The Laplace transform is named after mathematician and astronomer Pierre-Simon, Marquis de Laplace, who used a similar transform in his work on probability theory.
Nama transformasi ini diberikan untuk menghormati seorang ahli matematika dan astronomi, Pierre-Simon Laplace, yang menggunakan teknik transformasi ini pada hasil karyanya dalam teori kemungkinan.
Thus F ( s )L { f } ( s ) }\{f\}(s)} in functional notation.
}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}
∫ [ 0 , ∞ ) e − s t d μ ( t ) .
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
( s − s 0 ) ∫ 0 ∞ e − ( s − s 0 ) t β ( t ) d t , β ( u )
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
)=\lim _{s\to \infty }{sF(s)}.}
}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}
s ∫ − ∞ ∞ e − s t f ( t ) d ts ⋅ L { f ( t ) } .
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
}\{f'(t)\}=s\int _{-\infty }^{\infty }e^{-st}f(t)\,dt=s\cdot {\mathcal {L}}\{f(t)\}.}
}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}
d x∫ 0 ∞ ( L f ) ( s ) ⋅ ( L − 1 g ) ( s )
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
d x∫ 0 ∞ f ( s ) ( L g ) ( s ) d s .
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
^{\infty }({\mathcal {L}}f)(x)g(x)\,dx=\int _{0}^{\infty }f(s)({\mathcal {L}}g)(s)\,ds.}
}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}
∫ 0 ∞ f ( t ) e − σ t e − i τ t d t , {\displaystyle F(\sigma +i\tau )
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
F { f ( t ) }L { f ( t ) } | si ωF ( s ) | si ω∫ − ∞ ∞ e − i ω t f ( t )
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
d e f x ( t ) Δ T ( t )x ( t ) ∑ n0 ∞ δ ( t − n T )∑ n0 ∞ x ( n T ) δ ( t − n T )
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
The following table provides Laplace transforms for many common functions of a single variable.
Tabel berikut ini adalah daftar transformasi Laplace:Kutipan
Given a mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.
Dengan mengetahui deksripsi matematika atau fungsional sederhana dari masukan atau keluaran suatu sistem, transformasi Laplace dapat memberikan deskripsi funsional alternatif yang kadang dapat menyederhanakan proses analisis kelakukan dari sistem atau membuat suatu sistem baru yang berdasarkan suatu kumpulan spesifikasi.
}\left\{{\frac {f(t)}{t}}\right\}=\int _{s}^{\infty }F(p)\,dp.}
}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}
∫ 0 ∞ e − s t d μ ( t ) .
F ( s )L { f ( t ) }∫ 0 − ∞ e − s t f ( t ) d t .
}\mu (s)=\int _{0}^{\infty }e^{-st}d\mu (t).}
}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}
Bracewell, Ronald N. (1978), The Fourier Transform and its Applications (2nd ed.), McGraw-Hill Kogakusha, ISBN 978-0-07-007013-4 Bracewell, R. N. (2000), The Fourier Transform and Its Applications (3rd ed.), Boston: McGraw-Hill, ISBN 978-0-07-116043-8 Feller, William (1971), An introduction to probability theory and its applications.
Bracewell, Ronald N. (1978), The Fourier Transform and its Applications (Edisi 2nd), McGraw-Hill Kogakusha, ISBN 978-0-07-007013-4 Bracewell, R. N. (2000), The Fourier Transform and Its Applications (Edisi 3rd), Boston: McGraw-Hill, ISBN 978-0-07-116043-8 Feller, William (1971), An introduction to probability theory and its applications.
Vol. II., Second edition, New York: John Wiley & Sons, MR 0270403 Korn, G. A.; Korn, T. M. (1967), Mathematical Handbook for Scientists and Engineers (2nd ed.), McGraw-Hill Companies, ISBN 978-0-07-035370-1 Widder, David Vernon (1941), The Laplace Transform, Princeton Mathematical Series, v. 6, Princeton University Press, MR 0005923 Williams, J. (1973), Laplace Transforms, Problem Solvers, George Allen & Unwin, ISBN 978-0-04-512021-5 Takacs, J. (1953), "Fourier amplitudok meghatarozasa operatorszamitassal", Magyar Hiradastechnika (in Hungarian), IV (7–8): 93–96 Euler, L. (1744), "De constructione aequationum"
Vol. II., Second edition, New York: John Wiley & Sons, MR 0270403 Korn, G. A.; Korn, T. M. (1967), Mathematical Handbook for Scientists and Engineers (Edisi 2nd), McGraw-Hill Companies, ISBN 978-0-07-035370-1 Widder, David Vernon (1941), The Laplace Transform, Princeton Mathematical Series, v. 6, Princeton University Press, MR 0005923 Williams, J. (1973), Laplace Transforms, Problem Solvers, George Allen & Unwin, ISBN 978-0-04-512021-5 Takacs, J. (1953), "Fourier amplitudok meghatarozasa operatorszamitassal", Magyar Hiradastechnika (dalam bahasa Hungarian), IV (7–8): 93–96 Pemeliharaan CS1: Bahasa yang tidak diketahui (link)
[The Construction of Equations], Opera Omnia, 1st series (in Latin), 22: 150–161 Euler, L. (1753), "Methodus aequationes differentiales" [A Method for Solving Differential Equations], Opera Omnia, 1st series (in Latin), 22: 181–213 Euler, L. (1992)
[The Construction of Equations], Opera Omnia, 1st series (dalam bahasa Latin), 22: 150–161 Euler, L. (1753), "Methodus aequationes differentiales" [A Method for Solving Differential Equations], Opera Omnia, 1st series (dalam bahasa Latin), 22: 181–213 Euler, L. (1992)
[Institutions of Integral Calculus], Opera Omnia, 1st series (in Latin), 12, Basel: Birkhäuser, ISBN 978-3764314743{{citation}}: CS1 maint: work parameter with ISBN (link), Chapters 3–5 Euler, Leonhard (1769), Institutiones calculi integralis
[Institutions of Integral Calculus], Opera Omnia, 1st series (dalam bahasa Latin), 12, Basel: Birkhäuser, ISBN 978-3764314743, Chapters 3–5 Euler, Leonhard (1769), Institutiones calculi integralis
[Institutions of Integral Calculus] (in Latin), vol. II, Paris:
[Institutions of Integral Calculus] (dalam bahasa Latin), vol. II, Paris:
57–153 Grattan-Guinness, I (1997), "Laplace's integral solutions to partial differential equations", in Gillispie, C. C. (ed.), Pierre Simon Laplace 1749–1827: A Life in Exact Science, Princeton: Princeton University Press, ISBN 978-0-691-01185-1 Lagrange, J. L. (1773), Mémoire sur l'utilité de la méthode, Œuvres de Lagrange, vol. 2, pp.
57–153 Grattan-Guinness, I (1997), "Laplace's integral solutions to partial differential equations", dalam Gillispie, C. C. (ed.), Pierre Simon Laplace 1749–1827: A Life in Exact Science, Princeton: Princeton University Press, ISBN 978-0-691-01185-1 Lagrange, J. L. (1773), Mémoire sur l'utilité de la méthode, Œuvres de Lagrange, vol. 2, hlm.
171–234 Arendt, Wolfgang; Batty, Charles J.K.; Hieber, Matthias; Neubrander, Frank (2002), Vector-Valued Laplace Transforms and Cauchy Problems, Birkhäuser Basel, ISBN 978-3-7643-6549-3 Davies, Brian (2002), Integral transforms and their applications (Third ed.), New York: Springer, ISBN 978-0-387-95314-4 Deakin, M. A. B. (1981), "The development of the Laplace transform", Archive for History of Exact Sciences, 25 (4): 343–390, doi:10.1007/BF01395660, S2CID 117913073 Deakin, M. A. B. (1982), "The development of the Laplace transform", Archive for History of Exact Sciences, 26 (4): 351–381, doi:10.1007/BF00418754, S2CID 123071842 Doetsch, Gustav (1974), Introduction to the Theory and Application of the Laplace Transformation, Springer, ISBN 978-0-387-06407-9 Mathews, Jon; Walker, Robert L. (1970), Mathematical methods of physics (2nd ed.), New York: W. A. Benjamin, ISBN 0-8053-7002-1 Polyanin, A. D.; Manzhirov, A. V. (1998), Handbook of Integral Equations, Boca Raton: CRC Press, ISBN 978-0-8493-2876-3 Schwartz, Laurent (1952), "Transformation de Laplace des distributions", Comm.
171–234 Arendt, Wolfgang; Batty, Charles J.K.; Hieber, Matthias; Neubrander, Frank (2002), Vector-Valued Laplace Transforms and Cauchy Problems, Birkhäuser Basel, ISBN 978-3-7643-6549-3. Davies, Brian (2002), Integral transforms and their applications (Edisi Third), New York: Springer, ISBN 978-0-387-95314-4 Deakin, M. A. B. (1981), "The development of the Laplace transform", Archive for History of Exact Sciences, 25 (4): 343–390, doi:10.1007/BF01395660 Deakin, M. A. B. (1982), "The development of the Laplace transform", Archive for History of Exact Sciences, 26 (4): 351–381, doi:10.1007/BF00418754 Doetsch, Gustav (1974), Introduction to the Theory and Application of the Laplace Transformation, Springer, ISBN 978-0-387-06407-9 Mathews, Jon; Walker, Robert L. (1970), Mathematical methods of physics (2nd ed.), New York: W. A. Benjamin, ISBN 0-8053-7002-1 Polyanin, A. D.; Manzhirov, A. V. (1998), Handbook of Integral Equations, Boca Raton: CRC Press, ISBN 978-0-8493-2876-3 Schwartz, Laurent (1952), "Transformation de Laplace des distributions", Comm.
Mat. Sem.] (in French), 1952:
Mat. Sem.] (dalam bahasa French), 1952:
[1966], Mathematics for the Physical Sciences, Dover Books on Mathematics, New York: Dover Publications, pp.
[1966], Mathematics for the Physical Sciences, Dover Books on Mathematics, New York: Dover Publications, hlm. 215–241, ISBN 978-0-486-46662-0 - See Chapter VI.
Laplace Calculator to calculate Laplace Transforms online easily.
to calculate Laplace Transforms online easily.