* ENAS 0500a / APHY 0500a / PHYS 0500a, Science of Modern Technology and Public Policy  Daniel 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
HTBA

* ENAS 0800b and ENAS 1000b / APHY 0800b and APHY 1000b / EPS 0800b / EVST 0080b and EVST 1000b / PHYS 0800b and PHYS 1000b, Energy, Environment, and Public Policy  Daniel 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. Tours are be conducted of major examples of good energy design at Yale, including the Yale Power Plant and Kroon Hall. Students who take this course are not eligible to take APHY 100. Prerequisites: High school chemistry, physics, and Math. Calculus is not required. Enrollment limited to first-year students.  QR, SC
TTh 11:35am-12:50pm

* ENAS 1180a, Introduction to Engineering, Innovation, and Design  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 first-year students.  SC  RP
MW 9:25am-10:15am

* ENAS 1200a / CENG 1200a / ENVE 1200a / EVST 1200a, Introduction to Environmental Engineering  Colby Buehler

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 1610, 1650 or CHEM 1630, 1670 (may be taken concurrently) or permission of instructor.  QR, SC
TTh 1:05pm-2:20pm

ENAS 1300a, Introduction to Computing for Engineers and Scientists  Staff

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 1120 or equivalent. Recommended preparation: previous coding experience.  QR
MW 9am-10:15am

ENAS 1510a / APHY 1510a / PHYS 1510a, Multivariable Calculus for Engineers  Claudia Cea

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 1150 or equivalent.  QR
MW 11:35am-12:50pm

ENAS 1940a / APHY 1940a, Ordinary and Partial Differential Equations with Applications  Beth Anne Bennett

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 1510 or MATH 1200 or equivalent, and knowledge of matrix-based operations.  QR
HTBA

* ENAS 2170a, Disruptive Technologies and Responsible Innovation  Kathryn 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
M 1:30pm-3:25pm

* ENAS 3110a, Product Management Foundations  Staff

Product managers are responsible for defining what problems are worth solving, designing solutions that meet real user needs, and guiding teams through execution, launch, and iteration. They work at the intersection of customer insight, technical feasibility, business constraints, and organizational coordination and shape everything from the success of startups to the strategy of global companies. Understanding product management equips students with a way of thinking that is broadly applicable across business, engineering, design, and leadership roles. This seminar provides a foundation in product management as a craft. Students learn how to move from problem definition to solution design, from launch planning to roadmap construction, and from early signals to long-term decisions. The course emphasizes judgment, tradeoffs, and clear thinking rather than rigid frameworks. Throughout the course, students examine how changes in technology, including the increasing use of automation and intelligent systems, affect how products are built, how quickly plans evolve, and how teams operate. These shifts are treated as part of the modern product environment rather than as a standalone topic. Students work through a full product lifecycle in teams, culminating in a Minimum Viable Product (MVP) and Product Review that mirrors how product decisions are evaluated in professional settings. Learning how to identify meaningful problems, evaluate tradeoffs, and align stakeholders around a coherent plan is a foundational skill for anyone interested in building, scaling, or influencing complex systems in technology-driven organizations.
F 11:30am-1:25pm

* ENAS 3450b / CENG 3450b, Principles and Applications of Interfacial Phenomena  Kyle Vanderlick

This course covers the nature and consequences of both flexible and rigid interfaces, such as those associated with liquids and solids respectively. We examine the properties of interfaces as they exist alone, as a collective (e.g., colloids), and also as they interact demonstrably with one another. An integral part of this course is the introduction and application of engineering analysis to calculate and predict behaviors central to technological applications. This course is designed for engineering majors. Other STEM majors are welcome but physics and multivariable calculus are prerequisites. Ideally, students should also have taken thermodynamics but this is not formally required.  SC
TTh 2:35pm-3:50pm

* ENAS 3600b / ENVE 3600b, Bio-Inspired and Sustainable Design  Julie Zimmerman

Study of green engineering, focusing on key approaches to advancing sustainability through engineering design with an emphasis on biomimicry. 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; and life cycle design, management, and analysis. permission of instructor
MW 1:05pm-2:20pm

ENAS 4040b / MENG 4040b, Applied Numerical Methods for Algebraic Systems, Eigensystems, and Function Approximation  Beth 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 1150, and 2220 or 2250, or equivalents; ENAS 1300 or some experience with Matlab, C++, or Fortran.  QR
MW 2:35pm-3:50pm