This book provides an introduction to the basic properties of partial differential equations and to techniques that have proved useful in analyzing them. It is an undergraduate textbook, but graduate students, especially in the sciences, could surely learn from it.
The presentation is based on the following principles: All the important ideas can be understood in terms of the three classical equations. Do one spatial dimension before going onto more dimensions with their more complicated geometries. Do problems without boundaries before bringing in boundary conditions. Do not hesitate to present some facts without proofs, but provide the most critical proofs. Provide introductions to a variety of important advanced topics.
The titles of the chapters are: Where PDEs come from. Waves and diffusions. Reflections and sources. Boundary problems. Fourier series. Harmonic functions. Green’s identities and Green’s functions. Computation of solutions. Waves in space. Boundaries in the plane and in space. General eigenvalue problems. Distributions and transforms. PDE problems from physics. Nonlinear PDEs.