## UBC MATH 317 Jan-April 2013 Lecture Summary

 We ek Date Lec- ture 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