| 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 2-5 |
|
| 2 | 0912 | L03 | §13.1
Examples 6-7 §13.2 derivative of vector functions, geometric meaning, unit tangent vector, Examples 1-2 |
| 0914 | L04 | §13.2 tangent line, a nondifferentiable parametrization, differentiation rules, Examples
3-5 |
|
| 0916 | L05 | §13.2 integration, Examples 6 §13.3 arclength, arclength parametrization, Examples 1-4 |
|
| 3 | 0919 | L06 | §13.3 curvature, Examples 5-7 |
| 0921 | L07 | §13.3 normal and binormal vectors, normal and osculating
planes, Examples 8-9 |
|
| 0923 | L08 | §13.3 osculating circle, Examples 10-11 §13.4 position, velocity, speed and acceleration, Examples 1-2 |
|
| 4 | 0926 | L09 | §13.4 Examples 3-4 §16.1 vector fields, Examples 1-2 |
| 0928 | L10 | §16.1 Examples 3-7 §16.2 line integral of a scalar function with respect to arclength |
|
| 0930 |
L11 | §16.2 Examples 1-4 |
|
| 5 | 1003 |
L12 | §16.2 line integral
with respect to x,y,z; line integral of vector fields,
Examples 5-10 |
| 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 3-5 |
|
| 7 | 1017 |
L16 |
§16.3 Examples 5-6: finding potential §16.4 Green Theorem |
| 1019 |
L17 |
§16.4 Examples 1-5 |
|
| 1021 |
L18 | §16.4 Examples 6-8 §16.5 curl definition |
|
| 8 | 1024 |
L19 | §16.5 definitions of divergence and Laplacian, Examples 1-7 |
| 1026 |
L20 | §16.5 mechanic meanings of curl and div, vector forms of Green Theorem §16.6 parametric surfaces, Examples 1-3 |
|
| 1028 |
L21 | §16.6 Examples 4-7, 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
8b-12 |
| 1102 |
L23 | §16.6 special forms of surface area formulas, Examples 12-14 |
|
| 1104 |
L24 | §16.7 surface integral of scalar functions, Examples
1-3 |
|
| 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 5-7
|
| 1116 |
L27 | §16.8 Stokes' theorem, statement and partial proof, Example 1 |
|
| 1118 |
L28 | finish the proof of Stokes' theorem. Examples 2-3 |
|
| 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 5-7, variants of Divergence theorem |
|
| 1202 |
L34 |
conclusion and review |
