In a self-contained presentation, this book builds upon the standard mathematical background imparted in an undergraduate engineering program. It develops the often-encountered abstruse concepts by proceeding from concrete examples to abstract results. Based on the author's classroom experience, the author feels this approach will make it easier for readers to understand the subject efficiently. Practice-based and application-oriented, the book includes a number of chemical engineering optimal control problems in the examples and chapter problems that help readers practice the learned concepts.