Engineering and Applied Science

Director of undergraduate studies: Vincent Wilczynski, 107 BCT, 432-4221, vincent.wilczynski@yale.edu

Courses in Engineering and Applied Science fall into three categories: those intended primarily for students majoring in one of the several engineering and applied science disciplines; those designed for students majoring in subjects other than engineering, the applied sciences, and the natural sciences; and those designed to meet common interests of students majoring in engineering, the applied sciences, or the natural sciences.

In the first category, the departments of Biomedical Engineering, Chemical and Environmental Engineering, Computer Science, Electrical Engineering, and Mechanical Engineering and Materials Science offer courses intended primarily for majors in engineering and applied science disciplines. Courses in these departments may also be relevant for students with appropriate backgrounds who are majoring in chemistry, physics, biology, geology and geophysics, and mathematics. For information about majors in engineering and their related courses, see under Biomedical Engineering, Chemical Engineering, Computer Science, Electrical Engineering, Environmental Engineering, and Mechanical Engineering.

The School of Engineering and Applied Science is responsible for courses in the other two categories: technology for students majoring in subjects other than engineering, the applied sciences, and the natural sciences; and topics common to students majoring in engineering, the applied sciences, and the natural sciences. Courses for non–science majors are intended for all students seeking a broad perspective on issues of scientific and technological import, and they introduce students who may be planning careers in law, business, or public service to concepts and methods of engineering and applied science. Courses for science and engineering majors include topics in applied mathematics and computation.

Programs in Engineering and Applied Science are offered by five different departments, with six subjects of instruction: Biomedical Engineering, Chemical Engineering, Computer Science, Electrical Engineering, Environmental Engineering, and Mechanical Engineering. There are also interdepartmental programs in Electrical Engineering and Computer Science, Computer Science and Mathematics, and Computer Science and Psychology. Currently, fifteen different undergraduate degree options are available. First-year students interested in engineering or computer science are encouraged to attend the meeting scheduled in the fall, listed in the Calendar for the Opening Days, to learn more about the programs.

For all engineering and computer science programs, it is important to plan courses to ensure that necessary prerequisites have been completed in time for more advanced courses. In the first year, students usually take courses in mathematics and physics or, in the case of Chemical, Biomedical, or Environmental Engineering, chemistry. The specific choice of courses depends on preparation and the possible majors that may be contemplated.

All students considering a major in Engineering or Computer Science should contact one or more of the directors of undergraduate studies (DUS) before making decisions about courses in the first year. Contact information can be found on the School of Engineering and Applied Science Website.

In addition to courses for majors, the School of Engineering and Applied Science regularly offers several general engineering and computer science courses that do not presume advanced preparation in mathematics or science. Such courses are intended for students who wish to study science and technology from a broad perspective. See the individual program pages for more information.

Courses without Prerequisites in Engineering

* ENAS 100b / APHY 100b / EVST 100b / G&G 105b / PHYS 100b, Energy Technology and SocietyDaniel Prober, Michael Oristaglio, and Julie Paquette

The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for non–science majors with strong backgrounds in math and science.  QR, SC
MW 1pm-2:15pm

ENAS 110b / APHY 110b, The Technological WorldStaff

An exploration of modern technologies that play a role in everyday life, including the underlying science, current applications, and future prospects. Examples include solar cells, light-emitting diodes (LEDs), computer displays, the global positioning system, fiber-optic communication systems, and the application of technological advances to medicine. For students not committed to a major in science or engineering; no college-level science or mathematics required. Prerequisite: high school physics or chemistry.  QR, SC
TTh 11:35am-12:50pm

* ENAS 118a, Introduction to Engineering, Innovation, and DesignVincent Wilczynski and Lawrence Wilen

An introduction to engineering, innovation, and design process. Principles of material selection, stoichiometry, modeling, data acquisition, sensors, rapid prototyping, and elementary microcontroller programming. Types of engineering and the roles engineers play in a wide range of organizations. Lectures are interspersed with practical exercises. Students work in small teams on an engineering/innovation project at the end of the term. Priority to freshmen.  RP
MW 9:25am-10:15am

* ENAS 120b / CENG 120b / ENVE 120b, Introduction to Environmental EngineeringJordan Peccia

Introduction to engineering principles related to the environment, with emphasis on causes of problems and technologies for abatement. Topics include air and water pollution, global climate change, hazardous chemical and emerging environmental technologies. Prerequisites: high school calculus and chemistry or CHEM 161, 165 or CHEM 163, 167 (may be taken concurrently) or permission of instructor.  QR, SC
TTh 1pm-2:15pm

ENAS 156b / ASTR 156b, Introduction to Digital Dome MediaMichael Faison

The design and production of planetarium shows, art projects, or other immersive or interactive projects with a digital dome projection system, including the ScidomeHD digital system and the stereo projector system, both located at the Leitner Family Observatory and Planetarium (LFOP) and with the portable Starlab dome. Topics include real-time and scripted control of 3D graphics engines; mapping of images and video onto a spherical dome; 3D rendering using Blender, Processing, and vpython; audio and video editing for dome content; interactive projects; and basic design principles for narrative and interactive educational shows. Some programming or digital media experience is recommended.   SC½ Course cr
HTBA

ENAS 335a / EP&E 204a, Professional EthicsMercedes Carreras

A theoretical and case-oriented approach to ethical decision making. Concepts, tools, and methods for constructing and justifying solutions to moral problems that students may face as professionals.  SO
TTh 11:35am-12:50pm

ENAS 360b / ENVE 360b, Green Engineering and Sustainable DesignJulie Zimmerman

Study of green engineering, focusing on key approaches to advancing sustainability through engineering design. Topics include current design, manufacturing, and disposal processes; toxicity and benign alternatives; policy implications; pollution prevention and source reduction; separations and disassembly; material and energy efficiencies and flows; systems analysis; biomimicry; and life cycle design, management, and analysis. Prerequisites: CHEM 161, 165 or 163, 167 (or CHEM 112, 113, or 114, 115), or permission of instructor.
MW 1pm-2:15pm

Applied Mathematics and Computation Courses

ENAS 130b, Introduction to Computing for Engineers and ScientistsBeth Anne Bennett

An introduction to the use of the C and C++ programming languages and the software packages Mathematica and MATLAB to solve a variety of problems encountered in mathematics, the natural sciences, and engineering. General problem-solving techniques, object-oriented programming, elementary numerical methods, data analysis, and graphical display of computational results. Prerequisite: MATH 115 or equivalent. Recommended preparation: previous programming experience.  QR
TTh 2:30pm-3:45pm

ENAS 151a or b / APHY 151a or b / PHYS 151a or b, Multivariable Calculus for EngineersStaff

An introduction to multivariable calculus focusing on applications to engineering problems. Topics include vector-valued functions, vector analysis, partial differentiation, multiple integrals, vector calculus, and the theorems of Green, Stokes, and Gauss. Prerequisite: MATH 115 or equivalent.  QRRP
HTBA

ENAS 194a or b / APHY 194a or b, Ordinary and Partial Differential Equations with ApplicationsStaff

Basic theory of ordinary and partial differential equations useful in applications. First- and second-order equations, separation of variables, power series solutions, Fourier series, Laplace transforms. Prerequisites: ENAS 151 or equivalent, and knowledge of matrix-based operations.  QRRP
HTBA

ENAS 440a / MENG 440a, Applied Numerical Methods for Algebraic Systems, Eigensystems, and Function ApproximationBeth Anne Bennett

The derivation, analysis, and implementation of various numerical methods. Topics include root-finding methods, numerical solution of systems of linear and nonlinear equations, eigenvalue/eigenvector approximation, polynomial-based interpolation, and numerical integration. Additional topics such as computational cost, error analysis, and convergence are studied in several contexts throughout the course. Prerequisites: MATH 115, and 222 or 225, or equivalents; ENAS 130 or some experience with Matlab, C++, or Fortran programming.  QR
TTh 11:35am-12:50pm

* ENAS 450b / APHY 450b / MENG 450b, Advanced Synchrotron Techniques and Electron Spectroscopy of MaterialsCharles Ahn

Introduction to concepts of advanced x-ray and electron-based techniques used for understanding the electronic, structural, and chemical behavior of materials. Students learn from world-leading experts on fundamentals and practical applications of various diffraction, spectroscopy, and microscopy methods. Course highlights the use of synchrotrons in practical experiments. Prerequisites: physics and quantum mechanics/physical chemistry courses for physical science and engineering majors, or by permission of instructor.  QR, SC
Th 1:30pm-3:20pm

ENAS 496b / EENG 434b / MATH 251b / S&DS 351b, Stochastic ProcessesYihong Wu

Introduction to the study of random processes including linear prediction and Kalman filtering, Poison counting process and renewal processes, Markov chains, branching processes, birth-death processes, Markov random fields, martingales, and random walks. Applications chosen from communications, networking, image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, and genetics and evolution. Prerequisite: S&DS 241 or equivalent.  QR
MW 1pm-2:15pm