Students disassemble and analyze retractable pens. Through the process of "reverse engineering," they learn how the ink pens work.

Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi. Then students learn a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they find numbers close to phi. They solve a squares puzzle that creates an approximate Fibonacci spiral. Finally, the instructor demonstrates the rule of the Fibonacci sequence via a LEGO® MINDSTORMS® NXT robot equipped with a pen. The robot (already created as part of the companion activity, The Fibonacci Sequence & Robots) draws a Fibonacci spiral that is similar to the nautilus shape.

Students explore the concept of optical character recognition (OCR) in a problem-solving environment. They research OCR and OCR techniques and then apply those methods to the design challenge by developing algorithms capable of correctly "reading" a number on a typical high school sports scoreboard. Students use the structure of the engineering design process to guide them to develop successful algorithms. In the associated activity, student groups implement, test and revise their algorithms. This software design lesson/activity set is designed to be part of a Java programming class.

Testing is critical to any design, whether the creation of new software or a bridge across a wide river. Despite risking the quality of the design, the testing stage is often hurried in order to get products to market. In this lesson, students focus on the testing phase of the software/systems design process. They start by exploring existing examples of program testing using the CodingBat website, which contains a series of problems and challenges that students solve using the Java programming language. Working in teams, students practice writing test cases for other groups' code, and then write test cases for a program before writing the program itself.

Students practice creating rudimentary detail drawings. They learn how engineers communicate the technical information about their designs using the basic components of detail drawings. They practice creating their own drawings of a three-dimensional block and a special LEGO piece, and then make 3D sketches of an unknown object using only the information provided in its detail drawing.

Students use a compass and a permanent magnet to trace the magnetic field lines produced by the magnet. By positioning the compass in enough spots around the magnet, the overall magnet field will be evident from the collection of arrows representing the direction of the compass needle. In activities 3 and 4 of this unit, students will use this information to design a way to solve the grand challenge of separating metal for a recycling company.

In this lesson plan from NCTM Illuminations students learn to add fractions with like and unlike denominators to make a sum of one. The lesson plan includes two games utilizing fraction cards (PDF) and a fraction bar chart (PDF), and an online game through Calculation Nation which is cataloged separately.

Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. Application to nonlinear circuits and control systems. Alternate years. Description from course website: This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

In earth and space science, students study the origin, structure, and physical phenomena of the earth and the universe. Earth and space science studies include concepts in geology, meteorology, oceanography, and astronomy.

To gain an understanding of mixtures and the concept of separation of mixtures, students use strong magnets to find the element of iron in iron-fortified breakfast cereal flakes. Through this activity, they see how the iron component of this heterogeneous mixture (cereal) retains its properties and can thus be separated by physical means.

In this fictional case study, the state of Oklahoma has profited by giving incentives for companies to build power plants in rural areas of the state. The "scrubbing" systems used to minimize air pollution create potentially hazardous solid waste.To contain this waste, an impoundment facility has been built on unsuitable land from which water-soluble toxins can leach into groundwater. Student teams design a prototype sensor capable of measuring dissolved oxygen and fluorescein dye in water in order to analyze the runoff from the impoundment facility for toxins. The case was developed for an undergraduate laboratory course in photonics for junior- and senior-level students.

This course discusses applications of electromagnetic and equivalent quantum mechanical principles to classical and modern devices. It covers energy conversion and power flow in both macroscopic and quantum-scale electrical and electromechanical systems, including electric motors and generators, electric circuit elements, quantum tunneling structures and instruments. It studies photons as waves and particles and their interaction with matter in optoelectronic devices, including solar cells, displays, and lasers. The instructors would like to thank Scott Bradley, David Friend, Ta-Ming Shih, and Yasuhiro Shirasaki for helping to develop the course, and Kyle Hounsell, Ethan Koether, and Dmitri Megretski for their work preparing the lecture notes for OCW publication.

This text is an introductory treatment on the junior level for a two-semester electrical engineering course starting from the Coulomb-Lorentz force law on a point charge. The theory is extended by the continuous superposition of solutions from previously developed simpler problems leading to the general integral and differential field laws. Often the same problem is solved by different methods so that the advantages and limitations of each approach becomes clear. Sample problems and their solutions are presented for each new concept with great emphasis placed on classical models of physical phenomena such as polarization, conduction, and magnetization. A large variety of related problems that reinforce the text material are included at the end of each chapter for exercise and homework.

Students gain a better understanding of the different types of materials as pure substances and mixtures and learn to distinguish between homogeneous and heterogeneous mixtures by discussing an assortment of example materials they use and encounter in their daily lives.

" This is an advanced course on modeling, design, integration and best practices for use of machine elements such as bearings, springs, gears, cams and mechanisms. Modeling and analysis of these elements is based upon extensive application of physics, mathematics and core mechanical engineering principles (solid mechanics, fluid mechanics, manufacturing, estimation, computer simulation, etc.). These principles are reinforced via (1) hands-on laboratory experiences wherein students conduct experiments and disassemble machines and (2) a substantial design project wherein students model, design, fabricate and characterize a mechanical system that is relevant to a real world application. Students master the materials via problems sets that are directly related to, and coordinated with, the deliverables of their project. Student assessment is based upon mastery of the course materials and the student's ability to synthesize, model and fabricate a mechanical device subject to engineering constraints (e.g. cost and time/schedule)."

The students participate in many demonstrations during the first day of this lesson to learn basic concepts related to the forms and states of energy. This knowledge is then applied the second day as they assess various everyday objects to determine what forms of energy are transformed to accomplish the object's intended task. The students use block diagrams to illustrate the form and state of energy flowing into and out of the process.

Engineering is about extending the horizons of society by solving technical problems, ranging from the meeting of basic human needs for food and shelter to the generation of wealth by trade. This unit looks at the impact of changes in temperature on a variety of objects and looks at the problem of boiling water.

EDICS, or Engineering Design Instructional Computer System, is an interactive multimedia program started in 1981, which consists of three chapters on bearings, rotors and cylinders, lets students with little background in engineering learn about procedures on a computer with text, graphics, animation, sound and diagrams.

Students are introduced to genetic techniques such as DNA electrophoresis and imaging technologies used for molecular and DNA structure visualization. In the field of molecular biology and genetics, biomedical engineering plays an increasing role in the development of new medical treatments and discoveries. Engineering applications of nanotechnology such as lab-on-a-chip and deoxyribonucleic acid (DNA) microarrays are used to study the human genome and decode the complex interactions involved in genetic processes.

Under the "The Science Behind Harry Potter" theme, a succession of diverse complex scientific topics are presented to students through direct immersive interaction. Student interest is piqued by the incorporation of popular culture into the classroom via a series of interactive, hands-on Harry Potter/movie-themed lessons and activities. They learn about the basics of acid/base chemistry (invisible ink), genetics and trait prediction (parseltongue trait in families), and force and projectile motion (motion of the thrown remembrall). In each lesson and activity, students are also made aware of the engineering connections to these fields of scientific study.