Unique in its approach, content, and perspective, this book helps readers bridge the application gap between mathematics and chemistry and to acquire a fuller set of mathematical tools necessary for such applications. Using an abundance of fully-worked examples, it shows step-by-step how to directly apply mathematics to physical chemistry problems. It features numerous problems, many multi-part, that use the symbolism found in standard physical chemistry books or involve actual physical chemistry equations. It offers full-chapter coverage of many important topics relegated to appendices in other books. It also provides a full chapter on numerical methods and computer programming showing step-by-step how to write programs to do numerical integration, and covers areas of advanced mathematics - e.g., differential equations and operator mechanics.