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Sturm-Liouville problem. Partial differential equations: Characteristic curves, separation of variables and integral transforms (Laplace and Fourier), method of characteristics. Wave, heat and diffusion-equations. Calculus of variation. Software applications.

Elements of probability theory, random variables, analytical models of random phenomena, reliability, factor of safety, safety margin, extreme value statistics, Monte-Carlo simulation, empirical determination of distribution models, confidence intervals, regression and correlation analysis, general applications to engineering design problems, stochastic processes.

Norms, limits and condition numbers. Inverses of perturbed matrices. Integrative techniques for solving systems of equations. The LU, QR and singular value decompositions. Algorithms for the linear least squares and linear minimax problems. Computation of the eigenvalues of a matrix. the interpolation and polynomial approximation. Approximate methods for initial value problems and for boundary value problems.

Origin and basis of finite-element methods in continuum mechanics, stiffness method, assumed displacement field, potential energy and Rayleigh- Ritz method, types of elements, modeling, accuracy and convergence, solution techniques and computer application to structural and fluid mechanics.

Cartesian tensors. Basic principles of continuum mechanics: deformation, displacement, strain, stress, conservation of mass, continuum thermodynamics and constitutive equations. Illustrative applications in elasticity, fluid dynamics, viscoelasticity ad plasticity.

Basic Concepts: The gradient vector and the Hessian Matrix, multidimensional Taylor's theorem, linear and quadratic approximation of a function. Unconstrained optimization, necessary and sufficient conditions for optimality. Algorithms for single variable minimization, the Fibonacci search and the Golden section search, algorithms that use repeated polynomial interpolation. Algorithms for multi-dimensional minimization; The steepest descent, the Newton method and its variations, conjugate gradient algorithms such as the Flecter-Reeves, Polak and Ribieve, Quasi-Newton Methods such as the DEP- BFGS, Huang's family of algorithms. Constrained optimization: Necessary and sufficient conditions for constrained minima. Algorithms for constrained optimization: interior and exterior penalty function methods, augmented Lagrangian methods, Resen's gradient projection.

Introduction to probability theory and engineering applications of probability. random variables and expected values. distribution of functions of random variables and applications of R.V. to system problems. Stochastic processes, correlation and power spectra, systems and random signals. Engineering decisions and estimation theories.

Mathematics of fuzzy sets and logic, fuzzy rule based and fuzzy inference engines, fuzzifiers and defuzzifiers, fuzzy systems and their properties, design of fuzzy systems using clustering and table look-up schemes, fuzzy control using the trial and error approach, and fuzzy control of linear and nonlinear systems.

Operational amplifier, balanced three-phase circuits, circuit response using Laplace transform frequency selective circuits, Fourier series, Fourier transform, two-port networks.

Basic semiconductor properties. Electrons and holes. Continuity and currents equations: Generation recombination, drift & diffusion. The PN junction diode: Structure and I-V characteristics. Bipolar junction transistor: Structure and I-V characteristics. MOS transistor: Structure and C-V characteristics. DC analysis of BJT and MOSFET transistors.

Laboratory experiments related to 0610233 course contents.

Introduction to design process, creativity in design, development of skills needed for design including project specifications, planning and scheduling, circuits/components selection, circuit simulation using computer tools, circuits construction and testing. Effective application of communication skills and teamwork. Considerations are given to realistic constraints such as economic factors, safety, reliability, and ethics. Students are expected to work on multiple hands-on engineering projects.

Introduction to signals and systems, continuous and discrete, differential and difference equations, solution of differential and difference equations using Laplace and Z-transforms, convolution and its properties, frequency domain analysis of linear systems, transfer functions, BIBO Stability, introduction to state space analysis.

Plane waves in lossless and lossy media plane waves in good conductors, Poynting's theorem, Reflection and transmission of plane waves at planar interfaces, total internal reflection and zero reflection, transmission lines and matching schemes using Smith chart, Waveguides and resonators, topics of waves with applications, introduction to antennas.

Single stage amplifier circuits. Integrated circuit biasing and current mirrors. Multistage amplifiers. Frequency responses of single and multistage amplifiers. Differential amplifier. Feedback. Oscillators.