**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.

*Prerequisite: MATH 158.*

**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. Characteris tic 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 158.*

**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 158.*

**ES 222 Engineering Mechanics II (2-0)2**

Kinematics of a particle. Dynamics of a particle. Kinematics of a rigid body in plane motion. Dynamics of a rigid body in translation. Dynamics of a rigid body in rotation. Dynamics of a rigid body in plane motion. Impulse and momentum.

*Prerequisite: ES 221.*

**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 156 or MATH *158*.*

**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.*

**ES 301 Numerical Methods in Engineering (3-0)3**

Error analysis. Sources and propagation. Introductory linear algebra: review of systems of linear equations, matrix algebra and introductory vector differential calculus. Interpolation and extrapolation. Roots of polynomials. Data fitting and least squares problems. Numerical differentiation and integration. Numerical solution of ordinary differential equations.

*Prerequisites: MATH 158 and CENG 200.*

**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 centr al limit theorem. Regression analysis. Applications in engineering.

*Prerequisite: MATH 158.*

**ES 305 Computing Methods in Engineering (3-0)3**

Numerical solution of linear and nonlinear systems of equations. Interpolating polynomials. Numerical differentiation and integration. Numerical solution of ordinary differential equations.

*Prerequisites: ES 202 and CENG 200 or CENG 210.*

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

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

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

**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, Legendre polynomials to basic equati ons in engineering such as wave, continuity, heat conduction, beam and Navier equations.

*Prerequisite: Consent of the department.*

**ES 406 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, disadvantages. System reliability concepts. Statistical decision theory and its application in engineering.

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

**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. Applications in fluid mechanics and viscoelasticity.

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

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

Fundamental concepts of rheology. A 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.

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

**ES 434 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.

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

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

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

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

**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.

*Prerequisite: Consent of the department.*

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

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

*Prerequisite: Consent of the department.*

**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 non linear vibrations.

*Prerequisite: Consent of the department.*

**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.