DEPARTMENT OF ENGINEERING SCIENCES

 

GRADUATE COURSES

 

ES-500    M.S. Thesis  NC

ES-501    Analytical Methods in Engineering I  (3-0)3

ES-502    Analytical Methods in Engineering II  (3-0)3

ES-503    Finite Element Method  (3-0)3

ES-504    Numerical Solution of Partial Differential Equations  (3-0)3

ES-505    Variational Methods in Engineering  (3-0)3

ES-506    Reliability  (3-0)3

ES-507    Boundary Element Method  (3-0)3

ES-508    Statistical Methods for Engineering Sciences  (3-0)3

ES-509    Partial Differential Equations in Computer Vision / Image Processing  (3-0)3

ES-510    Numerical Solution of Ordinary Differential Equations  (3-0)3

ES-511    Basic Principles of Mechanics  (3-0)3

ES-512    Experimental Analysis  (3-0)3

ES-514    Mechanical Behavior of Deformable Bodies  (3-0)3

ES-516    Spectral Methods  (3-0)3

ES-521    Theory of Elasticity  (3-0)3

ES-522    Advanced Theory of Elasticity  (3-0)3

ES-523    Advanced Mechanics  (3-0)3

ES-524    Thermal Stress Analysis  (3-0)3

ES-525    Theory of Continuous Media I  (3-0)3

ES-526    Theory of Continuous Media II  (3-0)3

ES-527    Fracture Mechanics  (3-0)3

ES-528    Wave Propagation in Solids  (3-0)3

ES-531    Mechanics of Composite Materials  (3-0)3

ES-532    Theory of Plasticity  (3-0)3

ES-534    Elastic Stability  (3-0)3

ES-536    Energy Methods (3-0)3

ES-538    Soil-Structure Interaction Analysis  (3-0)3

ES-541    Introduction to Biomechanics  (3-0)3

ES-542    Advanced Biomechanics        (3-0)3

ES-545   Principles of Tissue Engineering  (3-0)3

ES-551    Stochastic Methods in Engineering Mechanics I  (3-0)3

ES-552    Stochastic Methods in Engineering Mechanics II  (3-0)3

ES-554    Nonlinear Dynamics  (3-0)3

ES-571    Basic Principles of Fluid Mechanics  (3-0)3

ES-572    Advanced Fluid Mechanics  (3-0)3

ES-591    Seminar  (0-2)  NC

ES-600    Ph.D. Thesis  NC

ES-691    Seminar  (0-2)  NC

ES-7XX   Special Topics in Engineering Sciences  (3-0)3

ES-8XX  Special Studies  (4-2)NC

ES-9XX   Advanced Studies  (4-0)NC

 

DESCRIPTION OF GRADUATE COURSES

 

(Common prerequisite for all following courses: Graduate standing and departmental consent)

 

ES-500       M.S.Thesis                                     NC

Program of research leading to M.S. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their second semester.

 

ES-501    Analytical Methods in Engineering I                           (3-0)3

Ordinary differential equations. Series solutions of ordinary differential equations. Fourier series and Fourier integral. Partial differential  equations. Separation of variables. Gamma,  Bessel, Laguerre functions, Legendre, Chebyshev polynomials.

 

ES-502    Analytical Methods in Engineering II                         (3-0)3

Formulation of basic engineering problems. Sturm-Liouville theory. Fourier series. Complex calculus; Cauchy-Riemann equations, power series, Cauchy’s integral formula, residue theorem, improper integrals. Laplace, Fourier, Hankel, Mellin transforms. Green's function method. Integral equations.  Prerequisite: ES 501.

 

ES-503    Finite Element Method         (3-0)3

Introduction to calculus of variations, weighted residuals method. Properties of finite elements. Ritz and Galerkin methods. Applications in boundary value problems. Two dimensional and time dependent problems.

 

ES-504    Numerical Solution of Partial Differential Equations                                 (3-0)3

Solution  of systems of equations. Initial and boundary-value problems. Parabolic, elliptic and hyperbolic equations. Selected topics from solid and fluid mechanics.

 

ES-505    Variational Methods in Engineering                             (3-0)3

Problems of minimization and maximization. Functionals. Classical problems in calculus of variations, Euler equations, Variational notation, Natural boundary conditions, Hamilton's principle, Lagrange equations. Transformation of boundary value problems into the problem of calculus of variation. Direct methods; Ritz method, Galerkin method, Kantorovich method, Weighted residual method.

 

ES-506    Reliability                                 (3-0)3

Brief review of applied probability. Distributions of sum and quotient of two random variables. Topics in risk-based engineering design. Methods available, advantages and disadvantages. System reliability concepts. Statistical decision theory and  its  application  in  engineering.

 

ES-507    Boundary Element Method            (3-0)3

Gradient and directional derivative of position vector. Numerical evaluation of surface and line integrals, review of the equations of elasto dynamics, acoustics and heat conduction. Formulation of boundary element method: basic integral equation, fundamental solutions. Boundary element equation. Numerical implementation of boundary element method. Codes based on boundary element method. Numerical applications.

 

ES-508    Statistical Methods for Engineers                                  (3-0)3

Advanced statistical techniques in the solutions of real life engineering problems. Analysis of experimental data, Analysis of Variance, k-variable analysis, statistical modeling, regression analysis, experimental design, topics in time series, Bayesian analysis, discriminant analysis and clustering and their application to engineering problems.

 

ES-509    Partial   Differential Equations in Computer  Vision / Image Processing                                (3-0)3

Axiomatic Approach in Computer Vision, Nonlinear Evolution equations, Representation of generic shape, Energy functionals and associated Euler equations, Heat   equation,  multi   resolution,  stochastic connection.

Prerequisite: Engineering Mathematics and working knowledge of a programming tool.

 

ES-510    Numerical Solution  of Ordinary Differential Equations                                 (3-0)3

Numerical solution of initial value problems: multi-step methods and Runge-Kutta methods, stability and convergence. Numerical solution of boundary value problems: shooting methods, finite difference and collocation methods, Green’s function methods, transform methods, introduction to the finite element method.  Nonlinear  boundary  problems.

Prerequisite: ES 305 or equivalent.

 

ES-511    Basic Principles of Mechanics                                (3-0)3

Fundamentals of mechanics. Equivalent force systems. Equations of equilibrium. Internal forces. Introduction to continuum mechanics. Mechanical behavior of Hookean materials. Stress-strain transformations. Strain energy. Introduction  to  viscoelastic  materials.

 

ES-512    Experimental Analysis          (3-0)3

General concepts. Measuring devices. Manipulation, transmission and recording of data.

 

ES-514     Mechanical Behavior of Deformable Bodies                (3-0)3

Materials properties; structure of materials; stress and strain concepts; stress and strain tensors; elastic behavior; three  dimensional analysis; plastic behavior; fracture;  viscoelastic  behavior.

Prerequisite: Consent of the department. 

 

ES-516    Spectral Methods                   (3-0)3

Introduction to the concept of spectral methods. Fourier-collocation spectral methods. Chebyshev-collocation spectral methods. Smoothness and accuracy. Boundary value problems. Polar coordinates. Time stepping. Initial value problems. Introduction to spectral element method.                                               

 

ES-521    Theory of Elasticity               (3-0)3

Stress and strain tensors. Strain-displacement relations. Compatibility equations. Constitutive equations. Plane strain, plane stress. Biharmonic equation, polynomial solutions, Fourier series solutions. Axisymmetric problems. Torsion, bending.

 

ES-522    Advanced Theory of Elasticity           (3-0)3

Indicial notation, Cartesian tensors and field equations of elasticity theory. Integral transform solutions. Complex variable formulation. Nonlinear elasticity.

Prerequisite: ES 521 or equivalent.

 

ES-523    Advanced Mechanics            (3-0)3

Axioms of mechanics. Mechanics of a particle. Mechanics of a system of particles. The virtual work principle. General survey of further variational principles of mechanics. Conservation theorems. Hamilton's equations of motion. Canonical transformations.The Hamilton-Jacobi theory.

ES-524    Thermal Stress Analysis       (3-0)3

Theory of heat conduction in solids and review of basic principles in thermal stress analysis. Various formulations of thermo-elastic problems, uncoupled and coupled theories. Some three-and two-dimensional problems in thermoelasticity. Formulation of thermal stresses in thermo-viscoelastic and thermo-elastoplastic media. Some illustrative examples.

 

ES-525    Theory of Continuous Media I                                      (3-0)3

Review of tensor analysis and integral theorems. Kinematics of deformation, strain tensor, compatibility condition. Material derivative of tensors, deformation rate, spin and vorticity. External and internal loads, Cauchy principle and stress tensor. Balance laws of momenta and energy, entropy principle. Constitutive theory and its axioms, thermomechanical materials. Some illustrative applications.

 

ES-526    Theory of Continuous Media II                                    (3-0)3

Theory of elasticity: General approach, linear constitutive equations, material symmetries, isotropic     materials.     Wave   propagation    in isotropic elastic solids. Thermo-elasticity: General approach, linear constitutive equations, isotropic materials. Thermo-elastic waves. Fluid dynamics: Incompressible and compressible fluids, propagation of shock waves. Viscoelasticity: Mechanical models, linear theories.

Prerequisite: ES 525 or equivalent.

 

ES-527    Fracture Mechanics               (3-0)3

Mechanisms of failure for brittle and ductile materials. Stress concentration. Elastic stress fields around cracks. Plasticity effect. Fracture criteria. Crack propagation and methods of crack arrest. Fatigue. Fracture testing.

 

ES-528    Wave Propagation in Solids                                         (3-0)3

Elements of wave motion. Wave propagation in unbounded elastic media. Plane, cylindrical and spherical waves. Harmonic and transient waves in half-space. Surface waves. Waves in layered media. Waves in rods. Method of characteristics.

 

ES-531    Mechanics of Composite Materials                                  (3-0)3

The nature and scope of composite materials. Fundamental aspects of the theory of  the linear anisotropic elasticity. Prediction of macroscopic mechanical properties of composite materials. Analysis of internal fields in  heterogeneous medium. Wave propagation and dynamic effects in composites. Effective stiffness theory considerations, lattice model representations.

 

ES-532    Theory of  Plasticity              (3-0)3

Physical background. Idealizations, yield criteria. Plastic-stress strain relations. Two measures of work-hardening. Extremum principles, the plastic potential and uniqueness. Elasto-plastic problems. Plane stress and plane strain (theory of slip-line field with some applications). Geometric effects. Plastic anisotropy.

 

ES-534    Elastic Stability                       (3-0)3

Various stability methods. Buckling of beams, columns, beams on elastic foundation. Bifurcation and snap through buckling. Plate and shell buckling. Introduction to dynamic buckling.

 

ES-536    Energy Methods                     (3-0)3

Force Fields. Work. Principles of dynamics. Elements of  calculus of variations, variational principles for discrete systems. Elements of the mechanics of continua. Hellinger, Reissner and Hamilton principles, Castigliano's theorem, theorems of work and reciprocity.Application to elastic rods, structural systems, elastic plates and shells. Stability.

 

ES-538    Soil-Structure Interaction Analysis                                     (3-0)3

Discrete Fourier transform. Soil-structure interaction analysis: direct and substructure methods, free field system, impedance relation, scattering analysis. Artificial boundary conditions: viscous boundary conditions in the absence and presence of free field. Description of seismic environment: types of control points, free displacements and forces in terms of control point motion.

 

ES-541    Introduction to Biomechanics         (3-0)3

Structural and physical properties of bone, muscle, tendon and  cartilage. Mechanics of joint and muscle action. Body equilibrium. Mechanics of the spinal column, of the pelvis and of the hip joint. Pathomechanics.

 

ES-542    Advanced Biomechanics      (3-0)3

The knee joint, foot and ankle, shoulder-arm complex, the elbow joint. Pathomechanics. Gait analysis.

 

ES-545   Principles of Tissue Engineering       (3-0)3

Engineering of Functional Tissues. Scaffold Design and Processing Techniques. Multifunctional Scaffolds. Vascularization Strategies in Tissue Engineering. Clinical Translational Research in Tissue Engineering.

ES-551    Stochastic Methods in Engineering Mechanics I     (3-0)3

Brief review of probability theory. Random processes. Random vibrations of linear single degree of freedom systems. Analysis of random response in the time and frequency domains. Statistical analysis of failure mechanisms.

 

ES-552    Stochastic Methods in Engineering Mechanics II    (3-0)3

Review of the deterministic multi-degree-of-freedom vibratory systems. Random vibration of multi-degree-of-freedom and continuous systems. Markov processes, random walk problems, Fokker-Planck equation. Introduction to random vibration of   nonlinear   systems,   stability  of  systems subjected    to    stochastic    excitations    and introduction    to    chaotic    dynamics.

Prerequisite : ES 551 or equivalent.

 

ES-554    Nonlinear Dynamics              (3-0)3

Fundamentals of nonlinear dynamics and brief review of random vibrations. Periodic and chaotic attractors, stability and bifurcations of equilibria and cycles. Iterated maps as dynamical systems. Criteria for the onset of chaos. Applications and current literature.

 

ES-571    Basic Principles of Fluid Mechanics                                (3-0)3

Fluid statics. Transport mechanisms. Compressible flow. Boundary layer. Introduction to unsteady flows.

 

ES-572    Advanced Fluid Mechanics                 (3-0)3

Development of the governing equations. Grid generation. Inviscid flows. Boundary layer type equations. Parabolized Navier-Stokes equations. Incompressible and compressible Navier-Stokes equations.

Prerequisite: ES 571 or equivalent.

 

ES-591    Seminar                                 (0-2)NC

Students prepare and pesent a progress report or literature review on their thesis topic. The course is normally taken by students in their third semester.

 

ES-600    Ph.D. Thesis                                  NC

Program of research leading to M.S. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their second semester.

 

ES-691    Seminar                                 (0-2)NC

Similar to ES 591 but open to doctoral students only.

 

ES-7XX  Special Topics in Engineering Sciences             (3-0)3

Courses not listed in the catalogue. Contents vary from year to year according to interest of students and instructor in charge. Typical contents include waves in viscoelastic media, mathematical simulation of engineering problems, cell biomechanics.

 

ES-8XX  Special Studies                   (4-2) NC

M.S. Students choose and study a topic under the guidance of a faculty member, normally his/her advisor.

 

ES-9XX  Advanced Studies              (4-0) NC

Graduate students as a group or a Ph.D. student choose and study advanced topics under the guidance of a faculty member, normally his/her advisor.