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【導(dǎo)讀】力問題,特別是當(dāng)驅(qū)動力為不連續(xù),脈衝或是正弦,餘弦及更複雜的周期性函數(shù).之齊次方程式之解.
【正文】 Transforms Suppose that f(x) is defined on [0, ?]. We define the Fourier sine transform to be )]x(f[dx)xs in ()x(f)(f? s0s ????? ? ?? ? ????? 0 s d)xs in ()(f?2)x(fIf Kx,0Kx0,1{)x(f????)]Kc os (1[1dx)xs i n (dx)xs i n ()x(f)(f? K00s ????????? ?? ?Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Fourier Sine Transforms Theorem 1. )]x(g[)]x(f[)]x(g)x(f[sss ??????2. )]x(f[)]x(f[ss ?????for any constant ? 3. Let f(x) and f ’(x) be piecewise continuous on [0,?]. Assume also that limx? ? f(x) = limx? ? f ‘(x) = 0, then )0(f)]x(f[)]x(f[ s239。39。s ????????? ??? ???????? 0 39。039。0 39。39。39。39。s dx)]xc o s ()[x(f)]xs i n ()x(f[dx)xs i n ()x(f)]x(f[)0(f)]x(f[}dx)]xs i n ()[x(f)]x(f)x{ [ c o s ( s200 ?????????????? ? ??Proof Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Fourier Cosine Transforms Suppose that f(x) is defined on [0, ?]. We define the Fourier cosine transform to be )]x(f[dx)xc o s ()x(f)(f? c0c ????? ? ?? ? ????? 0 c d)xc os ()(f?2)x(fIf Kx,0Kx0,1{)x(f????)]K[ s i n (1dx)xc os (dx)xc os ()x(f)(f? K00c ???????? ?? ?Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Fourier Cosine Transforms Theorem 1. )]x(g[)]x(f[)]x(g)x(f[ccc ??????2. )]x(f[)]x(f[cc ?????for any constant ? 3. Let f(x) and f ’(x) be piecewise continuous on [0,?]. Assume also that limx? ? f(x) = limx? ? f ‘(x) = 0, then )0(f)]x(f[)]x(f[ 39。c239。39。c ??????Proof Homework Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Fourier Transforms Definition : )]x(f[dxe)x(f)(f? xi ???? ? ??? ??? ??? ? ???? de)(f?21)x(f xi1. )]x(g[)]x(f[)]x(g)x(f[ ??????2. )]x(f[)]x(f[ ????? for any constant ? 3. If )(f?)i()]x(f[ n)n( ????0)x(flim)x(flim)x(flim)x(flim )1n(x39。39。x39。xx ???????? ?????????????and are sectionally continuous on [?,?], then )x(f) , . . . . . ,x(f)1n( ?Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Chapter 5 Laplace Transforms
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