This example-rich text fosters a smooth transition from elementary ordinary differential equations courses to more advanced concepts in a first course on PDEs. Asmar's relaxed style and emphasis on applications make the material accessible even to students with limited exposure to topics beyond calculus. Computer use is encouraged for illustrating results and applications, but the text is also suitable for use without computer access. The Second Edition has added more engineering and physics applications; more optional mathematical proofs; a new chapter on Green's Theorem and Conformal Mappings; and more geometric presentations throughout.