Sumario Transformaciones compuestas + Regla de la cadena
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Course
Análisis Matemático II
Institution
National University Of Luján (UNLu
)
En este resumen vas a encontrar explicaciones, propiedades, teoremas, ejemplos de ejercicios resueltos y respuesta a ejercicios de libro "Lecciones de Análisis II" de Alfredo Novelli.
Temas:
- Transformaciones compuestas
- Regla de la cadena
Sea la transformación definida en un abierto de : : → (donde los valores de están
contenidos en un abierto de )
Y sea : → definida en el abierto tal que a cada vector perteneciente al abierto (de )
le corresponde según un vector del abierto , ( ) ∈ (de ) y a éste le corresponde según , un
vector ( ( )) de .
( ) ( ( ))
Si y son transformaciones diferenciables, entonces ( ( )) es diferenciable y resulta:
( ( )) ´ = ´( ( )). ´( )
= (", #)
= ( , , ) donde ! = (", #)$
%& %&
%' %
= (", #)
Supongamos y queremos calcular y , entonces
primeramente debemos tener bien claro que la composición se realiza de la siguiente forma:
(", #) ( , , )
( )
depende de " y de #, las variables , , son variables intermedias, además:
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