Course Descriptions
Taken from the Undergraduate Calendar and the Graduate Calendar
Fundamental Concepts of Algebra 
3.0 Cr. 


Sets, algebraic techniques, inequalities, graphs of equations. 
Elementary Functions 
3.0 Cr. 


Sets, inequalities, graphs of functions, and relations. Trigonometric, exponential, and logarithmic functions. 
College Algebra 
3.0 Cr. 


Prerequisite: MATH201. Progressions, combinations, permutations, binomial theorem, mathematical induction, inequalities, polynomials, Cartesian and polar forms of complex numbers, conics. 
Differential and Integral Calculus I 
3.0 Cr. 


Prerequisite: MATH201. Functional notation. Differentiation of polynomials. The power, product, quotient, and chain rules. Differentiation of elementary functions. Implicit differentiation. Higher derivatives. Maxima and minima. Applications: tangents to plane curves, graphing, related rates. Approximations using the differential. Antiderivatives, definite integrals, area. 
Vectors and Matrices 
3.0 Cr. 


Prerequisite: MATH201. Algebra and geometry of vectors, dot and cross products, lines and planes. System of equations, operations on matrices, rank, inverse, quadratic form, and rotation of axes. 
Differential and Integral Calculus II 
3.0 Cr. 


Prerequisite: MATH203. Techniques of integration: substitutions, integration by parts, partial fractions. Improper integrals. Physical applications of the definite integral. Infinite series: tests for convergence. Power series, Taylor’s theorem. 
Algebra and Functions 
3.0 Cr. 


Coordinate systems. Radicals and distance formula. Polynomials, factoring, and graphing. Relations and functions. Linear and quadratic functions, equations, and systems. Exponents, exponential and logarithmic functions and equations. 
Fundamental Mathematics I 
3.0 Cr. 


Prerequisite: MATH206. Matrices, Gaussian elimination, inputoutput analysis, progressions, compound interest, annuities, permutations and combinations, probability, binomial theorem, exponential and logarithmic functions, inequalities, linear programming. 
Fundamental Mathematics II 
3.0 Cr. 


Prerequisite: MATH206. Limits; differentiation of rational, exponential, and logarithmic functions; theory of maxima and minima; integration. 
Linear Algebra I 
3.0 Cr. 


Matrices and linear equations; vector spaces; bases, dimension and rank; linear mappings and algebra of linear operators; matrix representation of linear operators; determinants; eigenvalues and eigenvectors; diagonalization. 
Numerical Analysis 
3.0 Cr. 


Error analysis in numerical algorithms; solution of nonlinear equations; fixed point iterations, rate of convergence. Interpolations and approximations, Legendre polynomials. Numerical integration and Quadrature. 
Probability I 
3.0 Cr. 


Axiomatic approach to probability; combinatorial probability; discrete and continuous distributions; expectation; conditional expectation; random sampling and sampling distributions. 
Faculty of Engineering and Computer Science
Applied Ordinary Differential Equations 
3.0 Cr. 


Prerequisite: MATH204, MATH205. Definition and terminology, initialvalue problems, separable differential equations, linear equations, exact equations, solutions by substitution, linear models, orthogonal trajectories, complex numbers, form of complex numbers: powers and roots, theory: linear equations, homogeneous linear equations with constant coefficients, undetermined coefficients, variation of parameters, CauchyEuler equation, reduction of order, linear models: initial value, review of power series, power series solutions, theory, homogeneous linear systems, solution by diagonalization, nonhomogeneous linear systems. Eigenvalues and eigenvectors. 
Applied Advanced Calculus 
3.0 Cr. 


Prerequisite: MATH204, MATH205. Functions of several variables, partial derivatives, total and exact differentials, approximations with differentials. Tangent plane and normal line to a surface, directional derivatives, gradient. Double and triple integrals. Polar, cylindrical, and spherical coordinates. Change of variables in double and triple integrals. Vector differential calculus; divergence, curl, curvature, line integrals, Green’s theorem, surface integrals, divergence theorem, applications of divergence theorem, Stokes’ theorem. 
Transform Calculus and Partial Differential Equations 
3.0 Cr. 


Prerequisite: ENGR233. Elements of complex variables. The Laplace transform: Laplace transforms and their properties, solution of linear differential equations with constant coefficients. Further theorems and their applications. The Fourier transform: orthogonal functions, expansion of a function in orthogonal functions, the Fourier series, the Fourier integral, the Fourier transform, the convolution theorem. Partial differential equations: physical foundations of partial differential equations, introduction to boundary value problems. 
Probability and Statistics in Engineering 
3.0 Cr. 


Prerequisite: ENGR213, ENGR233. Axioms of probability theory. Events. Conditional probability. Bayes theorem. Random variables. Mathematical expectation. Discrete and continuous probability density functions. Transformation of variables. Probabilistic models, statistics, and elements of hypothesis testing (sampling distributions and interval estimation). Introduction to statistical quality control. Applications to engineering problems. 
Numerical Methods in Engineering 
3.0 Cr. 


Prerequisite: ENGR213, ENGR233, COEN243. Roots of algebraic and transcendental equations; function approximation; numerical differentiation; numerical integration; solution of simultaneous algebraic equations; numerical integration of ordinary differential equations. 
Introduction to Discrete Mathematics 
3.0 Cr. 


Prerequisite: MATH204. Fundamental principles of counting: rules of sum and product; permutations, arrangements and combinations, the binomial theorem; combinations with repetition; distributions. Fundamentals of logic: basic connectives and truth tables; logical equivalence; the laws of logic; logical implication; rules of inference; the use of quantifiers; proofs of theorems. Sets: the laws of set theory. Boolean algebra. Relation of Boolean algebra to logical and set theoretic operations. Modulo arithmetic: representations of numbers in binary, octal and hexadecimal formats; binary arithmetic. Induction and recursion: induction on natural numbers; recursive definitions. Functions and relations: Cartesian products and relations; functions; function composition and inverse functions; computational complexity. Elements of graph theory: basic definitions of graph theory; paths, reachability and connectedness; computing paths from their matrix representation; traversing graphs represented as adjacency lists; trees and spanning trees. 
Digital Systems Design I 
3.5 Cr. 


Prerequisite: COEN231. Logic gates and their use in the realization of Boolean algebra statements; logic minimization, multiple output circuits. Designing with MSI and LSI chips, decoders, multiplexers, adders, multipliers, programmable logic devices. Introduction to sequential circuits; flipflops. Completely specified sequential machines. Machine equivalence and minimization. Implementation of clock mode sequential circuits. 
Signal and Systems I 
3.0 Cr. 


Prerequisite: ELEC273, ENGR213. Continuoustime and discretetime signals and systems. Linear Time Invariant [LTI] systems. Convolutionsum and convolutionintegral representation of systems. Causal LTI systems. Fourier series representation of continuoustime and discretetime periodic signals. Filters described by differential or difference equations. The continuoustime Fourier transform. Systems based on Linear Constant Coefficient Differential Equations [LCCDEDT]. The discretetime Fourier transform. Systems based on Linear Constant Coefficient Difference Equations [LCCDECT]. Computerbased simulation. 
Basic Circuit Analysis 
3.5 Cr. 


Prerequisite: ENGR213. Units: current, voltage, power, and energy. Elementary waveforms. Time averages. Ohm’s law. KVL and KCL. Ideal sources. Mesh and node analysis of resistive circuits. Network theorems. Inductors and capacitors and their response to the application of elementary waveforms. Transient response of simple circuits. Natural frequency and damping. Initial conditions. Steady state AC analysis: resonance, impedance, power factor. Introduction to three phase power, delta and Y connections. Ideal operational amplifiers. Ideal transformers. 
Principles of Electrical Engineering 
3.5 Cr. 


Prerequisite: ENGR213. Fundamentals of electric circuits: Kirchhoff's laws, voltage and current sources, Ohm’s law, series and parallel circuits. Nodal and mesh analysis of DC circuits. Superposition theorem, Thevenin and Norton Equivalents. Use of operational amplifiers. Transient analysis of simple RC, RL and RLC circuits. Steady state analysis: Phasors and impedances, power and power factor. Single and three phase circuits. Magnetic circuits and transformers. Power generation and distribution. 
Fundamentals of Telecommunications Systems 
3.5 Cr. 


Prerequisite: ELEC361, ENGR371. Introduction to basic telecommunications concepts and systems. Analog communications: AM and FM, system level consideration of noisebandwidth tradeoffs. Digital communications: sampling and quantization, digital modulation techniques, the matched filter. Redundancy encoding. 
Signal and Systems II 
3.0 Cr. 


Prerequisite: ELEC264. Sampling of continuoustime and discretetime signals. Reconstruction of a signal from its samples using interpolation. Laplace Transform. Inverse Laplace Transform. Analysis of systems using Laplace Transform. Unilateral Laplace Transform. The ZTransform and inverse ZTransform. Analysis of systems using ZTransform. Unilateral ZTransform. Time and frequency characteristics of signals and systems. Examples of continuoustime and discretetime first and secondorder systems. Amplitude modulation and demodulation. Pulse amplitude modulation. Frequency modulation. Computerbased simulation. 
Complex Variables and Partial Differential Equations 
3.0 Cr. 


Prerequisite: ENGR213, ENGR233. Review of complex arithmetic. Analytic functions. Taylor and Laurent series. Residue theory. Fourier series. Partial differential equations. Applications to Laplace, heat, and wave equations. Bessel and Legendre functions. 
Digital Signal Processing 
3.5 / 4.0 Cr. 


Prerequisite: ELEC361. Review of discretetime signals and systems; difference equation, the Fourier transform, the ztransform, the discrete Fourier series and transform; recursive and nonrecursive digital filters, common digital filter structures, common design approaches for digital filters; A/D and D/A converters, digital processing of analog signals, signal interpolation and decimation; effect of finite word lengths, description of a typical DSP chip. 
Digital Communications 
3.5 / 4.0 Cr. 


Prerequisite: ELEC363. Random processes and linear systems; baseband modulation/demodulation, optimal receivers in AWGN, correlation and matchedfilter receivers, pulse shaping for bandlimited channels; bandpass modulation techniques such as PAM, PSK, DPSK, FSK, QAM; introduction to error control coding, linear block codes, cyclic codes, convolutional codes. 
Wireless Communications 
3.0 / 4.0 Cr. 


Prerequisite: ELEC462. Review of modulation and error control coding. Modulation vs. coding tradeoff, communications link analysis. Introduction to cellular systems: frequency reuse, trunking and grade of services, sectoring and cell splitting, coverage and capacity. Modulation techniques for mobile communications. Mobile radio channels. Spreadspectrum techniques. Multiplexing and multiple access techniques. 
Advanced Engineering Graduate Courses
Engineering Analysis II 
4.0 Cr. 


SturmLiouville problem; orthogonal functions; integral transforms; partial differential equations; boundary value problems; applications of above; topics in engineering problems. 
Probabilistic Methods in Design 
4.0 Cr. 


Elements of probability theory, decision models, expected costs and benefits, models from random occurrences, extreme value statistics, Monte Carlo simulation, reliability analysis, general applications to engineering design problems. 
Probability and Stochastic Processes 
4.0 Cr. 


Axioms and rules of probabilities, Bayes’ Theorem, binary communication systems, Bernoulli trials and Poisson Theorem, random variables, distributions and density functions, moments, correlation, Chebyshev and Markov’s inequalities, characteristic functions, Chernoff inequality, transformation of random variable, random processes, stationarity, Bernoulli, Random Walk, Poisson, shot noise, random telegraph, and Wiener processes, stopping time; Wald’s equation, elements of Renewal Theory, MeanErgodic Theorem, auto and crosscorrelation functions, correlation time, autocorrelation receiver, WienerKhinchin Theorem, power spectral density, linear system with stochastic inputs, matched filtering. 
Stochastic Processes for Com. and Signal Processing 
4.0 Cr. 


Bayesian, maximum likelihood and meansquare estimation, mean square sense ergodicity, differentiation and integration, Wiener and Kalman filters, nonlinear systems with stochastic input, direct and Rice methods for calculation of an autocorrelation function, linearization methods, discretetime Markov chains, state occupancy time, global balance, limiting probabilities, Markov process, GaussMarkov (OrnsteinUlenbeck) process. 
Detection and Estimation Theory 
4.0 Cr. 


Prerequisite: ENCS6161. Basic hypothesis testing, cost functions, Bayes and Neyman Pearson tests, the power of a test, sequential tests; estimation, Bayes estimates, maximum a posteriori estimates. the CramerRao inequality, maximum likelihood estimates; composite hypothesis testing, application of estimation theory to phase locked loops, vector representation of signals in noise, application of the KharhunenLoeve expansion, complex analytic representation of signals; detection and estimation of signals in white and nonwhite noise, the matched filter, composite hypothesis testing, random amplitude and phase, multipath channels, waveform estimation, Wiener filters, Kalman filters. 
Spread Spectrum Communications 
4.0 Cr. 


Prerequisite: ELEC6831. Direct sequence, frequency hopping, time hopping, chirp and hybrids, maximal Gold and nonlinear codes, probability or error analysis, under tone, partial band jamming for different systems, serial and parallel, initial acquisition, delay lock loops and tau dither loops, fading effects and potential coding techniques, new acquisition and tracking techniques, interception and repeated jammers. 
Error Detecting and Correcting Codes 
4.0 Cr. 


Prerequisite: ENCS6161. Communication channels and the coding problem; important linear block codes (cyclic, Hamming and BCH codes); encoding and decoding with shift registers; threshold decoding; introduction to convolutional codes; coding in system design considerations, bit error rates and coding gain, tradeoffs in power, bandwidth, data rate and system reliability; codulation. 
Information Theory and Source Coding 
4.0 Cr. 


Prerequisite: ENCS6161. Entropy of a source, rate distortion functions, source coding, analog to digital conversion, effects of sampling and quantization, vector quantization, discrete memoryless channels and their capacity, cost functions, channel coding theorem, channel capacity, fundamental concepts of information theory with applications to digital communications, theory of data compression, broadcast channels, application to encryption, DES, public key encryption, computational complexity. 
Digital Communications II 
4.0 Cr. 


Prerequisites: ENCS6161, ELEC6831. Digital signaling over bandlimited channels: signal design for bandlimited channels, maximum likelihood sequence detection, equalization techniques, e.g., zeroforcing, minimum mean squared error, adaptive equalization. Advanced coding and modulation: concatenated coding with iterative decoding, coded modulation techniques. Diversity techniques for fading channels. Synchronization techniques: carrier and timing recovery, frequency estimation techniques, frame and network synchronization, maximumlikelihood estimation and CramerRao bounds. 
Fundamentals and Applications of MIMO Comm. 
4.0 Cr. 


Prerequisite: ELEC6141. Multiple Input Multiple Output (MIMO) communication systems and wireless channel models; Diversity techniques and array processing; MIMO channel capacity; Spacetime black and trellis codes; Spatial multiplexing and layered spacetime architectures, diversityversusmultiplexing tradeoff; Differential and unitary spacetime coding; MIMO OFDM and spacefrequency coding; Concatenated coding and iterative decoding for MIMO systems; Applications of MIMO in wireless systems. 
Digital Filters 
4.0 Cr. 


Prerequisite: ELEC6601. Approximation and design of recursive and nonrecursive digital filters. Transformations. Stability. Digital filter structures including wave and lattice structures. Effect of quantization, noise and limit cycles. Hardware implementation. Digital filter applications. 
Digital Waveform Compression 
4.0 Cr. 


Prerequisites: ELEC6601, ENCS6161. Numerical representation of waveform information; common waveform communication systems; statistical models used for waveforms; visual psychophysics. Differential PCM, motion estimation/compensation for video compressions. Transform coding: run length coding, Huffman and arithmetic coding, control of Q factor and Q table, segmentation/contour/edge based coding; preprocessing and postprocessing strategies. Vector quantization. Subband coding and Wavelet Transform. Zero trees. Channel concerns: robustness, error recovery, masking video/image bit rate source models. Coding of twolevel graphics. Review of standards: JPEG, MPEG, H.261. 
Digital Video Processing 
4.0 Cr. 


Prerequisites: ELEC6601, ENCS6161. Video processing fundamentals; video signals and systems. Fourier analysis of video signals, video scanning and transmission, spatiotemporal sampling, selected material on the Human Visual System, modelling of video components, motion estimation and representation. Video filtering and enhancement: noise reduction, noise estimation, deinterlacing, framerate conversion, signal processing for improved TVsystems. An introduction to video compression, Lowlevel video analysis: local operators, linear and nonlinear operators, rankorder filters, morphological filters, edge detection, segmentation. 
Adaptive Signal Processing 
4.0 Cr. 


Prerequisites: ELEC6601, ENCS6161. Optimal filtering; filter structures for adaptive filtering; the LMS stochastic gradient algorithm; block leastsquares methods; lattice structures. Convergence properties of transversal and lattice stochastic gradient algorithms. Stability and sensitivity analysis of adaptive filters. 
Multidimensional Signal and Image Processing 
4.0 Cr. 


Prerequisite: ELEC6601. Multidimensional signals and systems. Twodimensional discrete Fourier analysis: discrete Fourier transform, computation of DFT and computational considerations. Twodimensional FIR filters: convolutional and DFT implementations, design using windows, leastsquares design. Recursive systems. Twodimensional IIR filters: implementations, spacedomain design methods, frequency domain design, design for specialized structures. One of more specialized topics: finitewordlength effects, symmetry in twodimensional filters, signal reconstruction and realtime image processing. 
Doctoral Research Proposal 
6.0 Cr. 


The goal of the doctoral research proposal is to focus the student’s Ph.D. research. Students will be assessed on the basis of written and oral presentations. The proposal must include: (i) a critical review of previous work relevant to the subject of the thesis, and (ii) a detailed research plan of action and expected milestones. Students are required to defend their doctoral research proposal before a committee that will normally be comprised of the same members as the Comprehensive Examination Committee. Students must demonstrate the viability of their project and their capacity to undertake doctoral thesis research. The proposal may be accepted, returned for modifications, or rejected. The rejection of a proposal will result in the student’s withdrawal from the program. A student whose proposal is accepted will be admitted to candidacy for the Ph.D. 
Ph.D. Seminar 
2.0 Cr. 


Grading on a Pass/Fail basis only. No credit value!! 
Doctoral Research and Thesis 
70.0 Cr. 


Students are required to plan and carry out a suitable research, development, or design project, which leads to an advance in knowledge. The student must submit a thesis based upon this work and defend it in an oral examination. For purposes of registration, this work will be designated ENGR8911: Doctoral Research and Thesis (70 credits). Theses will be examined by a committee consisting of the student’s supervisory committee, an external examiner, and other examiners as approved by the Faculty Graduate Studies Committee and the Dean of Graduate Studies. 
Last Update: March 26, 2015 11:59 AM  Copyright © 20082015 Mouhamed Abdulla, Ph.D.