 0-13-334483-5

Real-Time Systems: Real-time scheduling, real-time communications, resource allocation, multiprocessor scheduling, fault tolerance techniques, clock synchronization, finite precision arithmetic and numeric representations.


  • “Real-Time Systems”, Jane W. S. Liu, Prentice Hall, ISBN 0130996513, 2000.
  • “Real-Time Systems”, C.M. Krishna, K. G. Shin, McGraw Hill, 1997, ISBN0070570434.
  • “Real-Time Systems Design Principles for Distributed Embedded Applications”, H. Kopetz, , Kluwer Academic Press, 1997, ISBN0792398947.
  • “Computer Arithmetic; Algorithms & Hardware Designs”, B. Parhami , Oxford Press, ISBN0195125835.

Scientific Computing: Solution of non-linear equations, interpolation, least squares regression, numerical differentiation and integration, direct and iterative solutions of systems of linear equations, differential equation based solutions of PDEs (Finite element method, finite difference techniques), integral equation based solutions of PDEs (method of moments, boundary element methods).


  • “Numerical Analysis”, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004.
  • “Elementary Numerical Analysis-An Algorithmic Approach”, S. D. Conte and Carl de Boor, McGraw-Hill, 1980.
  • “Numerical Methods for Engineers”, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, 2002.

Optics and Electromagnetism: Maxwell's equations, electrostatic and magnetostatic fields, properties of conductive, dielectric, magnetic materials, plane waves, time harmonic fields, reflection and guidance, scattering, ray optics, wave optics, beam optics, Fourier optics, polarization, waveguides.


  • “Fundamentals of Photonics”, B. E. A. Saleh and M. C. Teich, Wiley, 2007.
  • “Principles of Optics”, M. Born and E. Wolf, Cambridge University Press, 2006.
  • “Field and Wave Electromagnetics”, D. K. Cheng, Addison Wesley, 1989.
  • “Advanced Engineering Electromagnetics”, C.A. Balanis, Wiley, 1989.
  • “Electromagnetic Wave Theory”, J. A. Kong, Wiley, 1990.

Category 3): System Dynamics and Control:
Subject Areas:

Control Systems Design: Time and Frequency Domain Analysis, Dynamic Performance Criteria, Stability, Linear Controller Synthesis, Design of Observers, Digital Implementation, Disturbance Rejection.


  • “Feedback Control of Dynamic Systems”, 5th Edition by G. Franklin et al.
  • “Control System Design”, Graham, C. Goodwin, Graebe and Salgado, Prentice-Hall, 2001.
  • “Modern Control Engineering”, Ogata, Katsuhiko, , 2nd or later editions Prentice-Hall.

Motion Control Systems: Actuators, sensors, control in electromechanical systems, systems with friction, disturbance rejection, disturbance observers, systems with flexible links.


  • “Electric Drives, an Integrated approach”, Ned Mohan, MNPERE; ISBN: 0971529213
  • “Sliding Mode Control in Electromechanical Systems”, V.I. Utkin, J. Guldner and J. Shi:, Taylor and Francis, 1999
  • “DSP - Based Electromechanical Motion Control”, Stevan Campbell, CRC Press; 2003) ISBN: 0849319188
  • “Control of Electrical Drives”, W. Leonhard, Springer Verlag, 1985
  • “Precision Motion Control: Design and Implementation”, Lee Tong Heng (Ed), Springer-Verlag; (April 1, 2001), ISBN: 1852333286

Robotics: Geometry and Kinematics of Industrial manipulators and Mobile Robots, Robot Dynamics, Trajectory Generation, Position and velocity control using conventional sensors and vision.


  • “Robot Dynamics and Control”, Mark W. Spong, M. Vidyasagar, , John Wiley&Sons, 1989.
  • “Introduction to Robotics: Mechanics and Control”, John J. Craig, Pearson Education, 3rd Edition, 2005.
  • “Robot Motion Planning and Control”, Jean-Paul Lamound, , an online book (

Mobile Robotics: Mobile robot locomotion, kinematics of nonholonomic mobile robots, motion control of differential drive robots, perception using non-visual and visual sensors, sensor fusion, localization and mapping, SLAM problem, path planning.


  • Computational Principles of Mobile Robotics, Gregory Dudek, Michael Jenkin, Cambridge University Press, 2010.
  • Autonomous Robots, George A. Bekey, MIT Press, 2005.
  • Introduction to Autonomous Mobile Robots, Roland Siegwart, Illah R. Nourbakhsh, MIT Press, 2004.

Microsystems: Analysis and design of microsystems, basic microfabrication techniques, scaling laws and microsystems technology, measurement in micro-motion systems, actuation in micro-systems, nano-positioning systems.


  • “MEMS & Microsystems”, Hsu, McGraw-Hill (in library)
  • “Microsystems Design”, Senturia, KAP (in library)
  • “Mechanical Microsensors”, Elwenspoek and Wiegrink, Springer (in library)
  • “Nano- and Micro- electromechanical systems”, Lyshevski, CRC Press, 2001, Boca Raton
  • “Microsystem Technology and Microrobotics”, Ulrich Rembold, Sergej Fatikow, , ISBN: 354060658, Publishers - Springer Verlag, 1997
  • “Nanotechnology, Integrated Processing Systems for Ultra-Precision and Ultra-Fine Products”, Norio Taniguchi (Ed), , Oxford Science Press, 1996, ISBN 0 19 8562837

Category 4): Advanced Topics:
Subject Areas:

Control: Linear Systems, Nonlinear Control Systems, Modeling Of Dynamic Sytems, Digital Control Systems, Optimal Control, Sliding Mode Control, Advanced Motion Control, System Identification.

Robotics: Advanced Robotics, Visual Servoing, Force Control and Bilateral Teleoperation, Microrobotics, Autonomous Mobile Robotics, Cognitive Robotics, Motion Planning.

Mechanical Systems: Advanced Fluid Mechanics, Tribology, Two-Phase Flows, Finite Element Methods, Multi-Disciplinary Design Optimization, Kinematics and Dynamics of Machines, Mechanical Vibrations, CAD and Computer Prototyping, Renewable and Sustainable Energy Systems, Advanced Engineering Thermodynamics, Biomechanics, Computational Analysis and Simulation.

Electronics and Computing: Nano-Optics, Numerical Methods, Computer Vision, Geometric Modeling.

Subjects From Other FENS Programs: Microelectromechanical Systems (MEMS), Nanomechanics.

Category 5): Subjects From Other FENS Programs:
Subject Areas:

Any subject from the MATH, EE, CS, MAT, IE, BIO, or PHYS programs.