

Week  Topic  Notes 
1  (1.2, 1.3) Curves, regular curves. Arc length  
2  (1.4, 1.5) Curves parametrized by arc length  
3  (1.6, 1.7) Global properties  
4  (2.2, 2.3) Regular surfaces. Change of parameters  Midterm I 
5  (2.4, 2.5) Tangent plane. First fundamental form  
6  (1.6, 2.7, 2.8) Orientation. Definition of area  
7  Review and problems  
8  (3.2) The Gauss map  
9  (3.3) The Gauss map in local coordinates  Midterm II 
10  (3.4) Vector fields  
11  (3.5) Ruled and minimal surfaces  
12  (4.2, 4.3) Isometries, conformal maps, the Gauss theorem  
13  (4.4) Parallel transport, geodesics  
14  (4.5, 4.6) The GaussBonnet theorem. exponential map  
15  Review and problems  
Finals week  Final 