For courses in Partial Differential Equations taken by mathematics and engineering majors. An alternative to the obscure, jargon-heavy tomes on PDEs for math specialists and the cookbook, numerics-based “user manuals” (which provide little insight and questionable accuracy), this text presents full coverage of the analytic (and accurate) method for solving PDEs — in a manner that is both decipherable to engineering students and physically insightful for math students. The exposition is based on physical principles instead of abstract analyses, making the presentation accessible to a larger audience.