## A unique approach to Fourier's series and integral: With complete proofs for all the topics discussedEssay from the year 2011 in the subject Mathematics - Analysis, , language: English, abstract: This essay is a unique approach to Fourier's series and integral with complete proofs for all the topics discussed. |

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a-X a-X Alternating current approach to Fourier's appropriate function f(x appropriate selected f(x average value axis Setting t-x Bessel's inequality Bredakis Calculus change the value continuous at selected continuous function COS2X COS6X COSC cosk costk COSX delta function Dirac's domain a-X dt converges Euler's formula f x+ fixed somewhere fixed tt Fourier's series function Fourier's coefficients function R t-x graph Iff f(x iff k=O improper integral integrand function integration of ol integration of oo odd function f(t OO cos x/2 OO f(x oo oo Oo Principal OO Provided OO Sf oo sinx oo to oo orthogonality properties proof properties of trigonometric Remainder function Fourier's rn x semiperiod series and integral sin3x sin5x Sf sinkx sinx sin2x sinx sin2x sin3x smooth curve t-oo TI-X domain to.t triangular impulse trigonometric integrals Trigonometric serial expansion unique approach unit interval x=O this f(x