This revision is for the upper level course in partial differential equations (sometimes called Fourier Series and/or Boundary Value Problems) taken by math,physics,and engineering majors who have already taken calculus and differential equations. Pinsky's approach is an applied one. The second edition features new topics on perturbative solution of the vibrating string and vibrating membrane,Hermite polynomials and the uncertainty principle,variational methods,and systems of partial differential equations. Two new chapters covering Green's Functions and approximate Solutions have also been added as well as an appendix on using Mathematical Software to graph functions and solutions that occur in the text.