General Elective

ELEC 518 / NUMERICAL MODELING&SIMULATION**Sınıf:** **Credit:** 3**Precondition:**

Introduction to mathematical formulations and computational techniques for the modeling and simulation of engineering and other kinds of systems, including electronic, mechanical, biological, biochemical, virtual, abstract and multi-domain dynamical systems. Applications from various engineering disciplines and the sciences. Matrix formulation of equations for linear problems. Formulation of equations for nonlinear problems & linearization. Numerical solution of linear algebraic equations. Gaussian elimination, computations with sparse & structured matrices. Floating point number representation & arithmetic. Numerical conditioning, ill-conditioned problems. Numerical solution of nonlinear algebraic equations. Fixed point iteration & Newton’s method in one dimension. Newton’s method for system of coupled nonlinear algebraic equations. Improving convergence of Newton’s method. Numerical solution of ordinary differential equations. Forward & backward Euler, trapezoidal rule. Multistep methods, accuracy & stability. Implicit vs explicit techniques, region of stability, stiff problems.

ENGL 500 / ACADEMIC WRITING**Sınıf:** **Credit:** 0**Precondition:**

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

ENGR 500 / APPLIED OPTIMAL CONTROL**Sınıf:** **Credit:** 3**Precondition:**

Optimization problems for dynamical systems. Pontryagin?s Maximum Principle. Optimality conditions for nonlinear dynamical systems. Linear Quadratic Optimal Control of continuous and discrete linear systems using finite and infinite time horizons. Stability and performance analysis of the properties of the optimal feedback solutions. Moving horizon optimal control of constrained systems using Model Predictive Control formulation. Applications from different disciplines and case studies.

INDR 501 / OPTIMIZATION MODELS AND ALGORITHMS**Sınıf:** **Credit:** 3**Precondition:**

Convex analysis, optimality conditions, linear programming model formulation, simplex method, duality, dual simplex method, sensitivity analysis; assignment, transportation, and transshipment problems.

INDR 520 / NETWORK MODELS AND OPTIMIZATION**Sınıf:** **Credit:** 3**Precondition:** INDR. 262 or consent of the instructor

Network flow models and optimization problems. Algorithms and applications. Minimum spanning tree problem. Shortest path problems. Maximum flow problems, minimum cuts in undirected graphs and cut-trees. The minimum cost network flow problem. Matching problems. Generalized flows. Multicommodity flows and solution by Lagrangean relaxation, column generation and Dantzig-Wolfe decomposition. Network design problems including the Steiner tree problem and the multicommodity capacitated network design problem; their formulations, branch-and-cut approaches and approximation algorithms.

INDR 551 / SELECTED TOPICS IN INDUSTRIAL ENGINEERING**Sınıf:** **Credit:** 3**Precondition:**

Topics will be announced when offered.

INDR 553 / SELECTED TOPICS IN INDUSTRIAL ENGINEERING**Sınıf:** **Credit:** 3**Precondition:**

Topics will be announced when offered.

INDR 564 / DYNAMIC PROGRAMMING**Sınıf:** **Credit:** 3**Precondition:** (INDR. 501 and INDR. 503) or consent of the instructor

Theory and practice of dynamic programming, sequential decision making over time; the optimal value function and Bellman's functional equation for finite and infinite horizon problems; Introduction of solution techniques: policy iteration, value iteration, and linear programming; General stochastic formulations, Markov decision processes; application of dynamic programming to network flow, resource allocation, inventory control, equipment replacement, scheduling and queueing control.

INDR 568 / HEURISTIC METHODS**Sınıf:** **Credit:** 3**Precondition:** INDR. 501 or consent of the instructor

Constructive heuristics; improving heuristics; metaheuristics: simulated annealing, genetic algorithms, tabu search, scatter search, path relinking, ant colony

MASE 503 / ADVANCED THERMODYNAMICS**Sınıf:** **Credit:** 3**Precondition:**

Classical thermodynamics: enthalpy, entropy, free energies, equilibria; introduction to statistical thermodynamics to describe the properties of materials; kinetic processes; diffusion of mass, heat, energy; fundamentals of rate processes in materials, kinetics of transformations.

MASE 538 / INTERMOLECULAR AND SURFACE FORCES**Sınıf:** **Credit:** 3**Precondition:** CHEM. 301 or consent of the instructor

Intermolecular forces which govern self-organization of biological and synthetic nanostructures. Thermodynamic aspects of strong (covalent and coulomb interactions) and weak forces (dipolar, hydrogen bonding). Self-assembling systems: micelles, bilayers, and biological membranes. Computer simulations for ôhands-onö experience with nanostructures.

MASE 540 / SURFACE AND INTERFACE PROPERTIES OF MATERIALS**Sınıf:** **Credit:** 3**Precondition:**

Interaction forces in interfacial systems; fluid interfaces; colloids; amphiphilic systems; interfaces in polymeric systems & polymer composites; liquid coating processes.

MASE 542 / BIOMATERIALS**Sınıf:** **Credit:** 3**Precondition:**

Materials for biomedical applications; synthetic polymers, metals and composite materials as biomaterials; biopolymers, dendrimers, hydrogels, polyelectrolytes, drug delivery systems, implants, tissue grafts, dental materials, ophthalmic materials, surgical materials, imaging materials.

MATH 503 / APPLIED MATHEMATICS I**Sınıf:** **Credit:** 3**Precondition:**

Linear algebra: Vector and inner product spaces, linear operators, eigenvalue problems; Vector calculus: Review of differential and integral calculus, divergence and Stokes' theorems. Ordinary differential equations: Linear equations, Sturm-Liouville theory and orthogonal functions, system of linear equations; Methods of mathematics for science and engineering students.

MATH 504 / NUMERICAL METHODS I**Sınıf:** **Credit:** 3**Precondition:**

A graduate level introduction to matrix-based computing. Stable and efficient algorithms for linear equations, least squares and eigenvalue problems. Both direct and iterative methods are considered and MATLAB is used as a computing environment.

MATH 506 / NUMERICAL METHODS II**Sınıf:** **Credit:** 3**Precondition:**

Development and analysis of numerical methods for ODEs, an introduction to numerical optimization methods, and an introduction to random numbers and Monte Carlo simulations. The course starts with a short survey of numerical methods for ODEs. The related topics include stability, consistency, convergence and the issue of stiffness. Then it moves to computational techniques for optimization problems arising in science and engineering. Finally, it discusses random numbers and Monte Carlo simulations. The course combines the theory and applications (such as programming in MATLAB) with the emphasis on algorithms and their mathematical analysis.

MATH 545 / MATHEMATICS OF FINANCE**Sınıf:** **Credit:** 4**Precondition:**

From random walk to Brownian motion, quadratic variation and volatility, stochastic integrals, martingale property, Ito formula, geometric Brownian motion, solution of Black-Scholes equation, stochastic differentialequations, Feynman-Kac theorem, Cox-Ingersoll-Ross and Vasicek term structure models, Girsanov's theorem and risk neutral measures, Heath-Jarrow-Morton term structure model, exchange-rate instruments.

MATH 551 / SELECTED TOPICS IN ANALYSIS I**Sınıf:** **Credit:** 3**Precondition:**

MATH 552 / SELECTED TOPICS IN ANALYSIS II**Sınıf:** **Credit:** 3**Precondition:**

MECH 521 / ADVANCED FLUID DYNAMICS**Sınıf:** **Credit:** 3**Precondition:**

Foundations of fluid mechanics introduced at an advanced level. Aspects of kinetic theory as it applies to formulation of continuum fluid dynamics. Introduction to tensor analysis and derivation of Navier Stokes equations and energy equation for compressible fluids. Boundary conditions and surface phenomena. Viscous flows, boundary layer theory, potential flows and vorticity dynamics. Introduction to turbulence and turbulent flows.

MECH 522 / COMPUTATIONAL FLUID DYNAMICS**Sınıf:** **Credit:** 3**Precondition:**

Numerical methods for elliptic, parabolic, hyperbolic and mixed type partial differential equations arising in fluid flow and heat transfer problems. Finite-difference, finite-volume and some finite-element methods. Accuracy, convergence, and stability; treatment of boundary conditions and grid generation. Review of current methods. Assignments require programming a digital computer.

MECH 534 / COMPUTER BASED SIMULATION AND MODELING**Sınıf:** **Credit:** 3**Precondition:**

Geometric, physics-based, and probabilistic modeling methodology and associated computational tools for interactive simulation: computer programming, numerical methods, graphical modeling and programming, physics-based and probabilistic modeling techniques.

MECH 552 / SELECTED TOPICS IN MECHANICAL ENGINEERING**Sınıf:** **Credit:** 3**Precondition:**

Topics will be announced when offered.

PHYS 509 / CONDENSED MATTER PHYSICS I**Sınıf:** **Credit:** 3**Precondition:** PHYS. 203 or consent of the instructor

Free electron theory of metals. Crystal lattices. Reciprocal lattice. Classification of Bravais lattices. X-ray diffraction and the determination of crystal structures. Electrons in a periodic potential. Tight binding method. Band structures. Semi-classical theory of conduction in metals. Fermi surface. Surface effects.