Properties of Laplace Transform

Learn about the properties of Laplace Transform in this comprehensive 1.5-hour video lecture. Explore the Translation Theorem in s, calculate Laplace transforms of various functions including sqrt(t) without using the gamma function, t^2e^(4t), and t^n using series. Discover how to find Laplace transforms of f(at), first and second derivatives, and products like tf(t). Master techniques for solving Laplace transforms of trigonometric functions such as tsin(t) and t*cos(t). Conclude with a speed run on finding the Laplace transform of 1/sqrt(t), solidifying your understanding of these essential mathematical concepts.

Syllabus

Laplace Transform: Translation Theorem in s.
Laplace transform of sqrt(t), without using the gamma function.
Laplace transform of t^2e^(4t).
Laplace transform of t^n, using series.
Laplace transform of f(at).
Laplace Transform of the first derivative, Laplace transform of f'(t).
Laplace Transform of second derivative, laplace transform of f''(t).
Laplace transform of tf(t), ex: laplace transform of tsin(t).
Laplace Transform of t*cos(t).
Laplace transform of 1/sqrt(t), *SPEED RUN*.