We ek 
Date  Lec ture 
Contents 
1  0905 
Labour Day  
0907  L01 
outline and overview, notation §13.1 vector functions of one variable: definition and Example 1 

0909  L02  §13.1 limit and continuity of vector functions, space
curves,
Examples 25 

2  0912  L03  §13.1
Examples 67 §13.2 derivative of vector functions, geometric meaning, unit tangent vector, Examples 12 
0914  L04  §13.2 tangent line, a nondifferentiable parametrization, differentiation rules, Examples
35 

0916  L05  §13.2 integration, Examples 6 §13.3 arclength, arclength parametrization, Examples 14 

3  0919  L06  §13.3 curvature, Examples 57 
0921  L07  §13.3 normal and binormal vectors, normal and osculating
planes, Examples 89 

0923  L08  §13.3 osculating circle, Examples 1011 §13.4 position, velocity, speed and acceleration, Examples 12 

4  0926  L09  §13.4 Examples 34 §16.1 vector fields, Examples 12 
0928  L10  §16.1 Examples 37 §16.2 line integral of a scalar function with respect to arclength 

0930 
L11  §16.2 Examples 14 

5  1003 
L12  §16.2 line integral
with respect to x,y,z; line integral of vector fields,
Examples 510 
1005 
Midterm exam 1  
1007 
L13  §16.3 Conservative vector fields, Example 1, Theorem 1 

6  1010 
Thanksgiving Day 

1012 
L14 
§16.3 Theorem 2 (equivalent statements of conservative
vector fields), Example 2, statement of Theorem 3 

1014 
L15  §16.3 Theorem 3 (conservative if P_y=Q_x on a simply
connected domain), Examples 35 

7  1017 
L16 
§16.3 Examples 56: finding potential §16.4 Green Theorem 
1019 
L17 
§16.4 Examples 15 

1021 
L18  §16.4 Examples 68 §16.5 curl definition 

8  1024 
L19  §16.5 definitions of divergence and Laplacian, Examples 17 
1026 
L20  §16.5 mechanic meanings of curl and div, vector forms of Green Theorem §16.6 parametric surfaces, Examples 13 

1028 
L21  §16.6 Examples 47, 1b,
tangent plane,
Example 8a picture for Example 4 and its Maple code: plot3d([v*cos(u), v*sin(u), u], u = 0 .. 2*Pi, v = 2 .. 2) 

9  1031 
L22  §16.6 regular parametrization, surface area, Examples
8b12 
1102 
L23  §16.6 special forms of surface area formulas, Examples 1214 

1104 
L24  §16.7 surface integral of scalar functions, Examples
13 

10  1107 
L25  §16.7 surface integral of vector flux, physical meaning and
formulas,
orientable surfaces and
Mobius band,
Example 4 
1109 
Midterm exam 2 

1111 
Remembrance Day 

11  1114 
L26  §16.7 fluid flux and electric flux, Examples 57

1116 
L27  §16.8 Stokes' theorem, statement and partial proof, Example 1 

1118 
L28  finish the proof of Stokes' theorem. Examples 23 

12  1121 
L29  boundary of a surface, Example 4 
1123 
L30  second solution of Example 4, circulation, Examples 5 and 6 

1125 
L31 
§16.9 Divergence theorem, statement and sketch of proof,
Examples 1, 2 

13 
1128 
L32 
solution of example 2, physical interpretation, source and sink,
Example 3 (flux of
pipe flow), Example 4 (flux of point charge) 
1130 
L33 
Examples 57, variants of Divergence theorem 

1202 
L34 
conclusion and review 