The core idea of 1. is to obtain a sufficient number of special solutions (fundamental system of solutions) of differential equations by using the superposition principle, and then linearly combine these special solutions to meet the given initial conditions.

2. Assume that the special solution of the nontrivial solution of separable variables u(x, t)=X(x)T(t) and require it to satisfy the homogeneous boundary conditions u(x, 0)=0 and u(x, π)=0.

3. After separating variables, t "(t)+λ A2t (t) = 0? X”(t)+λX(t)= 0 .

4. Find the general solution of X(x).

5. Determine the undetermined coefficient λ.

6. The special solution of Uk(x, t)=Xk(x)*Tk(t) is obtained.

7. According to the initial conditions, determine Ak and BK by Fourier series (A1,A2 in the title).

8. Substitute Ak and Bk into u(x, t) to get the solution of partial differential equation in series form.

Partial Differential Equation is an open online course in Xiamen University's massive open online courses and national top-quality courses. This course was first opened in the large-scale open network course of China University on March 1 2065, and was taught by Tan Zhong. According to the statistics of China University's large-scale open online course official website 2021July, this course has been started for 9 times.

This course consists of 8 chapters, including introduction: from music aesthetics to revealing quantum entanglement; The establishment of typical partial differential equation model: the basic concept, mathematical problems and classification of partial differential equation; Cauchy problem of high-dimensional wave equation; Energy method, extreme principle and Green's function method.