# Courses Covering Topics Common to Engineering Programs

Below are the frequently offered Engineering & Applied Science (general courses for undergraduate students in any branch of Engineering) courses. For the most up-to-date course offerings and lecturer information, visit Yale University’s Online Course Information site.

## COURSES WITHOUT PREREQUISITES IN ENGINEERING

**ENAS 060b/APHY 060b/PHYS 060b, Energy Technology and Society **

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. Enrollment limited to freshmen. *Preregistration required; see under Freshman Seminar Program.*

**ENAS 110a or b/APHY 110a or b, The Technological World **

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. Enrollment limited to 80.*

**ENAS 120a/CENG 120a/ENVE 120a, Introduction to Environmental Engineering**

*For description see under Environmental Engineering.*

**ENAS 130b, Introduction to Computing for Engineers and Scientists **

An introduction to the use of the Fortran 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 a brief introduction to numerical simulations. *Prerequisite: MATH 115a or b or equivalent.*

**ENAS 151a or b, Multivariable Calculus for Engineers **

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 115a or b or equivalent.*

**ENAS 194a or b, Ordinary and Partial Differential Equations with Applications**

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 151a or b or equivalent, and knowledge of matrixbased operations.*

**ENAS 323a, Creativity and New Product Development **

An overview of the stages of product development in a competitive marketplace, with simulation of the process in class. A hands-on approach to creativity and the development process.

**ENAS 335a, Professional Ethics **

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.

**ENAS 360bG/ENVE 360b, Green Engineering and Sustainable Design**

*For description see under Environmental Engineering.*

**ENAS 371a/ENVE 371a, Introduction to Hydrology and Water Resources**

*For description see under Environmental Engineering.*

**ENAS 443a/ENVE 443aG/F&ES 380aG, Greening Business Operations**

*For description see under Environmental Engineering.*

**ENAS 391a, Dynamics of Evolving Systems**

Use of a computer to investigate the behavior of increasingly complex natural systems; construction of quantitative theories about natural phenomena. Emphasis on systems of biological interest. *After ENAS 194a or b or equivalent.*

**ENAS 397b/EENG 397b, Mathematical Methods in Engineering **

*For description see under Electrical Engineering.*

**ENAS 428bG/EENG 428bG, Sensors and Biosensors **

*For description see under Electrical Engineering.*

**ENAS 440aG/MENG 440a, Applied Numerical Methods I **

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 addressed in a variety of contexts. *Prerequisites: MATH 115a or b, and 222a or b or 225a or b, or equivalents; ENAS 130b or some knowledge of MATLAB, C++, or Fortran programming.*

**ENAS 441bG/MENG 441b, Applied Numerical Methods II **

The derivation, analysis, and implementation of numerical methods for the solution of ordinary and partial differential equations, both linear and nonlinear. Assessment of computational cost and error estimation for each method. Additional topics such as stability analysis explored in selected contexts. *Prerequisites: MATH 115a or b, and 222a or b or 225a or b, or equivalents; ENAS 130b or some knowledge of MATLAB, C++, or Fortran programming; ENAS 194a or b or equivalent.*

**ENAS 452a, MEMS Design **

An introduction to the broad field of microelectromechanical systems (MEMS), using examples and design projects drawn from real-world MEMS applications. Topics include material properties, microfabrication technologies, structural behavior, sensing techniques, actuation schemes, fluid behavior, simple electronic circuits, and feedback systems. *Prerequisites: ENAS 194a or b or equivalent, and knowledge of MATLAB. Recommended preparation: EENG 325b and some familiarity with microfabrication. Open only to seniors majoring in engineering disciplines except with permission of instructor.*

**ENAS 496bG, Probability and Stochastic Processes**

A study of stochastic processes and estimation, including fundamentals of detection and estimation. Vector space representation of random variables, Bayesian and Neyman-Pearson hypothesis testing, Bayesian and nonrandom parameter estimation, minimumvariance unbiased estimators, and the Cramer-Rao bound. Stochastic processes. Linear prediction and Kalman filtering. Poison counting process and renewal processes, Markov chains, branching processes, birth-death processes, and semi-Markov processes. Applications from communications, networking, and stochastic control.