Category:Examples of Laplace Transforms
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This category contains examples of Laplace Transform.
Let $f: \R_{\ge 0} \to \mathbb F$ be a function of a real variable $t$, where $\mathbb F \in \set {\R, \C}$.
The Laplace transform of $f$, denoted $\laptrans f$ or $F$, is defined as:
- $\ds \laptrans {\map f t} = \map F s = \int_0^{\to +\infty} e^{-s t} \map f t \rd t$
whenever this improper integral converges.
If this improper integral does not converge, then $\laptrans {\map f t}$ does not exist.
Subcategories
This category has the following 31 subcategories, out of 31 total.
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L
- Laplace Transform of 1 (3 P)
- Laplace Transform of Sine (9 P)
Pages in category "Examples of Laplace Transforms"
The following 77 pages are in this category, out of 77 total.
E
I
L
- Laplace Transform of 1
- Laplace Transform of a t cosh a t - sinh a t over 2 a^3
- Laplace Transform of b e^bt - a e^at over b - a
- Laplace Transform of Complex Power
- Laplace Transform of Constant Mapping
- Laplace Transform of cos a t by cosh a t
- Laplace Transform of cosh a t + half a t sinh a t
- Laplace Transform of Cosine
- Laplace Transform of cosine a t - half a t sine a t
- Laplace Transform of Cosine Integral Function
- Laplace Transform of Cosine of Root over Root
- Laplace Transform of Difference between Exponentials
- Laplace Transform of Dirac Delta Function
- Laplace Transform of Dirac Delta Function by Function
- Laplace Transform of Error Function
- Laplace Transform of Error Function of Root
- Laplace Transform of Exponential
- Laplace Transform of Exponential Integral Function
- Laplace Transform of Exponential times Cosine
- Laplace Transform of Exponential times Hyperbolic Cosine
- Laplace Transform of Exponential times Hyperbolic Sine
- Laplace Transform of Exponential times Sine
- Laplace Transform of Half Wave Rectified Sine Curve
- Laplace Transform of Heaviside Step Function
- Laplace Transform of Heaviside Step Function times Function
- Laplace Transform of Hyperbolic Cosine
- Laplace Transform of Hyperbolic Sine
- Laplace Transform of Identity Mapping
- Laplace Transform of Natural Logarithm
- Laplace Transform of Null Function
- Laplace Transform of Positive Integer Power
- Laplace Transform of Positive Integer Power times Exponential
- Laplace Transform of Positive Real Power times Exponential
- Laplace Transform of Power
- Laplace Transform of Real Power
- Laplace Transform of Reciprocal of Square Root
- Laplace Transform of Shifted Dirac Delta Function
- Laplace Transform of Sine
- Laplace Transform of sine a t + a t cosine a t over 2 a
- Laplace Transform of sine a t - a t cosine a t over 2 a^3
- Laplace Transform of Sine Integral Function
- Laplace Transform of Sine of Root
- Laplace Transform of Sine of t over t
- Laplace Transform of Sine of t over t/Corollary
- Laplace Transform of sinh a t + a t cosh a t over 2 a
- Laplace Transform of t cosh a t
- Laplace Transform of t cosine a t
- Laplace Transform of t sine a t
- Laplace Transform of t sine a t over 2 a
- Laplace Transform of t sinh a t
- Laplace Transform of t sinh a t over 2 a
- Laplace Transform of t^2 cosh a t
- Laplace Transform of t^2 cosh a t over 2
- Laplace Transform of t^2 cosine a t
- Laplace Transform of t^2 cosine a t over 2
- Laplace Transform of t^2 sine a t
- Laplace Transform of t^2 sine a t over 2 a
- Laplace Transform of t^2 sinh a t
- Laplace Transform of t^2 sinh a t over 2 a
- Laplace Transform of t^3 cosh a t
- Laplace Transform of t^3 cosh a t over 6
- Laplace Transform of t^3 cosine a t
- Laplace Transform of t^3 cosine a t over 6
- Laplace Transform of t^3 sine a t
- Laplace Transform of t^3 sine a t over 24 a
- Laplace Transform of t^3 sinh a t
- Laplace Transform of t^3 sinh a t over 24 a
- Laplace Transform/Examples
- Laplace Transform/Examples/Example 1
- Laplace Transform/Graphical Interpretation/Examples
- Laplace Transform/Graphical Interpretation/Examples/Cosine t of -3 + 12 i
- Laplace Transform/Graphical Interpretation/Examples/Cosine t of 3 - 9 i
- Laplace Transform/Graphical Interpretation/Examples/Cosine t of Half + 4 i