Learning Objectives & Matches
1. Demonstrate the ability to use a matrix factorization to solve a linear system;
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Direct the analysis, development, and operation of complete computer systems.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Analyze problems to develop solutions involving computer hardware and software.
Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
Collaborate with other operators to solve unit problems.
Direct the analysis, development, and operation of complete computer systems.
Compute dimensions, areas, volumes, and weights.
2. Recognize the role of the condition number of a matrix as a measure of the sensitivity of the solution to the related linear system of equations;
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
Measure and analyze system performance and operating parameters to assess operating condition of systems or equipment.
Observe temperature, humidity, pressure gauges, and product samples and adjust controls, such as thermostats and valves, to maintain prescribed operating conditions for specific stages.
Remove objects from solutions at periodic intervals and observe objects to verify conformance to specifications.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Devise or apply independent models or tools to help verify results of analytical systems.
Read specifications, such as blueprints, charts, or schematics, to determine machine settings or adjustments.
Analyze system performance or operational requirements.
Observe machine operations to detect any problems, making necessary adjustments to correct problems.
3. Provide details of backward stability analysis of an iterative scheme;
Perform computations and apply methods of numerical analysis to data.
Program computer numerical control machines.
Confer with numerical control programmers to check and ensure that new programs or machinery will function properly and that output will meet specifications.
4. Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)
Determine reference points, machine cutting paths, or hole locations, and compute angular and linear dimensions, radii, and curvatures.
Perform computations and apply methods of numerical analysis to data.
Consult with researchers to analyze problems, recommend technology-based solutions, or determine computational strategies.
Create novel computational approaches and analytical tools as required by research goals.
Develop or implement data analysis algorithms.
Analyze information processing or computation needs and plan and design computer systems, using techniques such as structured analysis, data modeling, and information engineering.
Design or coordinate successive phases of problem analysis, solution proposals, or testing.
Maintain awareness of new and emerging computational methods and technologies.
Specify manipulative or computational methods to be applied to models.
Devise or apply independent models or tools to help verify results of analytical systems.