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This textbook is for the standard, one-semester, junior-senior course that often goes by the title Elementary Partial Differential Equations or Boundary Value Problems. The audience consists of students in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains. The text differs from other texts in that it is a brief treatment; yet it provides coverage of the main topics usually studied in the standard course as well as an introduction to using computer algebra packages to solve and understand partial differential equations. To give this text an even wider appeal, the 2nd edition has been updated with a new chapter on partial differential equation models in biology, and with various examples from the life sciences throughout the text. There are more exercises, as well as solutions and hints to some of the problems at the end of the book.