Vasco Núñez de Balboa and Laplace transform: Difference between pages

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The '''Laplace transform''' of a [[function]] ''f''(''t'') defined for all [[real number|real numbers]] ''t'' ≥ 0 is the function ''F''(''s''), defined by:
'''Vasco Nuñez de Balboa''' (ca. 1475-1519) was a Spanish [[conquistador]] who was the father of the colony of [[Darien|Darién]] in [[Panama]], the oldest still-existing European settlement in mainland [[America]].
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Balboa sailed to [[Hispaniola]] in 1501 on an expedition under [[Rodrigo de Bastidas]] and [[Juan de la Cosa]].
During this voyage they crossed the [[Gulf of Uraba|Gulf of Urabá]] (on the coast of present-day [[Columbia]]), and saw
the indian village of [[Darien|Darién]] in present-day [[Panama]]. In Hispaniola, Balboa settled down as a planter.
However, he soon amassed a large amount of debts, and to escape from his creditors he hijacked on
a supplyship headed for San Sebastian on the Gulf of Uraiba, hidden in a cask. The ship was
commanded by [[Martin Fernandez de Enciso|Martín Fernández de Enciso]].


: ''F''(''s'') = &int;<sub>0</sub><sup>&infin;</sup> ''e''<sup>-''st''</sup> ''f''(''t'') d''t''
While under way, they met [[Francisco Pizarro]] (the later conqueror of [[Peru]]), who lead the colony in
San Sebastian and told them almost all members of the colony had been massacred by indians.
Enciso nevertheless decided to go on to San Sebastian, but his ship shipwrecked, the men being
rescued by Pizarro, but all supplies and livestock being lost, and the colony was in ashes. Balboa, by
now accepted as a crew member of Enciso's, convinced them to try again in the area around
Darién.


The Laplace transform ''F''(''s'') typically exists for all real numbers ''s'' > ''a'', where ''a'' is a constant which depends on the growth behavior of ''f''(''t'').
They subdued the indians, started a colony and built a village. Balboa made the colonists reject both
Enciso's authority and that of [[Diego de Nicuesa]], who was sent to Darién as governor after Enciso
See also: [[Fourier transform]], [[transfer function]], [[linear dynamic system]].
had sought redress with King [[Ferdinand of Aragon|Ferdinand]]. Balboa became de facto leader of the colony. Both the
colony and Balboa himself thrived under his policies, making friends with surrounding indians, and
subduing and looting those who did not want to. He heared of a great sea on the other side of the
mountains, and a land of great wealth (Birú, the [[Incas|Inca]] empire) to the south of this sea. As he heared
that the king wanted to sent him back to be tried for his conduct towards Enciso and Nicuesa, he
decided he had to move fast.

On [[September 1]], 1513, he sailed to [[San Blas]] (a lucky choice, as it just happens to be the smallest point of the isthmus), and went south across the [[isthmus]]. As before he befriended the indians who were inclined to do so, and captured, tortured and looted those that remained hostile, thus gaining substantial treasure. Finally he reached a top from where he could see the [[Pacific Ocean]]. When the others had joined him a [[Te Deum]] was chanted, a cross erected, and the sea was christened Mar del Sur (South Sea). He pushed on to the edge of the ocean, and Balboa claimed the ocean and all adjacent
lands for [[Spain]].

On the road back they captured an indian chief called Tubanama and got a huge ransom, but some
members almost died of hunger because they had loaded treasure in preference to provisions. On
[[January 18]], 1514, Balboa was back in Darién.

While Balboa was away, [[Pedrarias Davila|Pedro Arias de Ávila]] (generally known as Pedrarias) had been sent to Darién as a governor. Although this time Balboa did not oppose him openly, tension between them
remained, Pedrarias being envious because Balboa was much more popular than himself. Balboa
embarked on a new, courageous expedition by building ships on the Pacific coast. The transport of
the materials across the isthmus cost the lives of many indian slaves. Balboa made one expedition
with the ships, to the [[Pearl Islands]] in the [[Gulf of Panama]]. He tried to head south from there, but
found the wind unfavorable.

Pedrarias, being convinced that Balboa wanted to establish a government of his own on the west
coast, had him arrested and tried for treason. Under pressure of Pedrarias Balboa was convicted
and sentenced to death, and on [[January 21]], 1519 Balboa was beheaded.
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[http://www.win.tue.nl/~engels/discovery/balboa.html Original version] (copied with permission)

Revision as of 01:53, 29 January 2002

The Laplace transform of a function f(t) defined for all real numbers t ≥ 0 is the function F(s), defined by:

F(s) = ∫0 e-st f(t) dt

The Laplace transform F(s) typically exists for all real numbers s > a, where a is a constant which depends on the growth behavior of f(t).

See also: Fourier transform, transfer function, linear dynamic system.