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This question already has an answer here:

I have recently started teaching. It gets totally blank in front of the big crowd. Now, I am quite confused about how to start teaching the Fourier transform and Fourier series chapter.

I want students be convinced and motivated to learn this difficult concept .

Can anybody give mathematical explanation about

How Fourier Analysis is performed ? Can anybody give a simple example?

How Fourier Synthesis is performed ? Can anybody give a simple example ?

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marked as duplicate by Wrzlprmft, Chris C, Joonas Ilmavirta, Benjamin Dickman, Karl May 21 '15 at 19:53

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ The question of what is the need and why are they important has already been asked: matheducators.stackexchange.com/questions/7469/… $\endgroup$ – DavidButlerUofA May 17 '15 at 8:48
  • $\begingroup$ @DavidButlerUofA OK sir .I have skipped Fourier series from the question $\endgroup$ – devraj May 17 '15 at 9:01
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    $\begingroup$ General advice for beginning teachers: follow the textbook! Especially in elementary courses. Do not try to do anything different. $\endgroup$ – Gerald Edgar May 17 '15 at 13:18
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You could make the connection between Fourier synthesis and (musical) synthesizers. Maybe you could play some interesting tones from a synthesizer. How do we figure out what goes into the synthesis? Fourier analysis.

A lot of students will (sadly) shut down while you're telling them things that "won't be on the test". It would help if you could repeatedly loop back to the example as you cover topics in Fourier analysis.

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My opinion is that, as a teacher, you aren't responsible for "convincing" students that this is an interesting topic. You just have to teach it so that the subset of students that is actually hardworking will be able to solve the problems on the final exam.

You can give some general motivational examples from digital signal processing, but, honestly, an introductory course doesn't remotely bring students close to modern practical application along these lines.

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    $\begingroup$ I down-voted because (1) you have not answered the question, and (2) you have the sentence: "You just have to teach it so that the subset of students that is actually hardworking will be able to solve the problems on the final exam." $\endgroup$ – Benjamin Dickman May 18 '15 at 21:40
  • $\begingroup$ @BenjaminDickman Reason (1) is fair enough I suppose. $\endgroup$ – Atsby May 19 '15 at 2:25

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