**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

SYLLABUS:

EXAM INFORMATION: