数学分析数学分析PPT (14).pdf
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1、?(a)(b)?E tAt()sin?16.1.5(a)?f tA12()(sin?ftAt2()|sin|tt|sin|)?16.1.5(b)?)x)?1fx1(f2(,?Fourier?0a?11()f x dx?F2A?an?11()cosf xnxdx22(1An?)?2,4,6,n?Fna?11()cos0f xnxdx?F?1,3,5,n?1b?11()sin2Af xxdx?F?bn?11()sin0f xnxdx?F?2,3,4,n?1()f x?212cos2sin24k1AAAxk?kx?0a?21()fx dx?F4A?an?21()cosfxnxdx24(1An?)?2
2、,4,6,n?Fna?21()cos0fxnxdx?F?1,3,5,n?bn?21()sin0fxnxdx?F?1,2,3,n?2()fx?12142cos42kkkxAA?,?Fourier?xxfsgn)(?;?f xx()|cos|?;1?222)(?xxf;?f x()?);,0,0),0,?xxx?f x()?).,0,),0,?xbxxax?()f x0na?0,1,2,n?bn?1()sinf xnxdx?F2(1 cos()nn?1,2,3,n?()f x?112)12sin(4kkxk?()f x0nb?1,2,3,n?0a?1()f x dx?F4?na?1()cosf x
3、nxdx224(1)(1nn?)?2,4,6,n?Fna?1()cos0f xnxdx?F?1,3,5,n?()f x?122cos14)1(42kkkxk?()f x0nb?1,2,3,n?0a?1()f x dx?F253?na?1()cosf xnxdx22(1)nn?1,2,3,n?F()f x?nxnnncos)1(265122?0a?1()f x dx?F2?na?1()cosf xnxdx21(1)nn?1,2,3,n?Fbn?1()sinf xnxdx?Fcos()nn?1,2,3,n?()f x?02)12()12cos(24kkxk?nxnnnsin)1(11?0a?1()
4、f x dx?F()2ba?2na?1()cosf xnxdx?F2()(1(1)nabn?)?1,2,3,n?bn?1()sinf xnxdx()cos(abnn)?1,2,3,n?F()f x?02)12()12cos()(24)(kkxkbaba?nxnbannsin)1()(11?xxf?)(?,0?x;?f xx()e?2?,0?x;?f x()?;,),0,222?xxx?f x()?.2,1,0),1,0,2cosxxx?bn?02()sinf xnxdx?F1 2(1)2nn?2?1,2,3,n?()f x?11 2(1)2snnnxn?in?bn?02()sinf xnxdx
5、?F2221(1)(4)nnen?-#?,?1,2,3,n?()f x?*nxnennnsin4)1(12122?bn?02()sinf xnxdx?F22(1)2sin2nnnn?-#?+!,?1,2,3,n?()f x?nxnnnnnsin2sin4)1(2121?!#+,-?1b?2021()sin2f xxdx?F?bn?202()sin2f xnxdxF22(sin)2(1)nnn?2,3,4,n?()f x?xnnnnxn2sin12sin22sin122?f xxx()()?,0?x;?f xx()e?,0?x;3?f x()?;,1),0,2sin244?xxx?22)(?xx
6、xf?,0?x.?0a?02()f x dx?F23?na?02()cosf xnxdx?F22(1(1)nn?1,2,3,n?()f x?1222cos6kkkx?0a?02()f x dx?F2(1e?)?na?02()cosf xnxdx?F22(1)1(1)nen?-#?,?1,2,3,n?()f x?)1(1?e*nxnenncos11)1(212?0a?204()f x dx?F2?1a?204()cos2f xxdx?F1?na?204()cos2f xnxdx?F22sin(1)2nnnn?&)?$?%(?2,3,4,n?()f x?111()cos222211sin1 cos
7、212nnnxnn?&)?$?%(?2x?0a?02()f x dx?F2?na?02()cosf xnxdx?F24(1)cos2nnn?-#?+!,?1,2,3,n?()f x?nxnnnncos2cos)1(4412?!#+,-?2?2,?aa?Fourier?f x()4?f x()aanxbnnnn012?(cossin x)?2201()cos(cossin)cos2aannaanaf xmxdxanxbnxmxdx?-#?+!,?FF?22201cos(coscossincos)2aaannaaanamxdxanxmxdx bnxmxdx?FFF?ma?0,1,2,m?2201(
8、)sin(cossin)sin2aannaanaf xmxdxanxbnxmxd?-#?+!,?FFx?22201sin(cossinsinsin)2aaannaaanamxdxanxmxdx bnxmxdx?FFF?mb?1,2,m?an?F?2cos)(1aanxdxxf?,2,1,0?n?bn?F?2sin)(1aanxdxxf?,2,1?n?Fourier?2)(xxf?2,0?x;?f xx()?2?2,0?x;?xxf?)(?;x?,0 1?f x()?);1,0,0),0,1,e3xxx?f x()?),0,0),0,TxTxC?C?).?na?201()cos0f xnxdx?
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