Modeling
ODE’s
Fundamentals
Classification
Slope fields
System of ODE’s
Difference equations
Existence of solutions
Analytical methods for First Order ODEs
Separable Equations
Linear Equations
Homogeneous vs Inhomogeneous
Integrating Factor method
Graphical Methods **
Direction Fields
Orthogonal Trajectories
Nonlinear
Overview
Special cases
Analytical methods for Second Order ODEs
Homogeneous Linear Equations (Constant Coefficients)
Characteristic Equation
Cases
Real distinct roots, Repeated roots, Complex roots
Inhomogeneous Linear Equations
Principle of Superposition
Method of Undetermined Coefficients (Ansatz method)
Variation of Parameters
System of ODEs
Analytical methods
Oscillation problems
Numerical Methods
Taylor series expansion
Euler’s Method
Heun’s Method (Improved Euler)
Runge-Kutta Method (RK4)
Error, convergence and stability
Dynamical systems
One-dimensional continuous systems
Two-dimensional continuous systems
Three-dimensional continuous systems and chaos
Discrete dynamical systems
Form