Overview

Mechanics is a fundamental area of science and engineering. It is an exciting, expanding field of learning with its roots grounded in the laws of motion formulated by Newton and the principles governing the behavior of solids and fluids, branching out in modern times into interdisciplinary fields such as new engineering materials (adhesives, composites, polymers, light metals), biomechanics, transportation, wind engineering, and vehicular structures. Although the problems to which they are applied may change, the basic principles of mechanics remain current and relevant.

Engineering Science and Mechanics has a rich tradition for providing an interdisciplinary engineering education. We strive to prepare our graduates to succeed in advanced graduate or professional study, industry, and government. In these activities, our alumni will:

• Apply fundamentals of engineering mechanics and related areas of applied science to define, model, and solve a wide range of engineering problems.
• Apply fundamental mathematical and scientific principles, as well as computational and experimental techniques, to the demands of engineering and scientific practice.
• Function on and lead teams that engage in new areas of research and development in engineering, particularly those that cross the boundaries of traditional disciplines.
• Maintain high productivity and high ethical standards.
• Continually enhance their knowledge throughout their careers.
• Communicate effectively to a broad range of audiences.

These educational objectives are supported by a curriculum that provides its graduates with:

• an ability to apply fundamental knowledge of mathematics, science, and engineering
• an ability to design and conduct mechanics experiments
• an ability to analyze and interpret experimental and computational mechanics data
• an ability to design a system, component, or process to meet desired needs by synergistically combining mechanics of materials, fluid mechanics, and dynamics, when necessary
• an ability to effectively function as the leader, or member, of a multi-disciplinary team
• an ability to identify, formulate, and solve engineering problems involving mechanics of materials, fluid mechanics, and/or dynamics
• an understanding of professional and ethical responsibility
• an ability to communicate effectively orally, graphically, and in writing
• the broad education necessary to understand the impact of engineering solutions on society and the environment
• a recognition of the need for, and an ability to engage in, life-long learning and accomplishment
• a knowledge of contemporary issues (e.g., social, political, technical, economic, etc.)
• a fundamental understanding that will enable the appropriate use and development of the techniques, skills, and modern engineering tools necessary for engineering practice
• a recognition of the importance of safety in phases of engineering design and practice

A total of 12 credit hours of technical electives and 6 credit hours of senior design give the student freedom to develop individually tailored programs of concentrated study. The department has emphasis areas in Biomechanics, Engineering physics, Fluid mechanics, Motions, or Solid mechanics. Exposure to the design process exists throughout the curriculum, culminating in a senior level capstone design course. The department offers official university degree options in Biomechanics and Engineering Physics.

The Cooperative Education Program is available to qualified candidates at undergraduate and graduate levels.

Undergraduate courses in engineering science and mechanics are taught on a service basis for all engineering curricula. A minor in engineering science & mechanics is available. The department offers graduate programs leading to M.S. (thesis and non-thesis option), M.Eng., and Ph.D. The department also participates in the Accelerated Undergraduate/Graduate Degree Program. Students with an interest in this program should contact the department for additional information.

The Engineering Science and Mechanics program at Virginia Tech is accredited by the Engineering Accreditation Commission of ABET, www.abet.org.

Degree Requirements

The graduation requirements in effect at the time of graduation apply. When choosing the degree requirements information, always choose the year of your expected date of graduation. Requirements for graduation are referred to via university publications as "Checksheets". The number of credit hours required for degree completion varies among curricula. Students must satisfactorily complete all requirements and university obligations for degree completion.

The university reserves the right to modify requirements in a degree program. However, the university will not alter degree requirements less than two years from the expected graduation year unless there is a transition plan for students already in the degree program.

Please visit the University Registrar website at https://registrar.vt.edu/graduation-multi-brief/index1.html for degree requirements.

Undergraduate Course Descriptions (BMES)

2104: INTRODUCTION TO BIOMEDICAL ENGINEERING
Methods of mathematical modeling and engineering analyses related to human physiology. Emphasis placed on fundamental concepts such as biomaterials, biomechanics, tissue engineering, biomedical imagining and nanomedicine. Broad spectrum of current biomedical engineering research areas. Pre: (ENGE 1104 or ENGE 1114 or ENGE 1216), PHYS 2305. Co: MATH 2214. (3H,3C)

2984: SPECIAL STUDY
Variable credit course.

29844: SPECIAL STUDY
Variable credit course.

3024: BME CELL ENGINEERING LABORATORY AND DESIGN
Principles of cell engineering, experiment design, quantitative alyses. Laboratory notebook keeping, report writing and oral presentation in a team setting. Measurement of biological molecules such as DNA, RNA, and proteins. Assessment of animal cell viability, migration, mechanics and interactions with biomaterials. Identification of cell phenotypes. Pre: 2104, ESM 2204. (3H,1L,2C)

3034: BIOINSTRUMENTATION LABORATORY AND DESIGN FOR LIVING SYSTEMS
Principles of biomedical sensors and their usage for experimental design. Collection of biological signals using analog signal amplifiication and filters, biopotentials, digital acquisition, digital filtering and processing. Analysis of physiological signals on living systems with focus on neural, cadiovascular, respiratory, and muscular systems using a group problem solving approach. Instrumental regulation and safety considerations. Pre: 2104. (1H,3L,2C)

3114: PROBLEM DEFINITION IN BIOMEDICAL ENGINEERING DESIGN
Define open-ended biomedical engineering design projects, identify relevant broad social, global, economic, cultural needs, and technical design constraints. Technical skills to address complex biomedical engineering design challenges. Identify and define subjects worthy of future biomedical engineering design projects. Pre: 2104. (3H,3C)

3124: INTRODUCTION TO BIOMECHANICS
Basic principles of biomechanics. Basic musculoskeletal anatomy. Application of classical mechanics to biological systems. Emphasis placed on mechanical behavior (stress and strain), structural behavior, motion, and injury tolerance of the human body. Biomechanics of medical devices and implants. Advances in safety equipment used in automotive, military, and sports applications. Pre: 2104, ESM 2204, ESM 2304. (3H,3C)

3134: INTRODUCTION TO BIOMEDICAL IMAGING
Introduction to major biomedical imaging modalities. Emphasis on X-rays, computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), ultrasound, and optical imaging. Essential physics and imaging equations of the imaging system. Sources of noise and primary artifacts. Patient safety and clinical application. Pre: 2104, (MATH 2204 or MATH 2204H), PHYS 2306. (3H,3C)

3144: BIOMEDICAL DEVICES
Design and uses of biomedical devices for diagnosis and therapy of human and animal diseases. Disease eiologies, progression, risk factors, and epidemiology. Tissue, organ, and systems dysfunction and failure and relevance to life stages (pediatric, adolescent, adult, aged). Useful characteristics of engineered materials for device fabrication, including biocompatibility. Gaps between medical needs and current medical devices. Pre: 2104. (3H,3C)

3184: PROBLEM SOLVING IN BME
Computational and analytical approaches to analyzing biological systems and solving biomedical engineering problems. Problem formulation and exploration of problem-solving techniques to validate computational solutions. Self-directed inquiry and team-based approaches that use reverse engineering, user-in-mind design, and engineering software tools. Pre: 2104. (3H,3C)

4015-4016: BME SENIOR DESIGN AND PROJECT
4015: Apply biomedical engineering principles to the design of an approved project using the team approach. Define problem statements and constraints for biological conditions. Use mathematical modeling tools. Develop conceptual design skills through lectures and exercises involving the design process. Integrate ethical, global and social issues in engineering. 4016: Apply biomedical engineering principles to develop solutions for an approved design project using a team approach. Complete a project resulting in prototype medical device, circuit, or system. Refine design skills through lectures and exercises involving the design process. Integrate ethical, global, environmental and social issues in engineering. Pre: 3114 for 4015; 4015 for 4016. (2H,3L,3C)

4064 (BMVS 4064): INTRODUCTION TO MEDICAL PHYSIOLOGY
An introductory to the principles of medical physiology. Designed primarily for (but not limited to), undergraduate students minoring in biomedical engineering, and other related engineering and physical sciences majors with little or no formal background in biological sciences. Basic principles and concepts of human physiology. Special emphasis on the interactions of human systems biology in their entirety rather than individual genes and pathways. Pre: Junior standing or permission of instructor. (3H,3C)

4134: GLOBAL, SOCIETAL, AND ETHICAL CONSIDERATIONS IN BIOMEDICAL ENGINEERING
Overview of contemporary technological advances to improving human health. Comparison of healthcare systems, problems, and existing solutions throughout the developed and developing world. Consideration of legal and ethical issues associated with developing and implementing new medical technologies. Recognition and definition of gaps between medical needs and current methods and therapies between developed and developing countries. Conceptually design a novel technology. (3H,3C)

4154: COMMERCIALIZATION OF BME RES
Commercialization process applied to translational research. Regulatory aspects of biomedical engineering products and technologies (e.g. devices, diagnostics, drugs, biologics). Intellectual property, technology transfer processes, clinical trial design, commercialization of university research, modeling of development costs (e.g. cash flow and revenue projections). Small business startup approaches. Pre: 2104, 3024. (3H,3C)

4974: INDEPENDENT STUDY
Variable credit course.

4984: SPECIAL STUDY
Variable credit course.

4994: UNDERGRADUATE RESEARCH
Variable credit course.

4994H: UNDERGRADUATE RESEARCH
Variable credit course.

Undergraduate Course Descriptions (ESM)

2014: PROFESSIONAL DEVELOPMENT SEMINAR FOR ESM STUDENTS
Topics designed to foster the professional development of the ESM student. ESM program objectives and outcomes. Overview of solid mechanics, fluid mechanics, and dynamics. Synergistic applications in biotechnology, adhesion science, and other applied areas. (1H,1L,1C)

2074 (AOE 2074): COMPUTATIONAL METHODS
Solving engineering problems using numerical methods and software, truncation and round-off error, root finding, linear and polynomial regression, interpolation, splines, numerical integration, numerical differentiation, solution of linear simultaneous equations. A grade of C- or better required in the prerequisite. Pre: ENGE 1114 or ENGE 1216 or ENGE 1434. (2H,1.5L,2C)

2104: STATICS
Vector mechanics of forces and moments, free-body diagrams, couples, resultants, equilibrium of particles and rigid bodies in two and three dimensions, forces in trusses, frames, and machines, centroids, centers of mass, distributed forces, internal shear forces and bending moments in beams, shear and moment diagrams, friction, belt friction, area of moments of inertia, parallel axis theorem. Course requirements may be satisfied by taking MATH prerequisite prior to or concurrent with course. Corequisites: (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H or MATH 2406H) (3H,3C)

2114: STATICS & STRUCTURES
Vector algebra of forces, movements, couples and resultants. Free-body diagrams. Equilibrium of particles and rigid bodies in two and three dimensions. Friction. Forces in trusses and frames. Centroids, centers of mass, area moments of inertia. Internal axial forces, shear forces, and bending moments in bars in beams. Shear and moment diagrams. Stress and strain in bars in beams. Co: MATH 2204 or MATH 2204H or MATH 2406H. (3H,3C)

2204: MECHANICS OF DEFORMABLE BODIES
Concepts of stress, strain, and deformation. Factor of safety. Stress-strain relationships and material properties. Stress concentrations. Area moments of inertia. Axially loaded members, torsionally loaded members, bending of beams. Shear and moment diagrams. Stresses due to combined loading. Thin-walled pressure vessels. Transformation of stress including Mohr’s circle. Beam deflections and buckling stability. Pre: 2104 or 2114, (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H). (3H,3C)

2214: STATICS AND MECHANICS OF MATERIALS
Forces, moment, resultants, and equilibrium. Stress, strain, and stress-strain relations. Centroids and distributed loads. Analysis of axially loaded bars and beams. Principal stresses and Mohr’s circle, combined loading. Pressure vessels and buckling of columns. Partially duplicates 2104 and 2204. Must be CHE major. Co: MATH 2224. (3H,3C)

2304: DYNAMICS
Vector treatment of the kinematics and kinetics of particles and rigid bodies, Newton’s laws, work and energy, impulse and momentum, impact, mass moments of inertia, rotating axes. Pre: 2104 or 2114, (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H). Co: MATH 2214. (3H,3C)

2974: INDEPENDENT STUDY
Variable credit course.

2984: SPECIAL STUDY
Variable credit course.

2994: UNDERGRADUATE RESEARCH
Variable credit course.

2994H: UNDERGRADUATE RESEARCH
Variable credit course.

3024: INTRODUCTION TO FLUID MECHANICS
Fluid properties and hydrostatics. Derivation and application of the continuity, momentum, and energy equation (Bernoulli’s equation) for ideal and real fluid flow (laminar or turbulent). Dimensional analysis and similitude. Introduction to boundary layers, lift and drag. Pre: 2304, (MATH 2224 or MATH 2204 or MATH 2204H). (2H,2L,3C)

3034: FLUID MECHANICS LABORATORY
Introduction to experimental fluid mechanics. Dimensional analysis. Experiments on fluid properties, flow measurements, and flow visualization, including manometry, determining hydrostatic forces on submerged surfaces, applications of the impulse-momentum principle, velocity measurements, measuring drag forces, quantifying flow in channels. Modern data acquisition techniques. Pre: 2304, ECE 3054. Co: 3234. (3L,1C)

3054 (MSE 3054): MECHANICAL BEHAVIOR OF MATERIALS
Mechanical properties and behavior of solid materials subjected to static, cyclic, and sustained loads resulting from stress states, environments, and stress histories typical of service conditions; multiaxial failure criteria; behavior of cracked bodies; fatigue of materials; creep of materials; microstructure-property relationships; design methodologies. Pre: 2204, (MSE 2034 or MSE 2044 or MSE 3094 or AOE 3094 or CEE 3684). (3H,3C)

3064 (MSE 3064): MECHANICAL BEHAVIOR OF MATERIALS LABORATORY
Laboratory experiments on behavior and mechanical properties of solid materials. Tension, compression, bending, hardness, nano-indentation, and impact tests; behavior of cracked bodies; fatigue and crack growth tests; creep deformation; microstructure-property relationships; laboratory equipment, instrumentation, and computers. Pre: 2204. Co: 3054. (3L,1C)

3114: PROBLEM DEFINITION AND SCOPING IN ENGINEERING DESIGN
Define open-ended engineering design projects, identify relevant broad social, global, economic, cultural and technical needs and constraints, determine ways in which technical skills contribute to addressing complex engineering design challenges. Identify a capstone project for ESM 4015-4016. Pre-requisite: Junior standing in ESM. Pre: 2014. (2L,1C)

3124: DYNAMICS II- ANALYTICAL AND 3-D MOTION
Review of Newton’s Laws, introduction to Lagrange’s equations, rotating coordinate systems, particle dynamics, systems of particles, rigid-body dynamics, small amplitude oscillations, holonomic and nonholonomic constraints, phase space and energy methods. Pre: 2304, MATH 2214, (MATH 2224 or MATH 2204 or MATH 2204H). (3H,3C)

3134: DYNAMICS III - VIBRATION AND CONTROL
Single-degree-of-freedom vibration, n-degree-of-freedom systems, continuous systems, nonlinear systems, system stability, introduction to the feedback control of dynamic systems. Pre: 3124, MATH 4564. (3H,3C)

3154: SOLID MECHANICS
Introduction to tensors, mathematical description of deformations and internal forces in solids, equations of equilibrium, principle of virtual work, linear elastic material behavior, solution for linear elastic problems including axially and spherically symmetric solutions, stress function solutions to plane stress and strain problems, solutions to 3-D problems, energy methods. Pre: 2204, (MATH 2214 or MATH 2214H). Co: MATH 4574. (3H,3C)

3234: FLUID MECHANICS I-CONTROL VOLUME ANALYSIS
Fluid statics. Control volume approach to flow analysis: conservation laws, pipe flows, compressible flow, open channel flow. Pre: 2304, PHYS 2306. (3H,3C)

3334: FLUID MECHANICS II-DIFFERENTIAL ANALYSIS
Introduction to continuum mechanics for fluid systems. Fluid kinematics. Differential approach to flow analysis: conservation equations, exact solutions, potential flows, viscous flows. Pre: 3234 or ME 3404. Co: MATH 4574. (3H,3C)

3444: MECHANICS LABORATORY
Concepts in instrumentation, data acquisition, and signal analysis. Measurements of mechanics quantities and phenomena associated with solid, fluid, and dynamical systems. Open-ended problem definition and approach formulation. Application and synthesis of engineering mechanics fundamentals to the modeling and solution of open-ended problems. Group-working skills and effective written and oral communication. Pre: 3234, 3034, 3054, 3064, 3124, ECE 3054. Co: 3134, 3334, 3154. (1H,3L,2C)

3704: BASIC PRINCIPLES OF STRUCTURES
Static equilibrium of forces and moments, concurrent and nonconcurrent force systems, center of gravity, concentrated and distributed loads. Solution of trusses. Stress and strain, elastic behavior of materials, cables and arches, shear, bending, and deformation in beams, indeterminate structures. Not available to students in engineering. (3H,3C)

4014: APPLIED FLUID MECHANICS
Analysis of flow over practical configurations, panel methods, Reynolds-averaged Navier-Stokes equations, turbulent boundary layers, flow separation and three-dimensional effects. Unsteady flows, fluid-structure interactions. Pre: 2074, 3016. (3H,3C)

4015-4016: CREATIVE DESIGN AND PROJECT I
Design of engineering systems and projects encompassing the principles and practices of engineering science and of the several engineering fields. Investigation and report on a supervised design project. Senior standing required. Instructor consent. Pre: 3114 for 4015; 4015 for 4016. 4015: (2H,3L,3C) 4016: (1H,6L,3C)

4024: ADVANCED MECHANICAL BEHAVIOR OF MATERIALS
Mechanical behavior of materials, emphasizing solid mechanics aspects and methods for predicting strength and life of engineering components. Plasticity, failure criteria, fracture mechanics, crack growth, strain-based fatigue, and creep. Microstructure-property relationships, and laboratory demonstrations. Pre: 3054 or MSE 3054. (3H,3C)

4044: MECHANICS OF COMPOSITE MATERIALS
Introduction to the deformation, stress, and strength analysis of continuous-fiber-polymer-matrix laminated composites. Fabrication, micromechanics of stiffness and expansional coefficients, classical lamination theory (CLT). Environmentally induced stresses. Computerized implementation and design. Pre: 2204. (3H,3C)

4084 (AOE 4084): ENGINEERING DESIGN OPTIMIZATION
Use of mathematical programming methods for engineering design optimization including linear programming, penalty function methods, and gradient projection methods. Applications to minimum weight design, open-loop optimum control, machine design, and appropriate design problems from other engineering disciplines. Pre: (MATH 2224 or MATH 2204 or MATH 2204H). (3H,3C)

4105-4106: ENGINEERING ANALYSIS OF PHYSIOLOGIC SYSTEMS
Engineering analysis of human physiology. Physiologic systems are treated as engineering systems with emphasis input-output considerations, system interrelationships and engineering analogs. 4105 - Mass and electrolyte transfer, nerves, muscles, renal system. 4106 - cardiovascular mechanics, respiratory system, digestive systems, senses. Pre: 2304, MATH 2214. (3H,3C)

4114: NONLINEAR DYNAMICS AND CHAOS
Motion of systems governed by differential equations: stability, geometry, phase planes, bifurcations, Poincare’ sections, point attractors, limit cycles, chaos and strange attractors, Lyapunov exponents. Forced, nonlinear oscillations: jump phenomena, harmonic resonances, Hopf bifurcations, averaging and multiple-scales analysis. Systems governed by discrete maps: return maps, cobweb plots, period-multiplying bifurcations, intermittency, delay coordinates, fractal dimensions. Pre: (2304 or PHYS 2504), (MATH 2214 or MATH 2214H). (3H,3C)

4154: NONDESTRUCTIVE EVALUATION OF MATERIALS
Concepts and methods of nondestructive evaluation of materials. Discussion of techniques and mathematical bases for methods involving mechanical, optical, thermal, and electromagnetic phenomena; design for inspectability; technique selection criteria; information processing and handling; materials response measurement and modeling; signal analysis. Pre: 3054, (PHYS 2206 or PHYS 2306). (3H,3C)

4194 (ME 4194): SUSTAINABLE ENERGY SOLUTIONS FOR A GLOBAL SOCIETY
Addresses energy metrics, global and US energy supply and demand, transitional energy sources (natural gas, petroleum, coal, nuclear), sustainable/renewable source (solar, geothermal, hydro, tidal, wind, biofuels), and methods for increasing efficiencies (energy storage, batteries, green building, conservation). Options for transportation, electricity, lighting and heating needs of industry, agriculture, community, and citizens. Production, transmission, storage, and disposal issues considered in the context of global political, economic, and environmental impacts. Senior Standing in major may be substituted for pre-requisite ENGL 3764. Pre: (CHEM 1035 or CHEM 1055), PHYS 2306, ENGL 3764. (3H,3C)

4204: MUSCULOSKELETAL BIOMECHANICS
Skeletal anatomy and mechanics. Muscle anatomy and mechanics. Theory and application of electromyography. Motion and force measuring equipment and techniques. Inverse dynamics modeling of the human body. Current topics in musculoskeletal biomechanics research. Pre: CS 1044 or CS 1064 or CS 1114 or AOE 2074 or ESM 2074 or ESM 2304. (3H,3C)

4224: BIODYNAMICS AND CONTROL
Study of human movement dynamics and neuromuscular control of multi-degree-of-freedom systems. Computational simulation of forward-dynamics and state-space linear control of human movement to investigate functional performance and neuromuscular pathology. Pre: 2304. (3H,3C)

4234: MECHANICS OF BIOLOGICAL MATERIALS AND STRUCTURES
Anatomy and physiology of connective tissue. Techniques for determining the mechanical response of biological soft and hard tissues. Includes static, viscoelastic, creep, fatigue, and fracture. Simplified models of biological structures. Creation of geometric models from medical imaging and computational modeling. Specific topics may include bone, cartilage, ligaments, tendon, teeth, and skin. Pre: 3054, (2074 or ME 2004). (3H,3C)

4245,4246: MECHANICS OF ANIMAL LOCOMOTION
4245: Mechanical and biological principles of terrestrial animal locomotion, including walking, running, jumping, climbing, burrowing, and crawling. Terrestrial locomotion- based bio-inspired design. 4246: Mechanical and biological principles of animal locomotion in fluids, including active and gliding flight, swimming, jetting, and running on water. Engineering design inspired by fluid based biological locomotion. Pre: 3054 for 4245; 3015 for 4246. (3H,3C)

4304: HEMODYNAMICS
Study of the human cardiovascular system and blood flow. Anatomy and physiology of the human heart, vascular system, and its organization. Blood physiology and rheology. Non-Newtonian blood flow models. Steady and pulsatile blood flow in rigid and elastic arteries. Pressure waves in elastic arteries. Three-dimensional blood flow in the aortic arch and flow around heart valves. Pre: 3334 or ME 3404. (3H,3C)

4404: FUNDAMENTALS OF PROFESSIONAL ENGINEERING
A refresher of basic principles and problem solving techniques involving twelve subject areas most common to all engineering curricula. The topics include those tested by the National Council of Engineering Examiners on the EIT (Engineer in Training) examination, the first requirement, in all fifty states, toward P.E. (Professional Engineer) licensing. Duplicates material of other engineering courses and impracticable for non-engineers, hence not usable for credit toward any degree. Pre: Junior and senior standing in Engineering or in Building Construction or Graduate students in Engineering. Pass/Fail only. (2H,2C)

4444 (AOE 4054): STABILITY OF STRUCTURES
Introduction to the methods of static structural stability analysis and their applications. Buckling of columns and frames. Energy method and approximate solutions. Elastic and inelastic behavior. Torsional and lateral buckling. Use of stability as a structural design criterion. Pre: AOE 3024 or CEE 3404. (3H,3C)

4614: PROBABILITY-BASED MODELING, ANALYSIS, AND ASSESSMENT
Uncertainty analysis of engineering data, parameters estimation, probability concepts, random variables, functions of random variables, probability-based performance functions and failure modes, risk and reliability functions, probability of failure and safety index, random sequences and stochastic processes, correlation functions and spectral densities, return period and extreme values, failure rates, performance monitoring and service life prediction. Pre: 2204. (3H,3C)

4734 (AOE 4024): AN INTRODUCTION TO THE FINITE ELEMENT METHOD
The finite element method is introduced as a numerical method of solving the ordinary and partial differential equations arising in fluid flow, heat transfer, and solid and structural mechanics. The classes of problems considered include those described by the second-order and fourth-order ordinary differential equations and second-order partial differential equations. Both theory and applications of the method to problems in various fields of engineering and applied sciences will be studied. Pre: (CS 3414 or MATH 3414 or AOE 2074) or ESM 2074, (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H). (3H,3C)

4904: PROJECT AND REPORT
Variable credit course. X-grade allowed.

4974: INDEPENDENT STUDY
Variable credit course.

4974H: INDEPENDENT STUDY
Variable credit course.

4984: SPECIAL STUDY
Variable credit course.

4994: UNDERGRADUATE RESEARCH
Variable credit course.

4994H: UNDERGRADUATE RESEARCH
Honors Variable credit course.