Engineering & Applied Science (ENAS)

* ENAS 050a or b / APHY 050a or b / PHYS 050a or b, Science of Modern Technology and Public PolicyDaniel Prober

Examination of the science behind selected advances in modern technology and implications for public policy, with focus on the scientific and contextual basis of each advance. Topics are developed by the participants with the instructor and with guest lecturers, and may include nanotechnology, quantum computation and cryptography, renewable energy technologies, optical systems for communication and medical diagnostics, transistors, satellite imaging and global positioning systems, large-scale immunization, and DNA made to order. Enrollment limited to first-year students.   SC

* ENAS 100b / APHY 100b / EPS 105b / EVST 100b / PHYS 100b, Energy, Environment, and Public PolicyDaniel Prober

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, SCRP
MW 2:30pm-3:45pm

* ENAS 118a, Introduction to Engineering, Innovation, and DesignLawrence 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 first-year students.  RP
MW 9:25am-10:15am

* ENAS 120b / CENG 120b / ENVE 120b, Introduction to Environmental EngineeringJohn Fortner

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 11:35am-12:50pm

ENAS 130a or b, 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

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.  QR

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 MATH 120 or equivalent, and knowledge of matrix-based operations.  QR

ENAS 217a, Disruptive Technologies and Responsible InnovationKathryn Guarini

This course gives students insights into disruptive technologies and the mechanisms of driving responsible innovation. It helps demystify current-day innovations that are having a profound impact on the world – how they work and how they came to be. And it helps them understand how concepts take shape and get driven into the market. What makes an idea great? How do leaders develop robust solutions, mitigate risks, and extract value? This class covers concepts and frameworks and explores case studies of various disruptive technologies, establishing the technical underpinnings and discussing their societal implications. This course is appropriate for any students interested in exploring timely technology-related themes shaping society and the world. There are no prerequisites.  SC
MW 1pm-2:15pm

ENAS 289a / APHY 289a / PHYS 289a, Modern Technology: Electrons, Photons, and BitsOwen Miller

Modern technology is, to overly simplify, a consequence of our mastery over electrons, photons, and bits. This course aims to understand a wide swath of technologies, and the physical and mathematical principles of the electrons, photons, and bits underpinning them. Topics covered may include electric power generation, wireless communication, computing and storage devices (CPUs, GPUs, HDDs, SSDs), optical fibers and lithography, displays (including for AR/VR), and renewable-energy technologies. The physical principles underlying these technologies will be accompanied by unifying mathematical principles, including basic ideas in linear systems, Fourier analysis, differential equations, and information theory. The prerequisites for this course are multivariable calculus (e.g. APHY 151, ENAS 151, or PHYS 151) and electricity and magnetism at the level of PHYS 171, PHYS 181, PHYS 201, PHYS 261, or beyond. An excellent AP Physics C course would likely be sufficient E&M preparation.  SC
TTh 2:30pm-3:45pm

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

* ENAS 403a, Funding It: Innovation, Entrepreneurship, and Venture CapitalJorge Torres

A survey of the origins, practice, and business models of venture capital with application to engineering science. Consideration of three major areas: the history and purpose of venture capital; the practical details of venture investing; and advanced topics on business models, technology ecosystems, and ethics. Particular exposure to principles of entrepreneurship, including intellectual property strategy, market validation, customer discovery, positioning, and capital formation.    Separate application required at:  RP
Th 1:30pm-3:20pm

* ENAS 415a / BENG 415a, Practical Applications of Bioimaging and BiosensingDaniel Coman, Ansel Hillmer, and Evelyn Lake

Detecting, measuring, and quantifying the structural and functional properties of tissue is of critical importance in both biomedical research and medicine. This course focuses on the practicalities of generating quantitative results from raw bioimaging and biosensing data to complement other courses focus on the theoretical foundations which enable the collection of these data. Participants in the course work with real, cutting-edge data collected here at Yale. They become familiar with an array of current software tools, denoising and processing techniques, and quantitative analysis methods that are used in the pursuit of extracting meaningful information from imaging data. The subject matter of this course ranges from bioenergetics, metabolic pathways, molecular processes, brain receptor kinetics, protein expression and interactions to wide spread functional networks, long-range connectivity, and organ-level brain organization. The course provides a unique hands-on experience with processing and analyzing in vitro and in vivo bioimaging and biosensing data that is relevant to current research topics. The specific imaging modes which are covered include in vivo magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI), functional, structural, and molecular imaging (MRI), wide-field fluorescent optical imaging, and positron emission tomography (PET). The course provides the necessary background in biochemistry, bioenergetics, and biophysics for students to motivate the image manipulations which they learn to perform. Prerequisites: Math through first order differential equations, PHYS 180/181, CHEM 161, BIOL 101/102, BENG 249 or other experience with scientific software like MATLAB®, BENG 350 and BENG 410 (both of which can be taken at the same time as this course)  SC0 Course cr
F 1pm-2:15pm

ENAS 440b / MENG 440b, 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
MW 2:30pm-3:45pm

* ENAS 450a / APHY 450a / MENG 450a, 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 3:30pm-5:20pm

ENAS 475a / MENG 475a, Fluid Mechanics of Natural PhenomenaAmir Pahlavan

This course draws inspiration from nature and focuses on utilizing the fundamental concepts of fluid mechanics and soft matter physics to explain these phenomena. We study a broad range of problems related to i) nutrient transport in plants, slime molds, and fungi and the adaptation of their networks in dynamic environments, ii) collective behavior and chemotaxis of swimming microorganisms, and iii) pattern formation in nature, e.g. icicles, mud cracks, salt polygons, dendritic crystals, and Turing patterns. We also discuss how our understanding of these problems could be used to develop sustainable solutions for the society, e.g. designing synthetic trees to convert CO2 to oxygen, developing micro/nano robots for biomedical applications, and utilizing pattern formation and self-assembly to make new materials. Prerequisite: MENG 361.
MW 11:35am-12:50pm