Recent content by vish_maths

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    Calculating the value of 1/{D^2+a^2} sin ax

    Sorry I meant Don't we have the relation $$\dfrac {1}{f(D)}e^{cx} = \dfrac{1}{f(c)} e^{cx},~f(c) \ne 0$$
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    Calculating the value of 1/{D^2+a^2} sin ax

    Thanks for the reply. But, Don't we have the relation $$\dfrac {1}{f(D)}e^{cx} = \dfrac{1}{f(c)} e^{cx},~f(c) \ne 0$$
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    Calculating the value of 1/{D^2+a^2} sin ax

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    Calculus Difference between Calculus 4th edition and Calculus 3rd edi

    Thank you everyone for your replies. i bought the 4th edition itself
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    Calculus Difference between Calculus 4th edition and Calculus 3rd edi

    Difference between Calculus 4th edition and Calculus 3rd edition by Michael Spivak? I currently possesses Calculus 3rd edition by Michael Spivak in it's electronic form. However, I am considering buying a hard copy and have the option of buying either a used 3rd edition or a new 4th edition...
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    Graduate Algebraic Multiplicity of an Eigenvalue

    No problem :) . Do you think I made a good attempt at the proof? I just think i got stuck in the last stage of the proof
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    Graduate Algebraic Multiplicity of an Eigenvalue

    Thank you for the answer. The notes which I have say that the number of times λ appears on the diagonal of an upper triangular matrix is equal to dim null [T - λ I] dim V. Do you think there is error in this statement as well?" I have actually attempted the proof to prove this statement. Sorry...
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    Graduate Algebraic Multiplicity of an Eigenvalue

    Please have a look at the attached images.I am attempting a proof for the statement : The algebraic multiplicity of an eigen value λ is equal to dim null [T - λ I] dim V. Please advise me on how to move ahead. Apparently, I am at the final inference required for a proof but unable to move...
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    Every open subset of R^p is the union of countable collection of

    I think I got it. Thank you for your comments
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    Every open subset of R^p is the union of countable collection of

    Every open sub set of Rp is the union of countable collection of closed sets. I am attaching my attempt as an image file. Please guide me on how I should move ahead. Thank you very much for your help.
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    Graduate Prove that U_{m/n_1} (m) ,U_{m/n_k} (m) are normal subgroups

    prove that U_{m/n_1} (m) , ... U_{m/n_k} (m) are normal subgroups In the attached image I have proved that U_{m/n_1} (m) , ... U_{m/n_k} (m) are normal subgroups But how do i Prove that U(m) = U_{m/n_1} (m) ... U_{m/n_k} (m)? and that their intersection is identity alone. Help will be...
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    Supose that G is a finite abelian group that does not contain a subgro

    and pg. no 50
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    Supose that G is a finite abelian group that does not contain a subgro

    Supplementary exercise for chapters 5 - 8 . Question no. 50 . Gallian 7/e contemporary guide to abstract algebra
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    Supose that G is a finite abelian group that does not contain a subgro

    the book which i am reading ( GAllian ) has not introduced this topic as of yet. In fact, not even normal and factor groups. i am on the chapter on external direct products.
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    Supose that G is a finite abelian group that does not contain a subgro

    If |G| =p1p2...pn and all of the primes are different, then |H| will be one of those primes. Since a group of prime order is cyclic, then H will be cyclic in that case . In fact all proper subgroups of G will be cyclic. but i am not sure how to prove G as cyclic with this data..