This text is designed to update the Differential Geometry course by making it more relevant to today's students. This new approach emphasizes applications and computer programs aimed at twenty-first-century audiences. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research. The course can require students to carry out a daunting amount of time-consuming hand computations like the computation of the Christoffel Symbols. As a result, the scope of the applied topics and examples possible to cover might be limited. In addition, most books on this topic have only a scant number of applications. The book is meant to evolve the course by including topics that are relevant to students. To achieve this goal the book uses numerical, symbolic computations, and graphical tools as an integral part of the topics presented.

The provides students with a set of Maple/Matlab programs that will enable them to explore the course topics visually and in depth. These programs facilitate topic and application integration and provide the student with visual enforcement of the concepts, examples, and exercises of varying complexity. This unique text will empower students and users to explore in-depth and visualize the topics covered, while these programs can be easily modified for other applications or other packages of numerical/symbolic languages. The programs are available to download to instructors and students using the book for coursework.