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Solving ordinary differential equations (ODE)

I am amazed that it was established around 200 years ago… 1. I met the Laplace transform for the first time when I attended a classical control theory class in university. The transfer functions help us analyze and design feedback control systems systematically.Īs a side note, the Laplace transform was named after Pierre-Simon Laplace (1749-1827) ( Wikipedia) who is a distinguished French mathematician. Using the Laplace transform, we can create transfer function models from linear ODEs describing the behavior of control systems. Modeling, analyzing and designing control systems in control engineering.Solving linear ordinary differential equations (ODE) to analyze the behavior of physical systems such as electric circuits, machines, and anything with motion.The Laplace transform is often used for the following purposes in engineering fields. The Laplace transform is a historical and useful tool to convert equations including differential and integral calculus into algebraic expressions to solve more easily. The purpose of using the Laplace transform is to solve complex engineering problems easily and systematically. What is the purpose of Laplace transform? Some examples are shown for primitive signals such as step, ramp, parabola, exponential and sinusoidal signals, and general differential operation.Differential and integral operations are replaced to the multiplication of complex-variables. The Laplace transform convert a function f(t) in the real-variable (time) world into a function F(s) in the complex-variable world.In control engineering, we use it to create transfer function models from the ODEs of physical systems and controllers. We often use the Laplace transform to solve linear ordinary differential equations (ODE).The Laplace transform is a powerful tool to convert equations including differential and integral operations into algebraic equations to solve more easily.This article will guide the basic concept of the Laplace transform for beginners. The Laplace transform gives us a way to solve it. We often describe and analyze the behavior of physical systems by using ordinary differential equations (ODE) for engineering product research and development. Laplace transform helps us solve engineering problems.