Differential Equations
Study of equations involving derivatives and their applications.
Advanced Topics
Systems of Differential Equations
Working with Multiple Equations
Sometimes, you need to solve not just one, but several differential equations that are linked together.
Notation
- \( \frac{dx}{dt} = ax + by \)
- \( \frac{dy}{dt} = cx + dy \)
Why Use Systems?
Many real-life problems involve more than one changing quantity, like predator-prey populations or chemical reactions.
Solving Methods
- Substitution and elimination
- Matrix methods (for more advanced study)
Examples
Modeling rabbits and foxes in an ecosystem.
Simulating interacting chemicals in a reaction.
In a Nutshell
Systems model situations with multiple interacting variables.