MTH 465—Lectures in Geometry

Provides a broader understanding of differential geometry. Comprehensively introduces the theory of curves and surfaces in space. Moves toward the goal of viewing surfaces as special concrete examples of differentiable manifolds, reached by studying surfaces using tools that are basic to studying manifolds. Topics include curves in 3-D space, differential forms, Frenet formulae, patch computations, curvature, isometries, intrinsic geometry of surfaces. Serves as an introduction to more advanced courses involving differentiable manifolds.