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Differential equations are mathematical equations that relate a function to its derivatives. They can be used to model physical systems and predict their behavior. Dynamical systems are systems that change over time, and can be analyzed using differential equations. In this video, the instructor introduces the concepts of differential equations and dynamical systems, and shows how they can be used to solve problems in engineering and science.

**00:00:00**This video introduces differential equations, their applications, and the basics of calculus. After a brief review of calculus, the video jumps into a discussion of the Taylor series and exponential functions.**00:05:00**This video provides an overview of differential equations, including their simple and ordinary forms, and how systems of these equations behave. The video then moves on to more complicated systems of differential equations, discussing linear and nonlinear systems and how to solve them. Finally, the video discusses how to use numerical methods to solve differential equations and visualize the results.**00:10:00**This video provides an overview of differential equations and dynamical systems. It discusses how these mathematical concepts are related and how they can be used to solve problems in engineering and science.**00:15:00**Differential equations are used to model physical systems, and can be solved using Fourier and Laplace transforms. In this video, the instructor talks about how differential equations can be applied to a variety of fields, and how to solve them. After this, he introduces a couple of applications of differential equations.**00:20:00**Differential equations are a powerful tool for understanding how systems change over time, and can be used to analyze chaotic systems. In this tutorial, you will learn how to use differential equations to analyze systems like a double pendulum, and predict their movements.**00:25:00**Differential equations and dynamical systems are key tools for understanding and controlling systems. This lecture will introduce the concepts of eigenvalues and eigenvectors, and show how they are useful for solving differential equations.

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