As its name implies, the 3.042 Materials Project Laboratory involves working with …
As its name implies, the 3.042 Materials Project Laboratory involves working with such operations as investment casting of metals, injection molding of polymers, and sintering of ceramics. After all the abstraction and theory in the lecture part of the DMSE curriculum, many students have found this hands-on experience with materials to be very fun stuff - several have said that 3.042/3.082 was their favorite DMSE subject. The lab is more than operating processing equipment, however. It is intended also to emulate professional practice in materials engineering project management, with aspects of design, analysis, teamwork, literature and patent searching, web creation and oral presentation, and more.
Students investigate the materials properties such as acoustical absorptivity, light reflectivity, thermal …
Students investigate the materials properties such as acoustical absorptivity, light reflectivity, thermal conductivity, hardness, and water resistance of various materials. They use sound, light and temperature sensors to collect data on various materials. They practice making design decisions about what materials would be best to use for specific purposes and projects, such as designing houses in certain environments to meet client requirements. After testing, they use the provided/tested materials to design and build model houses to meet client specifications.
Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical …
Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams. Computation of phase diagrams. Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions. Applications to phase stability and properties of mixtures. Computational modeling. Interfaces.
Scientific computing: Fast Fourier Transform, finite differences, finite elements, spectral method, numerical linear algebra. Complex variables and applications. Initial-value problems: stability or chaos in ordinary differential equations, wave equation versus heat equation, conservation laws and shocks, dissipation and dispersion. Optimization: network flows, linear programming. Includes one computational project.
Topics vary from year to year. Topic for Fall: Eigenvalues of random …
Topics vary from year to year. Topic for Fall: Eigenvalues of random matrices. How many are real? Why are the spacings so important? Subject covers the mathematics and applications in physics, engineering, computation, and computer science. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.
How do populations grow? How do viruses spread? What is the trajectory …
How do populations grow? How do viruses spread? What is the trajectory of a glider?
Many real-life problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a real-life problem.
You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program.
If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way.
This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve real-world problems.
Students apply high school-level differential calculus and physics to the design of …
Students apply high school-level differential calculus and physics to the design of two-dimensional roller coasters in which the friction force is considered, as explained in the associated lesson. In a challenge the mirrors real-world engineering, the designed roller coaster paths must be made from at least five differentiable functions that are put together such that the resulting piecewise curving path is differentiable at all points. Once designed mathematically, teams build and test small-sized prototype models of the exact designs using foam pipe wrap insulation as the roller coaster track channel with marbles as the ride carts.
This course covers elementary discrete mathematics for computer science and engineering. It …
This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Students leach organic matter from soil to create a water sample with …
Students leach organic matter from soil to create a water sample with high dissolved organic matter content (DOM), and then make filters to see if the DOM can be removed. They experience the difficulties of removing DOM from water, and learn about other processes that might make DOM removal more effective.
Students play the role of engineers as they test, design and build …
Students play the role of engineers as they test, design and build Mentos(TM) fountains a dramatic example of how potential energy (stored energy) can be converted to kinetic energy (motion). They are challenged to work together as a class to optimize the design of the basic soda/candy geyser made by the teacher. To do this, three research teams each investigate how a different variable nozzle shape, soda temperature, number of candies affects fountain height. They devise and run experimental tests to determine the best variable values. Then they combine their results to design the highest fountain to compete head-to-head with the teacher's geyser design.
Students learn how to find the maximum power point (MPP) of a …
Students learn how to find the maximum power point (MPP) of a photovoltaic (PV) panel in order to optimize its efficiency at creating solar power. They also learn about real-world applications and technologies that use this technique, as well as Ohm's law and the power equation, which govern a PV panel's ability to produce power.
This lesson explores the drag force on airplanes. The students will be …
This lesson explores the drag force on airplanes. The students will be introduced to the concept of conservation of energy and how it relates to drag. Students will explore the relationship between drag and the shape, speed and size of an object.
Students revisit Bernoulli's Principle (Lesson 1 of the Airplanes unit) and learn …
Students revisit Bernoulli's Principle (Lesson 1 of the Airplanes unit) and learn how engineers use this principle to design airplane wings. Airplane wings create lift by changing the pressure of the air around it. This is the first of four lessons exploring the four key forces in flight: lift, weight, thrust and drag.
In this lesson, students will study how propellers and jet turbines generate …
In this lesson, students will study how propellers and jet turbines generate thrust. This lesson focuses on Isaac Newton's 3rd Law of Motion, which states that for every action there is an equal and opposite reaction.
The purpose of this lesson is to help students understand the relationship …
The purpose of this lesson is to help students understand the relationship between the mass and the weight of an object. Students will study the properties of common materials and why airplanes use specific materials.
This lesson begins with a demonstration of the deflection of an electron …
This lesson begins with a demonstration of the deflection of an electron beam. Students then review their knowledge of the cross product and the right hand rule with sample problems. After which, students study the magnetic force on a charged particle as compared to the electric force. The following lecture material covers the motion of a charged particle in a magnetic field with respect to the direction of the field. Finally, students apply these concepts to understand the magnetic force on a current carrying wire. Its associated activity allows students to further explore the force on a current carrying wire.
As the first engineering design challenge of the unit, students are introduced …
As the first engineering design challenge of the unit, students are introduced to the logic for solving a maze. First they observe a blindfolded student volunteer being guided through a classroom maze by the simple verbal instructions of another student. In this demonstration, the blindfolded student represents a robot and the guiding student represents programming commands. Then student groups apply that logic to program LEGO MINDSTORMS(TM) NXT robots to navigate through a maze, first with no sensors, and then with sensors. A PowerPoint® presentation, pre/post quizzes and a worksheet are provided.
Students experience data collection, analysis and inquiry in this LEGO® MINDSTORMS® NXT …
Students experience data collection, analysis and inquiry in this LEGO® MINDSTORMS® NXT -based activity. They measure the position of an oscillating platform using a ultrasonic sensor and perform statistical analysis to determine the mean, mode, median, percent difference and percent error for the collected data.
Students learn the metric units engineers use to measure mass, distance (or …
Students learn the metric units engineers use to measure mass, distance (or length) and volume. They make estimations using these units and compare their guesses with actual values. To introduce the concepts, the teacher needs access to a meter stick, a one-liter bottle, a glass container that measures milliliters and a gram scale.
Students learn about the statistical analysis of measurements and error propagation, reviewing …
Students learn about the statistical analysis of measurements and error propagation, reviewing concepts of precision, accuracy and error types. This is done through calculations related to the concept of density. Students work in teams to each measure the dimensions and mass of five identical cubes, compile the measurements into small data sets, calculate statistics including the mean and standard deviation of these measurements, and use the mean values of the measurements to calculate density of the cubes. Then they use this calculated density to determine the mass of a new object made of the same material. This is done by measuring the appropriate dimensions of the new object, calculating its volume, and then calculating its mass using the density value. Next, the mass of the new object is measured by each student group and the standard deviation of the measurements is calculated. Finally, students determine the accuracy of the calculated mass by comparing it to the measured mass, determining whether the difference in the measurements is more or less than the standard deviation.
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