Introduction to Ordinary Differential Equations

The course on Ordinary Differential Equations (ODEs) covers a comprehensive range of topics essential for understanding and solving differential equations. It begins with an introduction to the basic definitions and importance of differential equations in modeling real-world systems. The course then delves into various methods for solving first-order and second-order differential equations, including separation of variables, integrating factors, and numerical methods such as Euler's method and Runge-Kutta methods. Additionally, the course explores applications of ODEs in mechanical vibrations, electrical circuits, and other systems. Advanced topics such as stability theory, Lyapunov’s direct method, and bifurcation theory are also discussed to provide students with a thorough understanding of the subject .

The objectives of the course are to:

• Understand the fundamental concepts of ordinary differential equations (ODEs).
• Learn various methods to solve first-order and higher-order differential equations.
• Apply differential equations to model and solve real-world problems in engineering, physics, and other fields.
• Develop analytical and numerical skills to find solutions to differential equations.
• Gain insights into advanced topics such as stability theory and bifurcation theory.

In presence

The course utilizes a mix of instructional techniques to ensure a robust learning experience:

• Lectures: Comprehensive presentations of key concepts and methods.
• Lecture Notes: Detailed notes provided to supplement and reinforce lecture material.
• Projects: Hands-on projects to explore real-world applications of differential equations.
• Exams: Midterm and final exams to assess understanding and proficiency.

The evaluation structure of the course includes midterm exams, a final exam, and projects. The midterm exams will assess the understanding of the initial course material, ensuring that students grasp the foundational concepts. The final exam will offer a comprehensive assessment of all topics covered throughout the course, testing the overall knowledge and analytical skills of the students. Projects will provide an opportunity for students to apply and present their solutions to real-world problems using differential equations, contributing to the final grade and demonstrating their ability to integrate theory with practice.