## MATH 317 Sep-Dec 2016 Lecture Summary

 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