A closer look at the complex exponential term in Euler's Formula. We see that it represents a complex number, a distance of 1 from the origin of the complex plane. Created by Willy McAllister.
When we put time in the exponent of a complex exponential, the complex number it represent rotates in a circle on the complex plane. You can think of it as a spinning number! Created by Willy McAllister.
Complex numbers can be represented three ways on the complex plane: cartesian coordinates, radius and angle, and exponential form. Created by Willy McAllister.
Multiplying a real or complex number by the imaginary unit j corresponds to a rotation by +90 degrees. This is the key feature of j that makes it such a useful number. Created by Willy McAllister.
In this video we show you how and where to create the mounting holes in BIt-zee's Lexan base for the arduino, batteries, camera, on/off switch and wire routing. Created by Karl Wendt.
Students will build and test composite materials to determine if they increase strength without significantly increasing weight.
In a multi-week experiment, students monitor the core temperatures of two compost piles, one control and one tended, to see how air and water affect microbial activity. They daily aerate and wet the "treated" pile and collect 4-6 weeks' worth of daily temperature readings. Once the experiment is concluded, students plot and analyze their data to compare the behavior of the two piles. They find that the treated pile becomes hotter, an indication that more microbes are active and releasing heat. Through this activity, students see that microbes play a role in composting and how composting can be used as a carbon management process.
Students explore the concept of biodegradability by building and observing model landfills to test the decomposition of samples of everyday garbage items. They collect and record experiment observations over five days, seeing for themselves what happens to trash when it is thrown "away" in a landfill environment. This shows them the difference between biodegradable and non-biodegradable and serves to introduce them to the idea of composting. Students also learn about the role of engineering in solid waste management.
This course outlines the physics, modeling, application, and technology of compound semiconductors (primarily III-Vs) in electronic, optoelectronic, and photonic devices and integrated circuits. Topics include: properties, preparation, and processing of compound semiconductors; theory and practice of heterojunctions, quantum structures, and pseudomorphic strained layers; metal-semiconductor field effect transistors (MESFETs); heterojunction field effect transistors (HFETs) and bipolar transistors (HBTs); photodiodes, vertical-and in-plane-cavity laser diodes, and other optoelectronic devices.
Engineering thermodynamics is a branch of science that deals with the study of energy conversion and its relationship with heat and work. It's a fundamental discipline in engineering, providing the principles necessary for the analysis and design of various energy systems and processes. In this article, topics such as the systems, state, process, properties of pure substances, heat and work, and thermal equilibrium are meticulously explained to enable easy comprehension. This study guide would enable students to use thermodynamics to optimize the performance and efficiency of engines, power plants, refrigeration systems, and other devices that involve energy transfer. Additionally, understanding this concept of engineering thermodynamics would equip students with the initiative to design a sustainable system that helps mitigate greenhouse gases from fossil fuels.
The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.
2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department’s sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer.
The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. The emphasis will be on physical understanding of the phenomena and basic analytical techniques.
6.844 is a graduate introduction to programming theory, logic of programming, and computability, with the programming language Scheme used to crystallize computability constructions and as an object of study itself. Topics covered include: programming and computability theory based on a term-rewriting, “substitution” model of computation by Scheme programs with side-effects; computation as algebraic manipulation: Scheme evaluation as algebraic manipulation and term rewriting theory; paradoxes from self-application and introduction to formal programming semantics; undecidability of the Halting Problem for Scheme; properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences; logic for program specification and verification; and Hilbert’s Tenth Problem.
This course introduces architecture of digital systems, emphasizing structural principles common to a wide range of technologies. It covers the topics including multilevel implementation strategies, definition of new primitives (e.g., gates, instructions, procedures, processes) and their mechanization using lower-level elements. It also includes analysis of potential concurrency, precedence constraints and performance measures, pipelined and multidimensional systems, instruction set design issues and architectural support for contemporary software structures.
6.004 offers an introduction to the engineering of digital systems. Starting with MOS transistors, the course develops a series of building blocks — logic gates, combinational and sequential circuits, finite-state machines, computers and finally complete systems. Both hardware and software mechanisms are explored through a series of design examples.
6.004 is required material for any EECS undergraduate who wants to understand (and ultimately design) digital systems. A good grasp of the material is essential for later courses in digital design, computer architecture and systems. The problem sets and lab exercises are intended to give students “hands-on” experience in designing digital systems; each student completes a gate-level design for a reduced instruction set computer (RISC) processor during the semester.
This course covers the algorithmic and machine learning foundations of computational biology combining theory with practice. We cover both foundational topics in computational biology, and current research frontiers. We study fundamental techniques, recent advances in the field, and work directly with current large-scale biological datasets.
A computational camera attempts to digitally capture the essence of visual information by exploiting the synergistic combination of task-specific optics, illumination, sensors and processing. In this course we will study this emerging multi-disciplinary field at the intersection of signal processing, applied optics, computer graphics and vision, electronics, art, and online sharing through social networks. If novel cameras can be designed to sample light in radically new ways, then rich and useful forms of visual information may be recorded — beyond those present in traditional photographs. Furthermore, if computational process can be made aware of these novel imaging models, them the scene can be analyzed in higher dimensions and novel aesthetic renderings of the visual information can be synthesized.
We will discuss and play with thermal cameras, multi-spectral cameras, high-speed, and 3D range-sensing cameras and camera arrays. We will learn about opportunities in scientific and medical imaging, mobile-phone based photography, camera for HCI and sensors mimicking animal eyes. We will learn about the complete camera pipeline. In several hands-on projects we will build physical imaging prototypes and understand how each stage of the imaging process can be manipulated.
This course is an introduction to computational theories of human cognition. Drawing on formal models from classic and contemporary artificial intelligence, students will explore fundamental issues in human knowledge representation, inductive learning and reasoning. What are the forms that our knowledge of the world takes? What are the inductive principles that allow us to acquire new knowledge from the interaction of prior knowledge with observed data? What kinds of data must be available to human learners, and what kinds of innate knowledge (if any) must they have?
An introduction to computational theories of human cognition. Emphasizes questions of inductive learning and inference, and the representation of knowledge. Project required for graduate credit. This class is suitable for intermediate to advanced undergraduates or graduate students specializing in cognitive science, artificial intelligence, and related fields.
This class introduces design as a computational enterprise in which rules are developed to compose and describe architectural and other designs. The class covers topics such as shapes, shape arithmetic, symmetry, spatial relations, shape computations, and shape grammars. It focuses on the application of shape grammars in creative design, and teaches shape grammar fundamentals through in-class, hands-on exercises with abstract shape grammars. The class discusses issues related to practical applications of shape grammars.