Laplace Transform (Introduction for Physics and Engineering students)

Laplace Transform is a widely used mathematical tool to solve differential equations which appear often times in Physics and Engineering problems. @ArifSolvesIt presents a concise introduction to the concept, by deriving the Laplace Transform of various functions, time and frequency space properties, and the Initial and final value theorems. In the final, @ArifSolvesIt applies the Laplace Transform method to solve a second order differential equation which happens to be the equation of motion of a simple harmonic oscillator.

01:52 Definition of Laplace Transform and a Brief Introduction to its existence
05:59 Linearity Property
07:06 Laplace Transform of constants and exponential functions
08:35 Laplace Transform of hyperbolic and trigonometric functions
12:08 Laplace Transform of power functions with positive integer powers
17:22 Frequency Shifting
18:54 Time Shifting
21:15 Time Scaling
23:32 s-space derivative
25:44 Laplace Transform of derivatives
33:31 s-space integration
36:18 t-space integration
42:13 Initial Value Theorem
44:33 Final Value Theorem
47:45 A second order ordinary differential equation is solved by Laplace Transform method

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[JustNow]

I used Heaviside operatoren I steder ved design af regulerings systemer. Meget nemmere og mere intuitive.