Course Title: Euclidean Curves & Surfaces MATH 4530 - 1 Andrejs Treibergs M, W, F, 8:35 - 9:25 AM in ST 216. 12:40-1:30 M, W, F, in JWB 224 (tent.) treiberg@math.utah.edu Advanced calculus (e.g. MATH 2210 or consent of instructor.) Andrew Pressley, Elementary Differential Geometry, Springer, 2001.

# The  Final Exam  for Math 4530-1 is Tue., Mar. 29, 8:00 - 10:00 AM in class.

Half of the exam will cover sections 7.1 - 7.6, 8.1 - 8.3, 10.1 - 10.4, 11.1 - 11.3 of the text. The other half will be comprehensive over the material from the entier semester.
The exam is closed book except that you are allowed to bring a "Cheat Sheet", TWO 8.5"×11" sheets of notes.

# Supplementary Notes for M4530

http://www.math.utah.edu/~treiberg/M4530.ps, .pdf

MAPLE worksheet for reviewing of M4530

## The Hyperbolic Plane and its Immersions into R3

We study how to describe and compute geometric features of curved surfaces in Euclidean three space. We describe the Gauß and mean curvature of a surface. We shall discuss applications to cartography, soap films and bubbles. We shall touch opun mechanical and variational principles. We shall also mention non-Euclidean geometries. We shall use the MAPLE computer algebra system to illustrate text and lectures.

Topics include (depending on time):

• Curves in the plane and in three space.
• Isoperimetric Inequality.
• Differentiating functions and vector fields on a surface.
• Normal curvature of curves on a surface.
• Gauß curvature Surfaces of revolutiuon.
• Minimal surfaces. Conformal maps. Mercator projection.
• Constant Mean Curvature Surfaces.
• Isometric Immersions. Second fundamental form.
• Complete manifolds. Geodesics.
• Gauß Bonnet Theorem.
• Hilbert's theorems on immersing the sphere and the hyperbolc plane.

Last updated: 2 - 7 - 8