UBC MATH 317 Jan-April 2013 Lecture Summary


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Date Lec-
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Contents
1 1231


0102 L01
outline
§13.1 vector functions
0104 L02 §13.1 space curves
2 0107 L03 §13.1 more examples
§13.2 derivatives and tangent vectors
0109 L04 §13.2 differentiation rules, integrals, length of a curve
0111 L05 §13.3 arclength function and reparametrization using it, curvature
3 0114 L06 §13.3 more on curvature, normal and binormal vectors, normal and osculating planes
0116 L07 §13.3 osculating plane and osculating circle
0118 L08 §13.4 motion in space (materials beyond Example 6 are skipped)
4 0121 L09 §16.1 vector fields
0123 L10 §16.2 line integrals with respect to arclength
0125
L11 §16.2 center of mass, line integrals with respect to x and y
5 0128
L12 §16.2 line integrals in space and of vector fields
0130
L13 §16.3 When a line integral of vector field is independent of path
0201

midterm exam 1
6 0204
L14 §16.3 Equivalent statements of conservative vector fields
0206
L15
§16.3 necessary and sufficient conditions in terms of partial derivatives
0208
L16 §16.3 finding potential function
§16.4 Green's theorem: statement and proof
7 0211

Family Day
0213
L17 §16.4 examples for Green's theorem
0215
L18 §16.4 more examples
§16.5 algebraic definition of curl F
0218-0222
midterm break
8 0225
L19 §16.5 algebraic definition of div F, geometric meanings
0227
L20 §16.5 more on geometric meaning, vector forms of Green's theorem
§16.6 parametric surfaces
0301
L21 §16.6 more examples of parametric surfaces, tangent planes, surface area
9 0304
L22 §16.6 examples of surface area, area of graphs and surfaces of revolution
0306
L23 §16.7 surface integrals of scalar functions
0308
L24 §16.7 flux integral of a vector field through a surface
10 0311
L25 §16.7 more examples
0313
L26 §16.7 more examples
§16.8 Stokes theorem
0315

midterm exam 2
11 0318
L27 §16.8 Stokes theorem: proof and examples
0320
L28 §16.8 Stokes theorem: more examples
0322
L29 §16.8 Stokes theorem: more examples
§16.9 Divergence theorem
12 0325
L30 §16.9 Divergence theorem: continued
0327
L31 §16.9 Divergence theorem: continued
0329

Good Friday
13
0401

Easter Monday
0403
L32
§16.9 Divergence theorem: an example of channel flow
Final exam, review Final Exam of April 2010
0405
L33
review Final Exam of December 2011