@MISC{PDIFFEQ1.MIZ,
  AUTHOR = {Otsuki, Sora and Kawamoto, Pauline N. and Yamazaki, Hiroshi},
  TITLE = {A Simple Example for Linear Partial Differential Equations and
    Its Solution Using the Method of Separation of Variables},
  SECTION1 = {Preliminaries},
  SECTION2 = {The Method of Separation of Variables for One-dimensional Wave Equation},
  SECTION3 = {The Superposition Principle},
  DAY = {27},
  MONTH = {February},
  YEAR = {2019},
  ADDRESS1 = {Shinshu University, Nagano, JAPAN},
  ADDRESS2 = {Shinshu University, Nagano, JAPAN},
  ADDRESS3 = {Shinshu University, Nagano, JAPAN},
  SUMMARY = {In this article, we formalized simple partial differential
  equations.  In the first section, we formalized partial differentiability
  and partial derivative.  The next section contains the method of separation
  of variables for one-dimensional wave equation.  In the last section, we
  formalized the superposition principle.},
  ACKNOWLEDGEMENT = {We would like to thank Yasunari Shidama
  for useful advice on formalizing theorems.}}
