This course will answer these questions, and many more, with a survey of the range of levels of description for analytical, numerical, and data-driven mathematical modeling. The focus will be on understanding how these methods relate, and on how they can be implemented efficiently.
The schedule will be:
|2/9:||Mathematical Computing, Benchmarking, Linear Algebra and Calculus|
|2/16:||Ordinary Differential and Difference Equations|
|Partial Differential Equations|
|3/2:||Finite Differences: Ordinary Differential Equations|
|3/9:||Finite Differences: Partial Differential Equations|
|Filtering and State Estimation|
|5/4:||Machine Learning Architectures|
Relevant background for each of these areas will be covered. The assignments will include problem sets, programming tasks, and a semester modeling project. The course is based on the text The Nature of Mathematical Modeling, with draft revisions for a second edition to be provided throughout the semester.