In this video segment from Nature, learn about six different breeds of cattle.

In this segment from Curious, learn about creating energy from solar rays to meet the growing energy needs of the world.

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

These lesson ideas can be used to teach the key Digital Technology concepts.

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 learn about biomimicry and the engineering design process as they design and build model ptarmigan feet.

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.

This Doctoral Seminar in Engineering Systems examines the core theory and contextual applications of the emerging field of Engineering Systems. There is a focus on doctoral-level analysis of scholarship on key concepts such as complexity, uncertainty, fragility, and robustness, as well as a critical look at the historical roots of the field and related areas such as systems engineering, systems dynamics, agent modeling, and systems simulations. Contextual applications of the course range from aerospace to technology implementation to regulatory systems to large-scale systems change. Special attention is given to the interdependence of social and technical dimensions of engineering systems.

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.

In this interactive activity from the Building Big Web site, think like an engineer and use your knowledge of dome design to match the right type of dome to the right location in a fictitious city.

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.

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.

Ecologies of Construction examines the resource requirements for the making and maintenance of the contemporary built environment. This course introduces the field of industrial ecology as a primary source of concepts and methods in the mapping of material and energy expenditures dedicated to construction activities.

Choice of material has implications throughout the life-cycle of a product, influencing many aspects of economic and environmental performance. This course will provide a survey of methods for evaluating those implications. Lectures will cover topics in material choice concepts, fundamentals of engineering economics, manufacturing economics modeling methods, and life-cycle environmental evaluation.

This site, created by the Massachusetts Institute of Technology, introduces the electrical engineering and computer science department. Graduates of MIT's electrical engineering and computer science department work in diverse industries and conduct research in a broad range of areas. The site features lecture notes, assignments, solutions, online textbooks, projects, examples and exams.

This course introduces principles and mathematical models of electrochemical energy conversion and storage. Students study equivalent circuits, thermodynamics, reaction kinetics, transport phenomena, electrostatics, porous media, and phase transformations. In addition, this course includes applications to batteries, fuel cells, supercapacitors, and electrokinetics.