Differential Geometry and Its Applications

For undergraduate courses in Differential Geometry. Designed not just for the math major but for all students of science, this text provides an introduction to the basics of the calculus of variations and optimal control theory as well as differential geometry. It then applies these essential ideas to understand various phenomena, such as soap film formation and particle motion on surfaces. - NEW - New section on industrial applications of differential geometry - Shows engineering and physics students the practical applications of what they are learning to industry. - NEW - New Maple projects for calculation and visualization - Provides students with another practical side to pure math. - NEW - New examples for Gauss-Bonnet. - Immediate focus on surfaces - Allows the text to be used for a one-semester course while still covering interesting material that prepares students for future geometry courses. - Explorations of concepts using the symbolic computational software, MAPLE - Including how geodesics may be plotted on surfaces; an illustration of the Clairaut relation; how particles move under the influence of gravity, but constrained to a surface; why Ennepers surface is minimal,