Ph.D. Qualifying Exam

Ph.D. Qualifying Exam

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  • 1) The EE Qualifier Exam will consist of an equal number of questions from each of the following four areas, the number of questions is identified inside parentheses.
    • Electronic Circuits: ENS203 (2)
    • Signals: ENS211 (2)
    • Engineering (Basic) Math: MATH201 (1), MATH203 (1)
    • Electromagnetics: ENS201 (2)
  • Out of 8 questions students must select and submit only 5 questions consisting of, one question from each of the four areas and one other question from any of the four areas.  A sample selection is: Electronic Circuits (1), Signals (2), Basic Math (1), Electromagnetics (1).
  • 2) Students have to pass the EE Qualifier Exam with a minimum score of 70 to be considered successful at the written stage of the qualifying exam.
  • 3) Students can attempt the EE Qualifier exam at most twice.
  • 4) For each topic, relevant faculty members can provide exam questions and will be responsible for their grading.
  • 5) Relevant faculty members include: instructors of the course in the particular academic year, or instructors who have taught the course in prior semesters, or instructors in the related field. If > 2 relevant faculty members would like to contribute, they will form a sub-committee to agree on the questions.
  • 6) Exam questions will be gathered and combined by the Graduate Coordinator (in the particular academic year) and will be provided to the Dean’s Office for the management and execution of the exam. 

 

EE Qualifier Exam

(Total:8 Questions)

Topics (briefly)

Relevant Courses That Prepare Students (Courses Corresponding to Exam Topics)

Suggested Texts/Materials

Electronic Circuits

Passive components, basic circuit analysis, first order circuits, transient and steady state analysis, second order RLC circuits, resonance, amplifier fundamentals, operational amplifiers, introduction to diodes and transistors.

 

ENS 203 (2 questions)

Allan R. Hambley. Electrical Engineering: Principles & Applications.

7th edition.

J.W.Nilsson, S.A.Reidel, Electric Circuits, Prentice Hall

Adel S. Sedra, Kenneth C. Smit, Microelectronic Circuits, Oxford University Press

Signals

Continuous and discrete, periodic and aperiodic signals, impulse, unit step signals. Spectrum representation of a signal. Fourier series representation of periodic signals. System concept. Continuous and Discrete Finite Impulse Response (FIR) Systems. Linear Time Invariant (LTI) Systems. Impulse response and Frequency response of LTI systems. Fourier transform of aperiodic and periodic signals. Filtering in time and frequency domain. Sampling of continuous signals. Aliasing. Bandlimited reconstruction, interpolation. Basic Amplitude Modulation.

ENS 211 (2 questions)

DSP First

by James H. McClellan, Ronald W. Schafer, and Mark A. Yoder,

Pearson Education, 2nd edition 2016.

 Engineering Mathematics

Math 201 (Linear Algebra):

Systems of linear equations; Gaussian elimination. Vector spaces, subspaces, linear, independence, dimension, change of basic. Linear transformations. Inner product, orthogonality. Eigenvalues. Diagonalization and canonical forms. Cayley-Hamilton theorem.

Math 203 (Probability):

Counting techniques, combinatorial methods, random experiments, sample spaces, events, probability axioms, some rules of probability, conditional probability, independence, Bayes' theorem, random variables (r.v.'s), probability distributions, discrete and continuous r.v.'s, probability density functions, multivariate distributions, marginal and conditional distributions, expected values, moments, Chebyshev's theorem, product moments, moments of linear combinations of r.v.'s, special discrete distributions, uniform, Bernouilli, binomial, negative binomial, geometric, hypergeoemtric and Poisson distributions, special probability densities, uniform, gamma, exponential and normal densities, normal approximation to binomial, distribution of functions of r.v.'s, distribution function and moment-generating function techniques, distribution of the mean, law of large numbers, the central limit theorem.

MATH 201

(1 question)

 

MATH 203

(1 question)

Math 201:

G. Strang, Introduction to Linear Algebra. Fifth edition (2016) Wellesley-Cambridge Press and SIAM

 

 

Math 203:

John Freund's Mathematical Statistics with Applications, 8th Edition, Pearson-

Prentice Hall, 2004

Electromagnetics

Review of vectors and mathematical background. Static and magnetic fields and electromagnetic properties of materials. Faraday's Law with applications to electromechanical systems. Introduction to Maxwell's equations and electromagnetic waves.

 

ENS 201 (2 questions)

F.T. Ulaby, Fundamentals of Applied Electromagnetics, Prentice-Hall

D.K. Cheng, Field and Wave Electromagnetics, 2nd Ed, Addison –Wesley

J.D. Kraus D.A. Fleisch, Electromagnetics with applications, 5th Ed, McGraw-Hill