Corresponding exercises and quiz. 第四章Residue Theorem 1.教学日目标 Master the calculation of the residue of an analytical function at the pole understand the general proof of the residue theorem,and get familiar with different techniques to apply the residue theorem to calculate the integrals. 2.教学难点 The concept of residue and its calculations,residue theorem and its application to the calculation of various integrals. 3.教学内容 A.the definition of the residue based on the laurent expansion. B.the proof of the residue theorem based on the Cauchy integral theorem. C.Various techniques to calculate the residue,especially at the rank 1 pole. D.the application of the residue theorem to the calculation of the integrals. 1.the integrals of trigonometric function 2.the integrals over the whole real axis 3.the appropriate choice of the closed contours E.Principle integral 4.教学方法 Lectures,discussions,etc. 5.教学评价 Corresponding exercises and quiz. 第五章Laplace Transform and Fourier Analysis 1.教学目标 Master the Laplace transform,the Fourier series of a periodic function,the derivation of Fourier integrals,and the inverse Fourier transformation. 2.教学难点Corresponding exercises and quiz. 第四章 Residue Theorem 1. 教学目标 Master the calculation of the residue of an analytical function at the pole, understand the general proof of the residue theorem, and get familiar with different techniques to apply the residue theorem to calculate the integrals. 2. 教学难点 The concept of residue and its calculations, residue theorem and its application to the calculation of various integrals. 3. 教学内容 A. the definition of the residue based on the Laurent expansion. B. the proof of the residue theorem based on the Cauchy integral theorem. C. Various techniques to calculate the residue, especially at the rank 1 pole. D. the application of the residue theorem to the calculation of the integrals. 1. the integrals of trigonometric function 2. the integrals over the whole real axis 3. the appropriate choice of the closed contours E. Principle integral 4.教学方法 Lectures, discussions, etc. 5.教学评价 Corresponding exercises and quiz. 第五章 Laplace Transform and Fourier Analysis 1. 教学目标 Master the Laplace transform, the Fourier series of a periodic function, the derivation of Fourier integrals, and the inverse Fourier transformation. 2. 教学难点