Differential geometry is a major field of mathematics that uses tools from calculus, in particular integrals and derivatives, to study problems in geometry. Differential geometry has applications in several fields, including physics, economics, engineering, and computer vision. This book focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems look at how local properties relate to global ones. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena. Each section includes numerous interesting exercises that range from straightforward to challenging.
