Students explore Mars and Jupiter, the fourth and fifth planets from the Sun. They learn some of the unique characteristics of these planets. They also learn how engineers help us learn about these planets with the design and development of telescopes, deep space antennas, spacecraft and planetary rovers.

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.

Students learn about the separation techniques of sedimentation and centrifugation and investigate whether blood is a homogeneous or a heterogeneous mixture. Working in groups as if they are biomedical researchers, they employ the scientific method and make observations about the known characteristics of urine, milk and blood. They probe further by analyzing research on the properties and fractionation modes of blood. As students learn about certain strange characteristics with the fractionation behavior of blood, they formulate hypotheses on the unique nature of blood. Using provided materials —olive oil, tomato juice and petroleum jelly—they design an experiment and construct a blood model. They test their hypotheses by conducting experiments on the blood model, and then propose theories for the nature of blood as a mixture—arriving at the theory of mixture dualism in blood—that blood is a complex mixture system. An activity-guiding handout and PowerPoint® presentation are provided for this student-directed, project-based activity.

Given an assortment of unknown metals to identify, student pairs consider what unique intrinsic (aka intensive) metal properties (such as density, viscosity, boiling or melting point) could be tested. For the provided activity materials (copper, aluminum, zinc, iron or brass), density is the only property that can be measured so groups experimentally determine the density of the "mystery" metal objects. They devise an experimental procedure to measure mass and volume in order to calculate density. They calculate average density of all the pieces (also via the graphing method if computer tools area available). Then students analyze their own data compared to class data and perform error analysis. Through this inquiry-based activity, students design their own experiments, thus experiencing scientific investigation and experimentation first hand. A provided PowerPoint(TM) file and information sheet helps to introduce the five metals, including information on their history, properties and uses.

This lesson will allow students to explore an important role of environmental engineers: cleaning the environment. Students will learn details about the Exxon Valdez oil spill, which was one of the most publicized and studied environmental tragedies in history. In the accompanying activity, they will try many "engineered" strategies to clean up their own manufactured oil spill and learn the difficulties of dealing with oil released into our waters.

This hands-on experiment will provide students with an understanding of the issues that surround environmental cleanup. Students will create their own oil spill, try different methods for cleaning it up, and then discuss the merits of each method in terms of effectiveness (cleanliness) and cost. They will be asked to put themselves in the place of both an environmental engineer and an oil company owner who are responsible for the clean-up.

This is an art project where oil paints and water is used. Students will have already explored the densities of oil and water.

From drinking fountains at playgrounds, water systems in homes, and working bathrooms at schools to hydraulic bridges and levee systems, fluid mechanics are an essential part of daily life. Fluid mechanics, the study of how forces are applied to fluids, is outlined in this unit as a sequence of two lessons and three corresponding activities. The first lesson provides a basic introduction to Pascal's law, Archimedes' principle and Bernoulli's principle and presents fundamental definitions, equations and problems to solve with students, as well as engineering applications. The second lesson provides a basic introduction to above-ground storage tanks, their pervasive use in the Houston Ship Channel, and different types of storage tank failure in major storms and hurricanes. The unit concludes with students applying what they have learned to determine the stability of individual above-ground storage tanks given specific storm conditions so they can analyze their stability in changing storm conditions, followed by a project to design their own storage tanks to address the issues of uplift, displacement and buckling in storm conditions.

Students learn about population density within environments and ecosystems. They determine the density of a population and think about why population density and distribution information is useful to engineers for city planning and design as well as for resource allocation.

Students are presented with a challenge question that they must answer with scientific and mathematical reasoning. The challenge question is: "You have a large rock on a boat that is floating in a pond. You throw the rock overboard and it sinks to the bottom of the pond. Does the water level in the pond rise, drop or remain the same?" Students observe Archimedes' principle in action in this model recreation of the challenge question when a toy boat is placed in a container of water and a rock is placed on the floating boat. Students use terminology learned in the classroom as well as critical thinking skills to derive equations needed to answer this question.

Students build a saltwater circuit, which is an electrical circuit that uses saltwater as part of the circuit. Students investigate the conductivity of saltwater, and develop an understanding of how the amount of salt in a solution impacts how much electrical current flows through the circuit. They learn about one real-world application of a saltwater circuit — as a desalination plant tool to test for the removal of salt from ocean water.

This course is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. Upon successful completion of this course, students will be able to: Define and describe the indefinite integral; Compute elementary definite and indefinite integrals; Explain the relationship between the area problem and the indefinite integral; Use the midpoint, trapezoidal, and Simpson's rule to approximate the area under a curve; State the fundamental theorem of calculus; Use change of variables to compute more complicated integrals; Integrate transcendental, logarithmic, hyperbolic, and trigonometric functions; Find the area between two curves; Find the volumes of solids using ideas from geometry; Find the volumes of solids of revolution using disks, washers, and shells; Find the surface area of a solid of revolution; Compute the average value of a function; Use integrals to compute displacement, total distance traveled, moments, centers of mass, and work; Use integration by parts to compute definite integrals; Use trigonometric substitution to compute definite and indefinite integrals; Use the natural logarithm in substitutions to compute integrals; Integrate rational functions using the method of partial fractions; Compute improper integrals of both types; Graph and differentiate parametric equations; Convert between Cartesian and polar coordinates; Graph and differentiate equations in polar coordinates; Write and interpret a parameterization for a curve; Find the length of a curve described in Cartesian coordinates, described in polar coordinates, or described by a parameterization; Compute areas under curves described by polar coordinates; Define convergence and limits in the context of sequences and series; Find the limits of sequences and series; Discuss the convergence of the geometric and binomial series; Show the convergence of positive series using the comparison, integral, limit comparison, ratio, and root tests; Show the divergence of a positive series using the divergence test; Show the convergence of alternating series; Define absolute and conditional convergence; Show the absolute convergence of a series using the comparison, integral, limit comparison, ratio, and root tests; Manipulate power series algebraically; Differentiate and integrate power series; Compute Taylor and MacLaurin series; Recognize a first order differential equation; Recognize an initial value problem; Solve a first order ODE/IVP using separation of variables; Draw a slope field given an ODE; Use Euler's method to approximate solutions to basic ODE; Apply basic solution techniques for linear, first order ODE to problems involving exponential growth and decay, logistic growth, radioactive decay, compound interest, epidemiology, and Newton's Law of Cooling. (Mathematics 102; See also: Chemistry 004, Computer Science 104, Mechanical Engineering 002)

Students review what they know about the 20 major bones in the human body (names, shapes, functions, locations, as learned in the associated lesson) and the concept of density (mass per unit of volume). Then student pairs calculate the densities for different bones from a disarticulated human skeleton model of fabricated bones, making measurements via triple-beam balance (for mass) and water displacement (for volume). All groups share their results with the class in order to collectively determine the densities for every major bone in the body. This activity prepares students for the next activity, "Can It Support You? No Bones about It," during which they act as biomedical engineers and design artificial bones, which requires them to find materials of suitable density to perform as human body implants.

Students will explore with solids and liquids to discover what density is. Students will be involved in small group experiments and a full group experiment. Observing, predicting, exploring and discovering are all included in this lesson.

In this activity, the students will apply the concepts they learned regarding mass, volume and density in the previous activities to design a boat.

For many years, Cambridge, MA, as host to two major research universities, has been the scene of debates as to how best to meet the competing expectations of different stakeholders. Where there has been success, it has frequently been the result, at least in part, of inventive urban design proposals and the design and implementation of new institutional arrangements to accomplish those proposals. Where there has been failure it has often been explained by the inability - or unwillingness - of one stakeholder to accept and accommodate the expectations of another. The two most recent fall Urban Design Studios have examined these issues at a larger scale. In 2001 we looked at the possible patterns for growth and change in Cambridge, UK, as triggered by the plans of Cambridge University. And in 2002 we looked at these same issues along the length of the MIT 'frontier' in Cambridge, MA as they related to the development of MIT and the biotech research industry. In the fall 2003 Urban Design Studio we propose to focus in on an area adjacent to Cambridgeport and the western end of the MIT campus, roughly centered on Fort Washington. Our goal is to discover the ways in which good urban form, an apt mix of activities, and effective institutional mechanisms might all be brought together in ways that respect shared expectations and reconcile competing expectations - perhaps in unexpected and adroit ways.

The design of urban environments. Strategies for change in large areas of cities, to be developed over time, involving different actors. Fitting forms into natural, man-made, historical, and cultural contexts; enabling desirable activity patterns; conceptualizing built form; providing infrastructure and service systems; guiding the sensory character of development. Involves architecture and planning students in joint work; requires individual designs or design and planning guidelines.

Students use modeling clay, a material that is denser than water and thus ordinarily sinks in water, to discover the principle of buoyancy. They begin by designing and building boats out of clay that will float in water, and then refine their designs so that their boats will carry as great a load (metal washers) as possible. Building a clay boat to hold as much weight as possible is an engineering design problem. Next, they compare amount of water displaced by a lump of clay that sinks to the amount of water displaced by the same lump of clay when it is shaped so as to float. Determining the masses of the displaced water allows them to arrive at Archimedes' principle, whereby the mass of the displaced water equals the mass of the floating clay boat.