北京大学：《数学物理方法》精品课程电子教案（A类）第一部分 复变函数_第14讲 Laplace变换

Outline 第十四讲 Laplace变换 北京大学物理学院 2007年春

Outline 1 › o ù Laplace C † ®ŒÆÔnÆ 2007cS C. S. Wu 1›où LaplaceC†

Outline 讲授要点 O Laplace变换 定义 Laplace变换的基本性质 ③ Laplace变换的反演 Laplace变换像函数的必要条件 Laplace变换的反演 普遍反演公式

Outline ùLJ: 1 LaplaceC† ½Â LaplaceC†Ä5Ÿ 2 LaplaceC†‡ü LaplaceC†¼ê7‡^‡ LaplaceC†‡ü ÊH‡üúª C. S. Wu 1›où LaplaceC†

Outline 讲授要点 O Laplace变换 定义 Laplace变换的基本性质 ② Laplace变换的反演 Laplace变换像函数的必要条件 Laplace变换的反演 普遍反演公式

Outline ùLJ: 1 LaplaceC† ½Â LaplaceC†Ä5Ÿ 2 LaplaceC†‡ü LaplaceC†¼ê7‡^‡ LaplaceC†‡ü ÊH‡üúª C. S. Wu 1›où LaplaceC†

TransforM References 吴崇试,《数学物理方法》,第9章 ¤梁昆淼,《数学物理方法》,第6章 ¤胡嗣柱、倪光炯,《数学物理方法》,§6.1 6.2.6.3

Laplace Transform Inverse Laplace Transform References ÇÂÁ§5êÆÔn{6§19Ù ù&œ§5êÆÔn{6§16Ù nÎ!X1Á§5êÆÔn{6§§6.1, 6.2, 6.3 C. S. Wu 1›où LaplaceC†

Inverse ties of Laplace transform Laplace变换(简称拉氏变换)是常用的一种积 分变换,在数学、物理及工程科学中有广泛 的应用 本节介绍 Laplace变换的定义及其基本性质

Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform LaplaceC†({¡.¼C†)´~^«È ©C†©3êÆ!Ôn9ó§‰Æ¥k2 A^ !0LaplaceC†½Â9ÙÄ5Ÿ C. S. Wu 1›où LaplaceC†

Inverse ties of Laplace transform Laplace变换(简称拉氏变换)是常用的一种积 分变换,在数学、物理及工程科学中有广泛 的应用 ●本节介绍 Laplace变换的定义及其基本性质

Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform LaplaceC†({¡.¼C†)´~^«È ©C†©3êÆ!Ôn9ó§‰Æ¥k2 A^ !0LaplaceC†½Â9ÙÄ5Ÿ C. S. Wu 1›où LaplaceC†

讲授要点 O Laplace变换 定义 Laplace变换的基本性质 O Laplace变换的反演 Laplace变换像函数的必要条件 Laplace变换的反演 普遍反演公式

Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform ùLJ: 1 LaplaceC† ½Â LaplaceC†Ä5Ÿ 2 LaplaceC†‡ü LaplaceC†¼ê7‡^‡ LaplaceC†‡ü ÊH‡üúª C. S. Wu 1›où LaplaceC†

Definition Laplace变换是一种积分变換,它把f(t)变换为 F(p) F(p)=/e-pt f(t)dt

Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC†´«È©C†§§rf(t)C† F(p) F(p) = Z ∞ 0 e −ptf(t) dt ùpt´¢ê§p´Eê§p = s + iσ F(p)¡f(t)Laplace†ª§{¡.¼†ª e −pt´LaplaceC†Ø C. S. Wu 1›où LaplaceC†

Definition Laplace变换是一种积分变換,它把f(t)变换为 F(p) F(p)=/e-pt f(t)dt 这里的t是实数,p是复数,p=8+i F(P)称为f()的 Laplace换式,简称拉氏换式

Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC†´«È©C†§§rf(t)C† F(p) F(p) = Z ∞ 0 e −ptf(t) dt ùpt´¢ê§p´Eê§p = s + iσ F(p)¡f(t)Laplace†ª§{¡.¼†ª e −pt´LaplaceC†Ø C. S. Wu 1›où LaplaceC†

Definition Laplace变换是一种积分变換,它把f(t)变换为 F(p) F(p)=/e-pt f(t)dt 这里的t是实数,P是复数,p=s+io F(p)称为∫()的 Laplace换式,简称拉氏换式 e是 Laplace变换的核

Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC†´«È©C†§§rf(t)C† F(p) F(p) = Z ∞ 0 e −ptf(t) dt ùpt´¢ê§p´Eê§p = s + iσ F(p)¡f(t)Laplace†ª§{¡.¼†ª e −pt´LaplaceC†Ø C. S. Wu 1›où LaplaceC†