## Undergraduate Courses

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**DEPARTMENT OF ENGINEERING SCIENCES**

**DESCRIPTION OF UNDERGRADUATE COURSES**

**ES-202 Mathematics for Engineers (3-0)3**

Vector spaces, matrices, systems of linear equations, linear transformations, change of basis, eigenvalue problems, quadratic forms, and diagonalization. Vector calculus, line, surface, and volume integrals. Gradient, divergence, curl. Green, Gauss, and Stokes´ theorems. Complex Numbers.

*Prerequisite: MATH 120.*

**ES-204 Engineering Mathematics (4-0)4**

Introduction to vector spaces and linear algebra. Vector differential calculus. Line, surface, volume integrals, and integral theorems. Algebra of matrices. System equations and Gauss elimination. Linear transformations, change of basis. Characteristic value problems, diagonalization, and quadratic forms. Concept of probability, random variables, some useful distributions, estimation of parameters, confidence intervals and tests of hypothesis, linear regression.

*Prerequisite: MATH 119.*

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**ES-221 Engineering Mechanics I (3-0)3**

Principles of mechanics. Elements of statics in two and three dimensions, centroids, analysis of structures and machines, friction.

Internal force diagrams. Moment of inertia.

*Prerequisite: MATH 119.*

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**ES-223 Statics and Strength of Materials (4-0)4**

Principles of mechanics. Elements of statics in two dimensions. Centroids and moments of inertia. Analysis of simple plane structures. Internal force diagrams. Concepts of stress and strain. Axially loaded members. Torsion. Laterally loaded members.

*Prerequisite: MATH 119.*

**ES-224 Strength of Materials (3-0)3**

State of stress and strain. Idealizations and principles in solving engineering problems. Axially loaded members. Torsion. Laterally loaded members. Thermal stress and strain. Indeterminate problems. Deflections. Failure theories

*Prerequisite: ES 221 or ES 225.*

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**ES-225 Engineering Mechanics (4-0)4**

Application of principles of mechanics. Elements of statics in two and three dimensions, equivalent systems of forces. Equilibrium of rigid bodies, distributed forces, analysis of structures, forces in beams. Friction. Kinematics of particles, kinetics of particles, energy and momentum methods, kinematics of rigid bodies, plane motion of rigid bodies.

*Prerequisite: PHYS 105 and MATH 119.*

**ES-303 Statistical Methods for Engineers (3-0)3**

Descriptive statistics, histograms, central tendency, dispersion, and correlation measures. Basic probability concepts, random variables, probability density, and mass function. Hypothesis testing, confidence intervals. Law of large numbers and central limit theorem. Regression analysis. Applications in engineering.

*Prerequisite: MATH 119.*

**ES-361 Computing Methods in Engineering (3-0)3**

Mathematical modeling of engineering problems, Numerical solution of the nonlinear single variable equation, and system of linear and nonlinear equations. Curve fitting and interpolating polynomials. Numerical differentiation and integration. Numerical solution of ordinary differential equations. Optimization.

*Prerequisite: MATH 119*

**ES-401 Numerical Analysis in Engineering (3-0)3**

Analysis of error in numerical computations. Solution of a linear algebraic system of equations. Eigenvalues. Roots of nonlinear equations. Interpolation and approximations. Numerical differentiation and integration. Difference equations. Solution of a system of ordinary differential equations.

**ES-403 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-404 Advanced Engineering Mathematics (3-0)3**

Mathematical modeling and reduction of engineering problems to ordinary or partial differential systems. Applications of Fourier series, separation of variables, Fourier and Laplace transforms Bessel functions, and Legendre polynomials to basic equations in engineering such as wave, continuity, heat conduction, beam, and Navier equations.

**ES-406 Reliability (3-0)3**

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

**ES-412 Experimental Analysis (2-2)3**

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

**ES-421 Elasticity (3-0)3**

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

**ES-424 Introduction to Continuum Mechanics (3-0)3**

Geometrical foundations. Analysis of stress and deformation. Balance laws. Constitutive equations. Finite and infinitesimal theories of elasticity. Application in fluid mechanics and viscoelasticity.

**ES-425 Intermediate Mechanics (3-0)3**

Vibration and stability of systems with finite degrees of freedom. Rotation of rigid bodies about fixed and moving axes. Gyroscope. Impulsive motion. Nonholonomic systems. Selected problems of pursuit and orbital flight.

**ES-426 Engineering Rheology (3-0)3**

Fundamental concepts of rheology. Classification of material behavior. Linear viscoelasticity, creep, relaxation, and complex modulus. Relaxation and retardation spectra, correspondence principle. Nonlinear viscoelasticity. Elasto-plastic and viscoplastic substances. Engineering application.

**ES-427 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-434 Elastic Stability (3-0)3**

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

**ES-441 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. Panhomechanics.

**ES-442 Advanced Biomechanics (3-0)3**

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

**ES-443 Human Physiology for Engineers (3-0)3**

Engineering anthropometry. Fundamentals of cell and tissue physiology. Gross anatomy and physiology of human skeletal, muscular, nervous, cardiovascular, respiratory, and urinary systems. Energy metabolism and requirements of the human body. Body interactions with the environment. Sleep and body rhythms.

**ES-444 Fundamentals of Tissue Engineering (3-0)3**

Structure and organization of tissues. Mechanics of Tissues. Cell-matrix interactions. Introduction to basic concepts of tissue engineering: Cell source, cellular therapy, scaffold-guided tissue engineering, tissue dynamics, and microenvironment. Design principles of biomimetic environments. Cartilage, skin, and bone tissue engineering. Standards and regulatory considerations of tissue-engineered products.

**ES-450 Human Factors in Engineering Design (3-0)3**

Perceptual, central, and motor processes in man-machine systems. Human capabilities and limitations. Use of anthropometric data. Body mechanics and posture. Man-machine interface design. Physical work capacity. Thermal stress and comfort. Vision and illumination. Noise, vibrations. Fatigue, vigilance, and accidents. Technological skills and training.

**ES-464 Instrumentation for Engineering Measurements (2-2)3**

Measurement systems. Error analysis. Operational amplifiers. Force, pressure, temperature, flow, strain, and other relevant measurements. Microprocessor applications in measurement and control. Manipulation, transmission, and recording of data.

**ES-471 Fluid Mechanics (3-0)3**

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

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**ES-481 Dynamics of Engineering Systems (3-0)3**

Review of rigid body dynamics. Generalized coordinates and forces. Lagrangian and Hamiltonian formulations. Small oscillations. Natural modes. Response of multi-degree-of-freedom systems. Vibration of continuous elastic systems. Introduction to nonlinear vibrations.

**ES-490/498 Special Topics in Engineering Sciences (3-0)3**

These code numbers will be used for technical elective courses which are not listed regularly in the catalog. The course contents will be announced before the semester commences.

**ES-494 Special Topics in ES/Introduction to Bioengineering (3-0)3**

Introduction of the concept of bioengineering. Application of fluid mechanics, mass transfer, bioheat transfer, and control theory to physiological systems and artificial organs. Structure-property relationships of biomedical materials. Problems associated with the selection and function of biomedical materials. Design principles for biomaterials. The basis for the molecular therapeutics and drug delivery systems. Engineering of biomaterial structures and surfaces. Biomechanics of the human musculoskeletal system. Devices for medical imaging.