The Laplace transform is an integral transform that is widely used to solve linear differential equations with constant coefficients.
What is the formula for Laplace Transform?
L(f(t)) = F(s) = ∫_0^∞ e^(-st) f(t) dt
What are the properties of Laplace Transform?
Linearity, Time-Shifting, First Shifting, Second Shifting, Laplace Transform of Derivatives, Laplace Transform of Integrals, Convolution Theorem, Initial Value Theorem, Final Value Theorem are the properties of Laplace Transform.
What is the Laplace Transform of e^at ?
L(e^at) = 1 / (s-a)
What is the Laplace Transform of sin (at) ?
L(sin(at)) = a / (s^2 + a^2)
What is the Laplace Transform of cos (at) ?
L(cos(at)) = s / (s^2 + a^2)
What is Laplace Transform of t^n?
L(t^n) = n! / s^(n+1)
What is Initial Value Theorem (IVT)?
The Initial Value Theorem (IVT) states that the value of a function at t=0 can be calculated by taking the limit of sF(s) as s approaches infinity.
What is Final Value Theorem (FVT)?
The Final Value Theorem (FVT) states that the value of a function as t approaches infinity can be calculated by taking the limit of sF(s) as s approaches zero.
What is the Laplace Transform of the unit step function?
L(u(t)) = 1/s
What is inverse Laplace Transform?
The inverse Laplace transform of F(s) is the function f(t) such that L(f(t)) = F(s).
What is the Laplace Transform of the impulse function?
L(δ(t)) = 1
What is the Laplace Transform of a constant?
L(c)= c/s
What is a Z-transform?
The Z-transform is the discrete-time equivalent of the Laplace transform. It is used to analyze and design digital signal processing systems.
What are the applications of Laplace Transforms?
Laplace Transforms are useful in solving differential equations and in signal processing problems such as filtering and frequency analysis.
What is Laplace Transform?
The Laplace transform is an integral transform that is widely used to solve linear differential equations with constant coefficients.
What is the formula for Laplace Transform?
L(f(t)) = F(s) = ∫_0^∞ e^(-st) f(t) dt
What are the properties of Laplace Transform?
Linearity, Time-Shifting, First Shifting, Second Shifting, Laplace Transform of Derivatives, Laplace Transform of Integrals, Convolution Theorem, Initial Value Theorem, Final Value Theorem are the properties of Laplace Transform.
What is the Laplace Transform of e^at ?
L(e^at) = 1 / (s-a)
What is the Laplace Transform of sin (at) ?
L(sin(at)) = a / (s^2 + a^2)
What is the Laplace Transform of cos (at) ?
L(cos(at)) = s / (s^2 + a^2)
What is Laplace Transform of t^n?
L(t^n) = n! / s^(n+1)
What is Initial Value Theorem (IVT)?
The Initial Value Theorem (IVT) states that the value of a function at t=0 can be calculated by taking the limit of sF(s) as s approaches infinity.
What is Final Value Theorem (FVT)?
The Final Value Theorem (FVT) states that the value of a function as t approaches infinity can be calculated by taking the limit of sF(s) as s approaches zero.
What is the Laplace Transform of the unit step function?
L(u(t)) = 1/s
What is inverse Laplace Transform?
The inverse Laplace transform of F(s) is the function f(t) such that L(f(t)) = F(s).
What is the Laplace Transform of the impulse function?
L(δ(t)) = 1
What is the Laplace Transform of a constant?
L(c)= c/s
What is a Z-transform?
The Z-transform is the discrete-time equivalent of the Laplace transform. It is used to analyze and design digital signal processing systems.
What are the applications of Laplace Transforms?
Laplace Transforms are useful in solving differential equations and in signal processing problems such as filtering and frequency analysis.