local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive computer graphics applets supported by sound theory.

The book explains the reasons for various definitions while the interactive applets offer motivation for certain definitions, allow students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits.

• Reworked presentation to make it more approachable

• More exercises, both introductory and advanced

• New section on the application of differential geometry to cartography

• Additional investigative project ideas

• Significantly reorganized material on the Gauss–Bonnet theorem

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