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b.sc2 sem3 maths by dr dk pandey sir

HIGHR MATHMATICS BY DR DK PANDAY SIR・10 minutes read

The text discusses the Fourier series of a function in the interval from minus pi to pi, with A0 being a crucial component determined by the integral of the function. It explains the characteristics of an even function, emphasizing the calculation of A0 as an essential step in the process.

Insights

  • A0 in the Fourier series formula is derived from the integral of the function over its defined interval, reflecting the average value of the function over that range.
  • The concept of an even function is introduced, where symmetry around the y-axis is observed, indicating that the function remains unchanged when x is replaced with -x.

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Recent questions

  • What is the Farrier coefficient?

    A

  • How is an even function characterized?

    A

  • What is the formula for A0 in the Fourier series?

    A

  • How is Function A defined in the given interval?

    A

  • What is the period of the Fourier series?

    A

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Summary

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"Fourier Series: A0, A, B Explained"

  • Function A is defined in the interval from minus pi to pi.
  • The Farrier coefficient consists of A0, A, and B in the Fourier series.
  • A0 is determined by the value of 1 over 2pi times the integral of A(x) from minus pi to pi.
  • The even function is characterized by f(x) being unchanged when replacing x with -x.
  • The value of A0 is calculated as 1 over pi times the integral of f(x)cos(ax) from minus pi to pi.
  • The Fourier series of function f(x) is expressed in the interval from minus pi to pi with a period of 2pi.
  • The Fourier series formula includes A0, A, and B, with A0 being the integral of f(x) from minus pi to pi divided by 2pi.
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