Differential Equations
(Due Friday, January 14) |
Exponential and Logistic models:
- Read: Olinick, Chapter 3
- Topics:
the four steps involved in modeling;
solving differential equations using the seperation of variables technique;
assumptions, differential equation, and function for population model
(both exponential and logistic);
solving population growth and radioactive decay problems
- Homework 01: available
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Arms Race models:
- Read: Olinick, Chapter 2
- Topics:
arms race assumptions and corresponding terms in differential equations;
creating slope graphs to analyze long-term behavior of equations:
interpreting the lines dx/dt = 0 and dy/dt = 0,
the regions they bound, and their intersection;
analyzing effects of changing parameters in equations
- Homework 02: not yet available
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Predator-Prey models:
- Read: Olinick, Chapter 4
- Topics:
assumptions for predators and prey, and corresponding terms in differential equations;
finding a single equation relating predator and prey populations;
modifying assumptions and differential equations (prey population with logistic growth,
predator population dependent on "critical ratio")
- Homework 03: not yet available
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Epidemic models:
- Read: Olinick, Chapter 13
- Topics:
stages of disease; assumptions for population and progression of disease, corresponding
differential equations, and possible modifications;
time at which demand for medical services is highest;
how preventing an epidemic is reflected mathematically
- Homework 04: not yet available
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Problem Session:
- Extra problems: not yet available
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