Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: Numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed.

Deze cursus bestaat uit lesmodules te gebruiken in de bovenbouw van het Havo en het VWO met als onderwerp Optimaliseren in netwerken. Het materiaal is gemaakt door een kerngroep van vwo-docenten, aangevuld met universitaire medewerkers. Docenten kunnen er invulling mee geven aan het domein "Wiskunde in wetenschap" van het vak wiskunde D.

Using their knowledge of the phases of matter, the scientific method, and polymers, student teams work as if they are chemical engineers to optimize the formula for slime. Hired by the fictional company, Slime Productions, students are challenged to modify the chemical composition of the basic formula for slime to maximize its "bounce factor."

In this project, students are required to design a soda can using different shapes and materials. The students will begin with conducting research on the most cost efficient and marketing effective material and shape. They will then build an accurate representation of their model, and present their idea to the class and use evidence to reason why they think this is the best.

In this project, students will be designing their own soda can by using optimization skills to calculate costs. The will also have to do research to market the item to decide which shape and material is the most cost effective and markets the best.

Students work in engineering teams to optimize cleaner energy solutions for cooking and heating in rural China. They choose between various options for heating, cooking, hot water, and lights and other electricity, balancing between the cost and health effects of different energy choices.

Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.

Students learn about how a device made with dye from a plant, specifically cherries, blackberries, raspberries and/or black currents, can be used to convert light energy into electrical energy. They do this by building their own organic solar cells and measuring the photovoltaic devices' performance based on power output.

This class builds a bridge between the recreational world of algorithmic puzzles (puzzles that can be solved by algorithms) and the pragmatic world of computer programming, teaching students to program while solving puzzles. Python syntax and semantics required to understand the code are explained as needed for each puzzle.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Formalin-fixed, paraffin-embedded (FFPE) tissue is the gold standard for pathology tissue storage, making FFPE tissue libraries rich repositories for identifying and analyzing the bacterial microbiomes that stretch across the human body. Unfortunately, various facets of the FFPE process can compromise the integrity of tissue for this type of analysis. including DNA damage, susceptibility to contamination, and the lack of suitable DNA extraction methods. A new study proposes a system called Protoblock for standardizing and optimizing FFPE tissue-based research. A Protoblock is generated by embedding a known number of fixed cells in a molded agar matrix. After the agar solidifies, the block is processed following routine FFPE protocols and verified by microscopy. Experiments confirmed the quality and condition of DNA purified from Protoblocks, revealing important calibration information, such as how DNA damage evolves over fixation time. and how host DNA and sample prep method might bias bacterial analysis..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

In the past building prototypes of electronic components for new projects/products was limited to using protoboards and wirewrap. Manufacturing a printed-circuit-board was limited to final production, where mistakes in the implementation meant physically cutting traces on the board and adding wire jumpers - the final products would have these fixes on them! Today that is no longer the case, while you will still cut traces and use jumpers when debugging a board, manufacturing a new final version without the errors is a simple and relatively inexpensive task. For that matter, manufacturing a prototype printed circuit board which you know is likely to have errors but which will get the design substantially closer to the final product than a protoboard setup is not only possible, but desirable. In this class, you’ll learn to design, build, and debug printed-circuit-boards.

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

Students investigate the endothermic reaction involving citric acid, sodium bicarbonate and water to produce carbon dioxide, water and sodium citrate. In the presence of water [H2O], citric acid [C6H8O7] and sodium bicarbonate [NaHCO3] (also known as baking soda) react to form sodium citrate [Na3C6H5O7], water [H2O], and carbon dioxide [CO2]. Students test a stoichiometric version of the reaction followed by testing various perturbations on the stoichiometric version in which each reactant (citric acid, sodium bicarbonate, and water) is strategically doubled or halved to create a matrix of the effect on the reaction. By analyzing the test matrix data, they determine the optimum quantities to use in their own production companies to minimize material cost and maximize CO2 production. They use their test data to "scale-up" the system from a quart-sized ziplock bag to a reaction tank equal to the volume of their classroom. They collect data on reaction temperature and CO2 production.

Students learn about five types of renewable energy that are part of engineering solutions to help people in rural communities use less and cleaner energy for cooking and heating. Specifically, students learn about the pollution and health challenges facing families in rural China, and they are introduced to the concept of optimization. Through an energy game, students differentiate between renewable and non-renewable sources of energy.

Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.

This course covers principles and methods for technical System Architecture. It presents a synthetic view including: the resolution of ambiguity to identify system goals and boundaries; the creative process of mapping form to function; and the analysis of complexity and methods of decomposition and re-integration. Industrial speakers and faculty present examples from various industries. Heuristic and formal methods are presented. Restricted to SDM (System Design and Management) students.

This course studies what makes a good design and how one develops a good design. Students consider how the design of engineered systems (such as hardware, software, materials, and manufacturing systems) differ from the “design” of natural systems such as biological systems; discuss complexity and how one makes use of complexity theory to improve design; and discover how one uses axiomatic design theory (AD theory) in design of many different kinds of engineered systems. Questions are analyzed using Axiomatic Design Theory and Complexity Theory. Case studies are presented including the design of machines, tribological systems, materials, manufacturing systems, and recent inventions. Implications of AD and complexity theories on biological systems discussed.

One objective of 15.066J is to introduce modeling, optimization and simulation, as it applies to the study and analysis of manufacturing systems for decision support. The introduction of optimization models and algorithms provide a framework to think about a wide range of issues that arise in manufacturing systems. The second objective is to expose students to a wide range of applications for these methods and models, and to integrate this material with their introduction to operations management.

Systems engineering is an interdisciplinary approach and means to enable the realization of successful systems. It focuses on defining customer needs and required functionality early in the development cycle, documenting requirements, then proceeding with design synthesis and reliability improvement while considering the complete problem including operations, performance, test, manufacturing, cost, and schedule. This course emphasizes the links of systems engineering to fundamentals of decision theory, statistics, and optimization. The course also introduces the most current, commercially successful techniques for systems engineering.

This class is an applications-oriented course covering the modeling of large-scale systems in decision-making domains and the optimization of such systems using state-of-the-art optimization tools. Application domains include: transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning. Modeling tools and techniques include linear, network, discrete and nonlinear optimization, heuristic methods, sensitivity and post-optimality analysis, decomposition methods for large-scale systems, and stochastic optimization.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5223 (System Optimisation: Models and Computation).