MATH 4500.0001 Introduction to Differential Geometry I

FALL 2017

10:30A - 11:20A MWF 210 MLH

Office location: B20F MLH

Office hours: M W Th 9:00-10:20 and by appointment

Phone: 335-0774

E-mail: oguz-durumeric@uiowa.edu

Prerequisites: (MATH:3550 or MATH:2850) and (MATH:2700 or MATH:2550)

Description of the Course: Space curves, Frenet frames, intrinsic and extrinsic geometry of surfaces, first and second fundamental forms, isometries, Gauss map, Gaussian curvature, Theorema Egregium, geodesics, covariant differentiation; may include global theory of curves and Gauss-bonnet theorem.

 Objectives and Goals of the Course: We will study curves and surfaces in Euclidean spaces and introduce the notion of differentiable surfaces. The extrinsic properties of curves and surfaces in Euclidean Spaces will be studied and used to understand their intrinsic geometry. This will lay foundations to introduce the notion of abstract surfaces. We will study various "curvature" functions, and "extremal" objects, such as distance and energy minimizing curves on surfaces, and area minimizing surfaces. If the time permits, we will cover Gauss-Bonnet Theorem.

This course has heavy calculational content involving multivariable differential and integral calculus and linear algebra. The theory and geometric intuition will be introduced via derivations and calculations. The continuation of this course is MATH 4510, in which we cover the remainder of the textbook and further topics. These ideas have applications in Physics, Chemistry, Engineering and other disciplines.

Texts: Differential Geometry and its Applications by John Oprea, 2^nd edition,

ISBN: 9780883857489 (MAA version) Available in the University Bookstore and

Iowa Book and Supply, Amazon and many other possibilities for online purchases

ASSIGNMENTS:

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