Classification of the singularity d definition o 4 Problem 6,13,14; poles Definition of residue based on the 4 Laurent Prob1e7,8.9,10 expansion Various techniques to calculate the and the 8 Prob1em11,12,15,16 residue theorem to the integrals Fourier series and 9 5 the derivation of 4 the Fourier integrals Several theorems of the Fourier 10 5,6 introduction 0 4 Prob1em11,12,13,14,15,16 the partia. differential equations Use separation of 11 6 4 Problem 11,12 transform into several ODEs Classification of 2order ODEs 12 based on the 4 Problem 4.5,6 singularity properties Series method to solve ODEs.the 13 4 independent Problem 1,2,7,8 solutions The Laplace operator in the 4 spberical 4 Problem 2,3 coordinate system, and 6 4 Classification of the singularity and definition of poles 4 Problem 6，13,14； 7 4 Definition of residue based on the Laurent expansion 4 Problem 7,8,9,10 8 4 Various techniques to calculate the residues and the application of the residue theorem to the integrals 8 Problem 11,12,15,16 9 5 Fourier series and the derivation of the Fourier integrals 4 10 5,6 Several theorems of the Fourier analysis, introduction on the partial differential equations 4 Problem11,12,13,14,15,16； 11 6 Use separation of variables to transform PDE into several ODEs 4 Problem 11,12 12 7 Classification of 2 nd order ODEs based on the singularity properties 4 Problem 4,5,6 13 7 Series method to solve ODEs, the two independent solutions 4 Problem 1,2,7,8 14 8 The Laplace operator in the spherical coordinate system, and 4 Problem 2,3