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.
Fall: Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Method of characteristics. Review of Lebesgue integration. Distributions. Fourier transform. Homogeneous distributions. Asymptotic methods. Spring: Sobolev spaces. Fredholm alternative. Variable coefficient elliptic, parabolic and hyperbolic linear partial differential equations. Variational methods. Viscosity solutions of fully nonlinear partial differential equations. The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.
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.
In a multi-week experiment, student teams gather biogas data from the mini-anaerobic digesters that they build to break down different types of food waste with microbes. Using plastic soda bottles for the mini-anaerobic digesters and gas measurement devices, they compare methane gas production from decomposing hot dogs, diced vs. whole. They monitor and measure the gas production, then graph and analyze the collected data. Students learn how anaerobic digestion can be used to biorecycle waste (food, poop or yard waste) into valuable resources (nutrients, biogas, energy).
To reinforce students' understanding of the human digestion process, the functions of several stomach and small intestine fluids are analyzed, and the concept of simulation is introduced through a short, introductory demonstration of how these fluids work. Students learn what simulation means and how it relates to the engineering process, particularly in biomedical engineering. The teacher demo requires vinegar, baking soda, water and aspirin.
The digestive system is amazing: it takes the foods we eat and breaks them into smaller components that our body can use for energy, cell repair and growth. This lesson introduces students to the main parts of the digestive system and how they interact. In addition, students learn about some of the challenges astronauts face when trying to eat in outer space.
Geographic information systems (GIS), once used predominantly by experts in cartography and computer programming, have become pervasive in everyday business and consumer use. This unit explores GIS in general as a technology about which much more can be learned, and it also explores applications of that technology. Students experience GIS technology through the use of Google Earth on the environmental topic of plastics in the ocean in an area known as the Great Pacific Garbage Patch. The use of this topic in GIS makes the unit multidisciplinary, incorporating the physics of ocean currents, the chemistry associated with pollutant degradation and chemical sorption to organic-rich plastics, and ecological impact to aquatic biota.
This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace. Advances in integrated circuit technology have had a major impact on the technical areas to which digital signal processing techniques and hardware are being applied. A thorough understanding of digital signal processing fundamentals and techniques is essential for anyone whose work is concerned with signal processing applications. Digital Signal Processing begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinctions between discrete-time. The course proceeds to cover digital network and nonrecursive (finite impulse response) digital filters. Digital Signal Processing concludes with digital filter design and a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier transform.
Students create model elevator carriages and calibrate them, similar to the work of design and quality control engineers. Students use measurements from rotary encoders to recreate the task of calibrating elevators for a high-rise building. They translate the rotations from an encoder to correspond to the heights of different floors in a hypothetical multi-story building. Students also determine the accuracy of their model elevators in getting passengers to their correct destinations.
Students design and conduct experiments to determine what environmental factors favor decomposition by soil microbes. They use chunks of carrots for the materials to be decomposed, and their experiments are carried out in plastic bags filled with dirt. Every few days students remove the carrots from the dirt and weigh them. Depending on the experimental conditions, after a few weeks most of the carrots will have decomposed completely.
In this activity, students investigate different methods (aeration and filtering) for removing pollutants from water. They will design and build their own water filters.
Students disassemble and analyze retractable pens. Through the process of "reverse engineering," they learn how the ink pens work.
With a simple demonstration activity, students are introduced to the concept of friction as a force that impedes motion when two surfaces are in contact. Then, in the Associated Activity (Sliding and Stuttering), they work in teams to use a spring scale to drag an object such as a ceramic coffee cup along a table top or the floor. The spring scale allows them to measure the frictional force that exists between the moving cup and the surface it slides on. By modifying the bottom surface of the cup, students can find out what kinds of surfaces generate more or less friction. They also discover that both static and kinetic friction are involved when an object initially at rest is caused to slide across a surface.
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.
Representation, analysis, and design of discrete time signals and systems. Review of Z-transforms, discrete-time Fourier transforms, and difference equations. Discrete-time processing of continuous-time signals. Decimation, interpolation, and sampling rate conversion. Flowgraph structures for DT systems. Time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform, FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms, Cepstral analysis, various applications.
Students pass around and distort messages written on index cards to learn how we use signals from GPS occultations to study the atmosphere. The cards represent information sent from GPS satellites being distorted as they pass through different locations in the Earth's atmosphere and reach other satellites. Analyzing GPS occultations enables better global weather forecasting, storm tracking and climate change monitoring.
Students learn about the amazing adaptations of the ptarmigan to the alpine tundra. They focus one adaptation, the feathered feet of the ptarmigan, and ask whether the feathers serve to only keep the feet warm or to also provide the bird with floatation capability. They create model ptarmigan feet, with and without feathers, and test the hypothesis on the function of the feathers. Ultimately, students make a claim about whether the feathers provide floatation and support this claim with their testing evidence.
In this activity, students squeeze a tennis ball to demonstrate the strength of the human heart. Working in teams, they think of ways to keep the heart beating if the natural mechanism were to fail. The goal of this activity is to get students to understand the strength and resilience of the heart.
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.