This course provides a deep understanding of engineering systems at a level intended for research on complex engineering systems. It provides a review and extension of what is known about system architecture and complexity from a theoretical point of view while examining the origins of and recent developments in the field. The class considers how and where the theory has been applied, and uses key analytical methods proposed. Students examine the level of observational (qualitative and quantitative) understanding necessary for successful use of the theoretical framework for a specific engineering system. Case studies apply the theory and principles to engineering systems.

This final lesson in the unit culminates with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they have learned throughout the unit to answer the grand challenge question in a writing assignment.

In this simulation of a doctor's office, students play the roles of physician, nurse, patients, and time-keeper, with the objective to improve the patient waiting time. They collect and graph data as part of their analysis. This serves as a hands-on example of using engineering principles and engineering design approaches (such as models and simulations) to research, analyze, test and improve processes.

This lab demonstrates Ohm's law as students set up simple circuits each composed of a battery, lamp and resistor. Students calculate the current flowing through the circuits they create by solving linear equations. After solving for the current, I, for each set resistance value, students plot the three points on a Cartesian plane and note the line that is formed. They also see the direct correlation between the amount of current flowing through the lamp and its brightness.

Students are introduced to the "Walk the Line" challenge question. They write journal responses to the question and brainstorm what information they need to answer the question. Ideas are shared with the class (or in pairs and then to the class, if class size is large). Then students read an interview with an engineer to gain a professional perspective on linear data sets and best-fit lines. Students brainstorm for additional ideas and add them to the list. With the teacher's guidance, students organize the ideas into logical categories of needed knowledge.

Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph.

A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.

Using a website simulation tool, students build on their understanding of random processes on networks to interact with the graph of a social network of individuals and simulate the spread of a disease. They decide which two individuals on the network are the best to vaccinate in an attempt to minimize the number of people infected and "curb the epidemic." Since the results are random, they run multiple simulations and compute the average number of infected individuals before analyzing the results and assessing the effectiveness of their vaccination strategies.

Motion is vital to life, and to science. This unit will help you to understand why classical motion is probably the most fundamental part of physics. You will examine motion along a line and the ways in which such motion can be represented, through the use of graphs, equations and differential calculus.

Students design and build model landfills using materials similar to those used by engineers for full-scale landfills. Their completed small-size landfills are "rained" on and subjected to other erosion processes. The goal is to create landfills that hold the most garbage, minimize the cost to build and keep trash and contaminated water inside the landfill to prevent it from causing environmental damage. Teams create designs within given budgets, test the landfills' performance, and graph and compare designs for capacity, cost and performance.

Student teams design and create LEGO® structures to house and protect temperature sensors. They leave their structures in undisturbed locations for a week, and regularly check and chart the temperatures. This activity engages students in the design and analysis aspects of engineering.

Students quantify the percent of light reflected from solutions containing varying concentrations of red dye using LEGO© MINDSTORMS© NXT bricks and light sensors. They begin by analyzing a set of standard solutions with known concentrations of food coloring, and plot data to graphically determine the relationship between percent reflected light and dye concentration. Then they identify dye concentrations for two unknown solution samples based on how much light they reflect. Students gain an understanding of light scattering applications and how to determine properties of unknown samples based on a set of standard samples.

Students use two different methods to determine the densities of a variety of materials and objects. The first method involves direct measurement of the volumes of objects that have simple geometric shapes. The second is the water displacement method, used to determine the volumes of irregularly shaped objects. After the densities are determined, students create x-y scatter graphs of mass versus volume, which reveal that objects with densities less than water (floaters) lie above the graph's diagonal (representing the density of water), and those with densities greater than water (sinkers) lie below the diagonal.

Students drop water from different heights to demonstrate the conversion of water's potential energy to kinetic energy. They see how varying the height from which water is dropped affects the splash size. They follow good experiment protocol, take measurements, calculate averages and graph results. In seeing how falling water can be used to do work, they also learn how this energy transformation figures into the engineering design and construction of hydroelectric power plants, dams and reservoirs.

Students learn how to use and graph real-world stream gage data to create event and annual hydrographs and calculate flood frequency statistics. Using an Excel spreadsheet of real-world event, annual and peak streamflow data, they manipulate the data (converting units, sorting, ranking, plotting), solve problems using equations, and calculate return periods and probabilities. Prompted by worksheet questions, they analyze the runoff data as engineers would. Students learn how hydrographs help engineers make decisions and recommendations to community stakeholders concerning water resources and flooding.

Students learn about four forms of equations: direct variation, slope-intercept form, standard form and point-slope form. They graph and complete problem sets for each, converting from one form of equation to another, and learning the benefits and uses of each.

Students use graph theory to create social graphs for their own social networks and apply what learn to create a graph representing the social dynamics found in a dramatic text. Students then derive meaning based on what they know about the text from the graphs they created. Students learn graph theory vocabulary, as well as engineering applications of graph theory.

Students learn about an important characteristic of lines: their slopes. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero or undefined. Students get an explanation of when and how these different types of slope occur. Finally, they learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.

Students analyze their social networks using graph theory. They gather data on their own social relationships, either from Facebook interactions or the interactions they have throughout the course of a day, recording it in Microsoft Excel and using Cytoscape (a free, downloadable application) to generate social network graphs that visually illustrate the key persons (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity, nodes are people in students' social networks). After the analysis, the graphs are further examined to see what can be learned from the visual representation. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory.

Students are introduced to different ways of displaying visual spectra, including colored "barcode" spectra, like those produced by a diffraction grating, and line plots displaying intensity versus color, or wavelength. Students learn that a diffraction grating acts like a prism, bending light into its component colors.