Description
This material is from a wealth of other material authored by Grant B. Gustafson in the Mathematics Department at the University of Utah.
See http://www.math.utah.edu/~gustafso/ Accessed 29 March 2023.
Up to date information on his productivity! One could spend hours looking through here for examples, models, and exercises.
Here is the index of this material:
11.1: Examples of Systems
11.2: Basic First-order System Methods
11.3: Structure of Linear Systems
11.4: Matrix Exponential
11.5: The Eigenanalysis Method for x′ = Ax
11.6: Jordan Form and Eigenanalysis
11.7: Nonhomogeneous Linear Systems
11.8: Second-order Systems
11.9: Numerical Methods for Systems
There are many applications from compartment and cascade analysis, recycling brine tank, home heating with multiple rooms, chemostat, microbes, heartbeats, lidocaine, nutrient flow in an aquarium, biomass transfer, pesticides, forecasting prices, electric networks, logging, earthquake, building. There is also good development of main concepts such as eigenvalues, exponential matrix, variation of parameters, numerical methods, etc.
Keywords: compartment, cascade, brine, tank, heating, chemostat, microbes, heartbeats, lidocaine, nutrient flow, aquarium, biomass, transfer, pesticides, forecasting, electric networks, circuits, logging, earthquake, building
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