🔵33 - Solving Initial Value Problems using Laplace Transforms method

In this lesson we are going to learn how to solve initial value problems using laplace transforms. Given a differential equation and asked to find the general solution to that d.e, you first take the laplace transforms of both sides of the d.e and find the inverse transform of the resulting complex rational function. The method of partial fractions helps us to decompose a complex rational function into the sum of simple rational functions. We shall consider three cases: Rational functions with 1. Non-repeated Linear Factors 2. Repeated Linear Factors 3. Quadratic Factors If F(s) = L(f(t)), then f(t) = inverse L(f(t)). The inverse Laplace Transforms is used to obtain an inverse mapping of a given Laplace Transform F(s). Playlists on various Course 1. Applied Electricity https://www.youtube.com/playlist?list=PLInywrvFyvq7pFsDEDu2-n0f5UOhpqWBD 2. Linear Algebra / Math 151 https://www.youtube.com/playlist?list=PLInywrvFyvq4IE-nW-ikwkZ2v81n31HQX 3. Basic Mechanics https://www.youtube.com/playlist?list=PLInywrvFyvq6FUfAigJ3157kg-nZ020fd 4. Calculus with Analysis / Calculus 1 / Math 152 https://www.youtube.com/playlist?list=PLInywrvFyvq6_G3iA7LHbt5exJgGbp4Ok 5. Differential Equations / Math 251 https://www.youtube.com/playlist?list=PLInywrvFyvq408vWA5OYXShA6rlT51TdS 6. Electric Circuit Theory / Circuit Design https://www.youtube.com/playlist?list=PLInywrvFyvq4sNicTbLBUpgkxrkcs2OGN Make sure to watch till the end. Like, share, and subscribe. Thank you.