This is a classroom-tested and developed textbook designed for use in either one- or two term courses in Partial Differential Equations taught at the advanced undergradute and beginning graduate levels of instruction. In addition to covering the standard PDE topics taught in such courses, there is a heavy focus on vector analysis. Maple examples and exercises for the students are presented strategically within the book, and an Appendix on Maple facilitates the use of this computer algebra language, acting as a quick reference source for readers. This book will have strong appeal to interdisciplinary audiences of engineers and scientists, particulary in regard to its treatments of fluid mechanics, heat equations, and continuum mechanics, inclusion of the latter being a unique feature of the presentation.