Good Book for methods of Convergence
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First of all I'm interested in methods of convergence (for sums and integrals) so are there good books which tackle these methods one after the other and with examples that are not too trivial?
For example how would you proof that
$$
int_{-infty}^infty frac{{rm e}^{ikt} , {rm d}k}{left(1+a^2sin^2(k)right)left(k-bright)^{epsilon}}
$$
where $Im (b) < 0$, $0<epsilonleq 1$, $a>0$, converges and for which $t$. Analogously one could ask when does
$$
sum_{n=-infty}^infty frac{ {rm e}^{ipi tn} }{ left( n + c right)^{epsilon} }
$$
converge $(Im(c)>0)$? Feel free to try this.
integration improper-integrals conditional-convergence
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
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add a comment |
$begingroup$
First of all I'm interested in methods of convergence (for sums and integrals) so are there good books which tackle these methods one after the other and with examples that are not too trivial?
For example how would you proof that
$$
int_{-infty}^infty frac{{rm e}^{ikt} , {rm d}k}{left(1+a^2sin^2(k)right)left(k-bright)^{epsilon}}
$$
where $Im (b) < 0$, $0<epsilonleq 1$, $a>0$, converges and for which $t$. Analogously one could ask when does
$$
sum_{n=-infty}^infty frac{ {rm e}^{ipi tn} }{ left( n + c right)^{epsilon} }
$$
converge $(Im(c)>0)$? Feel free to try this.
integration improper-integrals conditional-convergence
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
$endgroup$
add a comment |
$begingroup$
First of all I'm interested in methods of convergence (for sums and integrals) so are there good books which tackle these methods one after the other and with examples that are not too trivial?
For example how would you proof that
$$
int_{-infty}^infty frac{{rm e}^{ikt} , {rm d}k}{left(1+a^2sin^2(k)right)left(k-bright)^{epsilon}}
$$
where $Im (b) < 0$, $0<epsilonleq 1$, $a>0$, converges and for which $t$. Analogously one could ask when does
$$
sum_{n=-infty}^infty frac{ {rm e}^{ipi tn} }{ left( n + c right)^{epsilon} }
$$
converge $(Im(c)>0)$? Feel free to try this.
integration improper-integrals conditional-convergence
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
$endgroup$
First of all I'm interested in methods of convergence (for sums and integrals) so are there good books which tackle these methods one after the other and with examples that are not too trivial?
For example how would you proof that
$$
int_{-infty}^infty frac{{rm e}^{ikt} , {rm d}k}{left(1+a^2sin^2(k)right)left(k-bright)^{epsilon}}
$$
where $Im (b) < 0$, $0<epsilonleq 1$, $a>0$, converges and for which $t$. Analogously one could ask when does
$$
sum_{n=-infty}^infty frac{ {rm e}^{ipi tn} }{ left( n + c right)^{epsilon} }
$$
converge $(Im(c)>0)$? Feel free to try this.
integration improper-integrals conditional-convergence
integration improper-integrals conditional-convergence
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
edited Dec 6 '18 at 0:40
Diger
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
asked Dec 5 '18 at 22:27
DigerDiger
1,6021413
1,6021413
add a comment |
add a comment |
1 Answer
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A nice book in my opinion is "Advanced Mathematical Methods with Maple", by D. Richards.
It is used as a text book in the homonymous course in the MSc in mathematics by the Open University. It is not only about convergence, but it has quite a theoretical underpinning and practical exercises too about that topic, where maple is used to illustrate and investigate the subject.
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
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1 Answer
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1 Answer
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active
oldest
votes
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active
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votes
$begingroup$
A nice book in my opinion is "Advanced Mathematical Methods with Maple", by D. Richards.
It is used as a text book in the homonymous course in the MSc in mathematics by the Open University. It is not only about convergence, but it has quite a theoretical underpinning and practical exercises too about that topic, where maple is used to illustrate and investigate the subject.
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
$endgroup$
add a comment |
$begingroup$
A nice book in my opinion is "Advanced Mathematical Methods with Maple", by D. Richards.
It is used as a text book in the homonymous course in the MSc in mathematics by the Open University. It is not only about convergence, but it has quite a theoretical underpinning and practical exercises too about that topic, where maple is used to illustrate and investigate the subject.
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
$endgroup$
add a comment |
$begingroup$
A nice book in my opinion is "Advanced Mathematical Methods with Maple", by D. Richards.
It is used as a text book in the homonymous course in the MSc in mathematics by the Open University. It is not only about convergence, but it has quite a theoretical underpinning and practical exercises too about that topic, where maple is used to illustrate and investigate the subject.
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
$endgroup$
A nice book in my opinion is "Advanced Mathematical Methods with Maple", by D. Richards.
It is used as a text book in the homonymous course in the MSc in mathematics by the Open University. It is not only about convergence, but it has quite a theoretical underpinning and practical exercises too about that topic, where maple is used to illustrate and investigate the subject.
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
answered Dec 10 '18 at 20:10
Marco BellocchiMarco Bellocchi
4881412
4881412
add a comment |
add a comment |
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