Introduction to Ordinary Differential Equations
2024-fall, Master of Science in Artificial Intelligence and Computational Science, Lecture, Elective, 1st and 2nd year. Università della Svizzera italiana, Faculty of Informatics, 2024
This course provides a comprehensive foundation in ordinary differential equations (ODEs), emphasizing their importance in modeling real-world systems. Students will gain both theoretical insights and practical skills through analytical methods, numerical techniques, and real-world applications.
Course Resources
- Lecture Notes: Download Lecture Notes (PDF)
- Interactive Course App: Explore ODE Concepts & Solutions
- Official Course Page: Introduction to Ordinary Differential Equations - USI
Course Content
- Introduction to Differential Equations
- Definitions and classifications of differential equations
- Real-world applications in science, engineering, and biology
- Fundamental theorem of calculus
- First-Order Differential Equations
- Separable and linear equations
- Growth and decay models
- Slope fields and geometric solutions
- Second-Order Differential Equations
- Homogeneous equations and the characteristic equation
- Nonhomogeneous equations: methods of undetermined coefficients and variation of parameters
- Applications in mechanical vibrations and electrical circuits
- Linear Systems of Differential Equations
- Eigenvalue and eigenvector methods
- Phase plane analysis
- Compartmental models and practical systems
- Numerical Methods for Differential Equations
- Picard iteration and Euler’s method
- Improved Euler’s and Runge-Kutta methods
- Numerical applications to practical problems
- Introduction to Nonlinear Systems
- Equilibrium points, stability, and bifurcations
- Linearization techniques
- Nonlinear applications: Lotka-Volterra and SIR epidemic models
- Advanced Topics in ODEs
- Higher-order differential equations
- Neural ordinary differential equations
- Interdisciplinary applications in game theory and ecology