ODE book recommendation
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I have just completed my first year study and know elementary analysis and a little bit functional analysis.
I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?
reference-request ordinary-differential-equations
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add a comment |
$begingroup$
I have just completed my first year study and know elementary analysis and a little bit functional analysis.
I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?
reference-request ordinary-differential-equations
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Possible duplicate: math.stackexchange.com/questions/34233/…
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– Belgi
Jul 27 '12 at 16:37
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Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.
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– copper.hat
Jul 27 '12 at 17:30
add a comment |
$begingroup$
I have just completed my first year study and know elementary analysis and a little bit functional analysis.
I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?
reference-request ordinary-differential-equations
$endgroup$
I have just completed my first year study and know elementary analysis and a little bit functional analysis.
I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?
reference-request ordinary-differential-equations
reference-request ordinary-differential-equations
asked Jul 27 '12 at 15:44
community wiki
Ben
$begingroup$
Possible duplicate: math.stackexchange.com/questions/34233/…
$endgroup$
– Belgi
Jul 27 '12 at 16:37
$begingroup$
Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.
$endgroup$
– copper.hat
Jul 27 '12 at 17:30
add a comment |
$begingroup$
Possible duplicate: math.stackexchange.com/questions/34233/…
$endgroup$
– Belgi
Jul 27 '12 at 16:37
$begingroup$
Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.
$endgroup$
– copper.hat
Jul 27 '12 at 17:30
$begingroup$
Possible duplicate: math.stackexchange.com/questions/34233/…
$endgroup$
– Belgi
Jul 27 '12 at 16:37
$begingroup$
Possible duplicate: math.stackexchange.com/questions/34233/…
$endgroup$
– Belgi
Jul 27 '12 at 16:37
$begingroup$
Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.
$endgroup$
– copper.hat
Jul 27 '12 at 17:30
$begingroup$
Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.
$endgroup$
– copper.hat
Jul 27 '12 at 17:30
add a comment |
3 Answers
3
active
oldest
votes
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A classical theoretical book on ODE is Hartman.
A very good book, and slightly less demanding than Hartman is Hale's book
A geometric picture of differential equations is given in two Arnold's books: one and two
ODE from a dynamical system theory point of view are presented in Wiggins' book
Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.
The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.
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2
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Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
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– user31373
Jul 27 '12 at 20:13
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@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
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– Artem
Jul 29 '12 at 15:05
add a comment |
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You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.
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add a comment |
$begingroup$
You can try this one also...
'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)
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add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A classical theoretical book on ODE is Hartman.
A very good book, and slightly less demanding than Hartman is Hale's book
A geometric picture of differential equations is given in two Arnold's books: one and two
ODE from a dynamical system theory point of view are presented in Wiggins' book
Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.
The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.
$endgroup$
2
$begingroup$
Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
$endgroup$
– user31373
Jul 27 '12 at 20:13
$begingroup$
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
$endgroup$
– Artem
Jul 29 '12 at 15:05
add a comment |
$begingroup$
A classical theoretical book on ODE is Hartman.
A very good book, and slightly less demanding than Hartman is Hale's book
A geometric picture of differential equations is given in two Arnold's books: one and two
ODE from a dynamical system theory point of view are presented in Wiggins' book
Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.
The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.
$endgroup$
2
$begingroup$
Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
$endgroup$
– user31373
Jul 27 '12 at 20:13
$begingroup$
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
$endgroup$
– Artem
Jul 29 '12 at 15:05
add a comment |
$begingroup$
A classical theoretical book on ODE is Hartman.
A very good book, and slightly less demanding than Hartman is Hale's book
A geometric picture of differential equations is given in two Arnold's books: one and two
ODE from a dynamical system theory point of view are presented in Wiggins' book
Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.
The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.
$endgroup$
A classical theoretical book on ODE is Hartman.
A very good book, and slightly less demanding than Hartman is Hale's book
A geometric picture of differential equations is given in two Arnold's books: one and two
ODE from a dynamical system theory point of view are presented in Wiggins' book
Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.
The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.
edited Jul 29 '12 at 15:08
community wiki
2 revs
Artem
2
$begingroup$
Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
$endgroup$
– user31373
Jul 27 '12 at 20:13
$begingroup$
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
$endgroup$
– Artem
Jul 29 '12 at 15:05
add a comment |
2
$begingroup$
Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
$endgroup$
– user31373
Jul 27 '12 at 20:13
$begingroup$
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
$endgroup$
– Artem
Jul 29 '12 at 15:05
2
2
$begingroup$
Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
$endgroup$
– user31373
Jul 27 '12 at 20:13
$begingroup$
Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading.
$endgroup$
– user31373
Jul 27 '12 at 20:13
$begingroup$
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
$endgroup$
– Artem
Jul 29 '12 at 15:05
$begingroup$
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post.
$endgroup$
– Artem
Jul 29 '12 at 15:05
add a comment |
$begingroup$
You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.
$endgroup$
add a comment |
$begingroup$
You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.
$endgroup$
add a comment |
$begingroup$
You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.
$endgroup$
You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.
edited Jul 29 '12 at 15:18
community wiki
2 revs, 2 users 57%
Robert Israel
add a comment |
add a comment |
$begingroup$
You can try this one also...
'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)
$endgroup$
add a comment |
$begingroup$
You can try this one also...
'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)
$endgroup$
add a comment |
$begingroup$
You can try this one also...
'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)
$endgroup$
You can try this one also...
'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)
answered Dec 7 '18 at 17:27
community wiki
N. Masanta
add a comment |
add a comment |
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$begingroup$
Possible duplicate: math.stackexchange.com/questions/34233/…
$endgroup$
– Belgi
Jul 27 '12 at 16:37
$begingroup$
Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.
$endgroup$
– copper.hat
Jul 27 '12 at 17:30