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Questions about differential operator
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if $f(fracddt)=a_nfracd^ndt^n+dots+a_1fracddt+a_0$,then whether $$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$ or
$$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0$$
I am confused.
differential-equations
edited 1 hour ago
LutzL
51.1k31850
asked 1 hour ago
kenkenb
13518
add a comment |Â
up vote
1
down vote
favorite
if $f(fracddt)=a_nfracd^ndt^n+dots+a_1fracddt+a_0$,then whether $$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$ or
$$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0$$
I am confused.
differential-equations
edited 1 hour ago
LutzL
51.1k31850
asked 1 hour ago
kenkenb
13518
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
if $f(fracddt)=a_nfracd^ndt^n+dots+a_1fracddt+a_0$,then whether $$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$ or
$$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0$$
I am confused.
differential-equations
edited 1 hour ago
LutzL
51.1k31850
asked 1 hour ago
kenkenb
13518
if $f(fracddt)=a_nfracd^ndt^n+dots+a_1fracddt+a_0$,then whether $$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$ or
$$f(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0$$
I am confused.
differential-equations
differential-equations
edited 1 hour ago
LutzL
51.1k31850
asked 1 hour ago
kenkenb
13518
edited 1 hour ago
LutzL
51.1k31850
asked 1 hour ago
kenkenb
13518
edited 1 hour ago
LutzL
51.1k31850
edited 1 hour ago
LutzL
51.1k31850
edited 1 hour ago
LutzL
51.1k31850
51.1k31850
asked 1 hour ago
kenkenb
13518
asked 1 hour ago
kenkenb
13518
asked 1 hour ago
kenkenb
13518
13518
add a comment |Â
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
2
down vote
accepted
It is
$$
fleft(fracddtright)(y) = a_n fracd^ndt^ny + cdots + a_1 fracddty + a_0 y.
$$
If this notation confuses you, it might help to write the operator as
$$
a_n fracd^ndt^n + cdots + a_1 fracddt + a_0 I
$$
where $I$ is the identity operator.
answered 1 hour ago
Ernie060
1,744212
add a comment |Â
up vote
1
down vote
The correct answer is $$(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$
Otherwise you lose the linearity of your operator.
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
It is
$$
fleft(fracddtright)(y) = a_n fracd^ndt^ny + cdots + a_1 fracddty + a_0 y.
$$
If this notation confuses you, it might help to write the operator as
$$
a_n fracd^ndt^n + cdots + a_1 fracddt + a_0 I
$$
where $I$ is the identity operator.
answered 1 hour ago
Ernie060
1,744212
add a comment |Â
up vote
2
down vote
accepted
It is
$$
fleft(fracddtright)(y) = a_n fracd^ndt^ny + cdots + a_1 fracddty + a_0 y.
$$
If this notation confuses you, it might help to write the operator as
$$
a_n fracd^ndt^n + cdots + a_1 fracddt + a_0 I
$$
where $I$ is the identity operator.
answered 1 hour ago
Ernie060
1,744212
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
It is
$$
fleft(fracddtright)(y) = a_n fracd^ndt^ny + cdots + a_1 fracddty + a_0 y.
$$
If this notation confuses you, it might help to write the operator as
$$
a_n fracd^ndt^n + cdots + a_1 fracddt + a_0 I
$$
where $I$ is the identity operator.
answered 1 hour ago
Ernie060
1,744212
It is
$$
fleft(fracddtright)(y) = a_n fracd^ndt^ny + cdots + a_1 fracddty + a_0 y.
$$
If this notation confuses you, it might help to write the operator as
$$
a_n fracd^ndt^n + cdots + a_1 fracddt + a_0 I
$$
where $I$ is the identity operator.
answered 1 hour ago
Ernie060
1,744212
answered 1 hour ago
Ernie060
1,744212
answered 1 hour ago
Ernie060
1,744212
answered 1 hour ago
Ernie060
1,744212
1,744212
add a comment |Â
add a comment |Â
up vote
1
down vote
The correct answer is $$(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$
Otherwise you lose the linearity of your operator.
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
add a comment |Â
up vote
1
down vote
The correct answer is $$(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$
Otherwise you lose the linearity of your operator.
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
add a comment |Â
up vote
1
down vote
up vote
1
down vote
The correct answer is $$(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$
Otherwise you lose the linearity of your operator.
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
The correct answer is $$(fracddt)(y)=a_nfracd^ndt^ny+dots+a_1fracddty+a_0y$$
Otherwise you lose the linearity of your operator.
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
answered 58 mins ago
Mohammad Riazi-Kermani
35.5k41855
35.5k41855
add a comment |Â
add a comment |Â
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