Systems of Differential Equations

Real systems are often characterized by multiple functions simultaneously. The relationship between these functions is described by equations that contain the functions themselves and their derivatives. In this case, we speak of systems of differential equations. In this section we consider the different types of systems of ordinary differential equations, methods of their solving, and some applications to physics, engineering and economics.

• Linear Homogeneous Systems of Differential Equations with Constant Coefficients
• Method of Eigenvalues and Eigenvectors
• Construction of the General Solution of a System of Equations Using the Method of Undetermined Coefficients
• Construction of the General Solution of a System of Equations Using the Jordan Form
• Method of Matrix Exponential
• Linear Nonhomogeneous Systems of Differential Equations with Constant Coefficients
• Linear Systems of Differential Equations with Variable Coefficients
• Basic Concepts of Stability Theory
• Equilibrium Points of Linear Autonomous Systems
• Stability in the First Approximation
• Method of Lyapunov Functions
• Routh-Hurwitz Criterion
• First Integrals
• Mass-Spring System
• Double Pendulum
• Home Heating
• Price and Inventory Dynamics