Table of Contents
Differential Equations and Dynamical Systems
Finite Difference Equations.
- Phase portrait.
- The 2X2 real case.
- Stability of fixed point.
- The diagonalisable case: general solution (real and complex).
- The Jordan case: general solution (real and complex).
- Nonhomogeneous equation: variation of constants.
System of Differential Equations.
- Phase Portrait.
- Equilibrium points and stability analysis.
- Exponential of a matrix.
- The diagonalisable case: general solution (real and complex).
- The Jordan case: general solution (real and complex).
- Nonhomogeneous equation: variation of constants.
Non-linear system.
- Null-clines and phase portrait.
- Equilibrium points.
- Linearization around equilibrium point and stability analysis.