In what subject is the Fourier Transform and Fourier Series introduced?

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Typically, what subject introduces these?




soft-question fourier-analysis fourier-series fourier-transform




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  • 4




    The aptly named "Fourier Analysis" (but also classes on Real Analysis)
    – Lorenzo
    Jan 23 '17 at 21:29







  • 1




    PDE's, signal pricessing, mathematical methods for physicists and engineers, etc.
    – Mark Viola
    Jan 23 '17 at 21:35






  • 1




    Ordinary and Partial Differential Equations (ODEs and PDEs) are usually subjects where Fourier analysis is introduced for a lot of undergraduates. Some study it from the first semester (electronic engineers) and for some its neither. Fourier touches a lot of subjects in physics and engineering, so don't worry, you'll get to it sooner or later.
    – Ofek Gillon
    Jan 23 '17 at 21:35






  • 1




    My personal experience involved a class titled "Lebesgue Measure and Fourier Analysis". It proved to be quite challenging for an undergrad course but also quite rewarding..Outside of strictly Math studies, well engineering has a variety of applications which involve Fourier transforms, such as signal processing..
    – MathematicianByMistake
    Jan 23 '17 at 21:45






  • 1




    To be a bit more specific, it comes as a very natural tool in the analysis of Linear Time Invariant systems(LTI).
    – WalterJ
    Jan 23 '17 at 21:53














up vote
1
down vote

favorite












Typically, what subject introduces these?




soft-question fourier-analysis fourier-series fourier-transform




share|cite|improve this question
















  • 4




    The aptly named "Fourier Analysis" (but also classes on Real Analysis)
    – Lorenzo
    Jan 23 '17 at 21:29







  • 1




    PDE's, signal pricessing, mathematical methods for physicists and engineers, etc.
    – Mark Viola
    Jan 23 '17 at 21:35






  • 1




    Ordinary and Partial Differential Equations (ODEs and PDEs) are usually subjects where Fourier analysis is introduced for a lot of undergraduates. Some study it from the first semester (electronic engineers) and for some its neither. Fourier touches a lot of subjects in physics and engineering, so don't worry, you'll get to it sooner or later.
    – Ofek Gillon
    Jan 23 '17 at 21:35






  • 1




    My personal experience involved a class titled "Lebesgue Measure and Fourier Analysis". It proved to be quite challenging for an undergrad course but also quite rewarding..Outside of strictly Math studies, well engineering has a variety of applications which involve Fourier transforms, such as signal processing..
    – MathematicianByMistake
    Jan 23 '17 at 21:45






  • 1




    To be a bit more specific, it comes as a very natural tool in the analysis of Linear Time Invariant systems(LTI).
    – WalterJ
    Jan 23 '17 at 21:53












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Typically, what subject introduces these?




soft-question fourier-analysis fourier-series fourier-transform




share|cite|improve this question












Typically, what subject introduces these?





soft-question fourier-analysis fourier-series fourier-transform





share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 23 '17 at 21:27









user409495

61




61







  • 4




    The aptly named "Fourier Analysis" (but also classes on Real Analysis)
    – Lorenzo
    Jan 23 '17 at 21:29







  • 1




    PDE's, signal pricessing, mathematical methods for physicists and engineers, etc.
    – Mark Viola
    Jan 23 '17 at 21:35






  • 1




    Ordinary and Partial Differential Equations (ODEs and PDEs) are usually subjects where Fourier analysis is introduced for a lot of undergraduates. Some study it from the first semester (electronic engineers) and for some its neither. Fourier touches a lot of subjects in physics and engineering, so don't worry, you'll get to it sooner or later.
    – Ofek Gillon
    Jan 23 '17 at 21:35






  • 1




    My personal experience involved a class titled "Lebesgue Measure and Fourier Analysis". It proved to be quite challenging for an undergrad course but also quite rewarding..Outside of strictly Math studies, well engineering has a variety of applications which involve Fourier transforms, such as signal processing..
    – MathematicianByMistake
    Jan 23 '17 at 21:45






  • 1




    To be a bit more specific, it comes as a very natural tool in the analysis of Linear Time Invariant systems(LTI).
    – WalterJ
    Jan 23 '17 at 21:53












  • 4




    The aptly named "Fourier Analysis" (but also classes on Real Analysis)
    – Lorenzo
    Jan 23 '17 at 21:29







  • 1




    PDE's, signal pricessing, mathematical methods for physicists and engineers, etc.
    – Mark Viola
    Jan 23 '17 at 21:35






  • 1




    Ordinary and Partial Differential Equations (ODEs and PDEs) are usually subjects where Fourier analysis is introduced for a lot of undergraduates. Some study it from the first semester (electronic engineers) and for some its neither. Fourier touches a lot of subjects in physics and engineering, so don't worry, you'll get to it sooner or later.
    – Ofek Gillon
    Jan 23 '17 at 21:35






  • 1




    My personal experience involved a class titled "Lebesgue Measure and Fourier Analysis". It proved to be quite challenging for an undergrad course but also quite rewarding..Outside of strictly Math studies, well engineering has a variety of applications which involve Fourier transforms, such as signal processing..
    – MathematicianByMistake
    Jan 23 '17 at 21:45






  • 1




    To be a bit more specific, it comes as a very natural tool in the analysis of Linear Time Invariant systems(LTI).
    – WalterJ
    Jan 23 '17 at 21:53







4




4




The aptly named "Fourier Analysis" (but also classes on Real Analysis)
– Lorenzo
Jan 23 '17 at 21:29





The aptly named "Fourier Analysis" (but also classes on Real Analysis)
– Lorenzo
Jan 23 '17 at 21:29





1




1




PDE's, signal pricessing, mathematical methods for physicists and engineers, etc.
– Mark Viola
Jan 23 '17 at 21:35




PDE's, signal pricessing, mathematical methods for physicists and engineers, etc.
– Mark Viola
Jan 23 '17 at 21:35




1




1




Ordinary and Partial Differential Equations (ODEs and PDEs) are usually subjects where Fourier analysis is introduced for a lot of undergraduates. Some study it from the first semester (electronic engineers) and for some its neither. Fourier touches a lot of subjects in physics and engineering, so don't worry, you'll get to it sooner or later.
– Ofek Gillon
Jan 23 '17 at 21:35




Ordinary and Partial Differential Equations (ODEs and PDEs) are usually subjects where Fourier analysis is introduced for a lot of undergraduates. Some study it from the first semester (electronic engineers) and for some its neither. Fourier touches a lot of subjects in physics and engineering, so don't worry, you'll get to it sooner or later.
– Ofek Gillon
Jan 23 '17 at 21:35




1




1




My personal experience involved a class titled "Lebesgue Measure and Fourier Analysis". It proved to be quite challenging for an undergrad course but also quite rewarding..Outside of strictly Math studies, well engineering has a variety of applications which involve Fourier transforms, such as signal processing..
– MathematicianByMistake
Jan 23 '17 at 21:45




My personal experience involved a class titled "Lebesgue Measure and Fourier Analysis". It proved to be quite challenging for an undergrad course but also quite rewarding..Outside of strictly Math studies, well engineering has a variety of applications which involve Fourier transforms, such as signal processing..
– MathematicianByMistake
Jan 23 '17 at 21:45




1




1




To be a bit more specific, it comes as a very natural tool in the analysis of Linear Time Invariant systems(LTI).
– WalterJ
Jan 23 '17 at 21:53




To be a bit more specific, it comes as a very natural tool in the analysis of Linear Time Invariant systems(LTI).
– WalterJ
Jan 23 '17 at 21:53










2 Answers
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I took a class called "Systems and Transforms" where we introduced fourier transform and laplace transforms to solve differential equations of the form $y'' +ay' + y =f(t)$. In a class about PDE:s called "continuous systems" we introduced the fourier series and showed for which PDE:s the series was a solution. And now I'm taking a class in fourier analysis.






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    Also modern number theory makes intense use of Fourier transform, Fourier series, and many other integral/spectral transforms and decompositions. Spherical harmonics, for example. When I teach (graduate) courses on number theory or modular forms or representation theory or... certainly Fourier series and Fourier transforms play a central role.






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      2 Answers
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      I took a class called "Systems and Transforms" where we introduced fourier transform and laplace transforms to solve differential equations of the form $y'' +ay' + y =f(t)$. In a class about PDE:s called "continuous systems" we introduced the fourier series and showed for which PDE:s the series was a solution. And now I'm taking a class in fourier analysis.






      share|cite|improve this answer
























        up vote
        0
        down vote













        I took a class called "Systems and Transforms" where we introduced fourier transform and laplace transforms to solve differential equations of the form $y'' +ay' + y =f(t)$. In a class about PDE:s called "continuous systems" we introduced the fourier series and showed for which PDE:s the series was a solution. And now I'm taking a class in fourier analysis.






        share|cite|improve this answer






















          up vote
          0
          down vote










          up vote
          0
          down vote









          I took a class called "Systems and Transforms" where we introduced fourier transform and laplace transforms to solve differential equations of the form $y'' +ay' + y =f(t)$. In a class about PDE:s called "continuous systems" we introduced the fourier series and showed for which PDE:s the series was a solution. And now I'm taking a class in fourier analysis.






          share|cite|improve this answer












          I took a class called "Systems and Transforms" where we introduced fourier transform and laplace transforms to solve differential equations of the form $y'' +ay' + y =f(t)$. In a class about PDE:s called "continuous systems" we introduced the fourier series and showed for which PDE:s the series was a solution. And now I'm taking a class in fourier analysis.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 23 '17 at 21:39









          Olba12

          1,051615




          1,051615




















              up vote
              0
              down vote













              Also modern number theory makes intense use of Fourier transform, Fourier series, and many other integral/spectral transforms and decompositions. Spherical harmonics, for example. When I teach (graduate) courses on number theory or modular forms or representation theory or... certainly Fourier series and Fourier transforms play a central role.






              share|cite|improve this answer
























                up vote
                0
                down vote













                Also modern number theory makes intense use of Fourier transform, Fourier series, and many other integral/spectral transforms and decompositions. Spherical harmonics, for example. When I teach (graduate) courses on number theory or modular forms or representation theory or... certainly Fourier series and Fourier transforms play a central role.






                share|cite|improve this answer






















                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Also modern number theory makes intense use of Fourier transform, Fourier series, and many other integral/spectral transforms and decompositions. Spherical harmonics, for example. When I teach (graduate) courses on number theory or modular forms or representation theory or... certainly Fourier series and Fourier transforms play a central role.






                  share|cite|improve this answer












                  Also modern number theory makes intense use of Fourier transform, Fourier series, and many other integral/spectral transforms and decompositions. Spherical harmonics, for example. When I teach (graduate) courses on number theory or modular forms or representation theory or... certainly Fourier series and Fourier transforms play a central role.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Oct 4 '17 at 21:16









                  paul garrett

                  30.9k360116




                  30.9k360116






















                       

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