Math 251:01-03 (MonTh, 9-10:20am)  Fall 2021

                     Syllabus and General Information    

Date Lecture Topic(s) and text sections Suggested Homework
09/02 1 12.1 Three Dimensional Coordinate Systems
12.2 Vectors		 12.1/ #3,9,15,16,21,23,39,59
12.2/ #9,19,23,25,31,41,47
09/08 2 12.3 The Dot Product 
12.4 The Cross Product 		 12.3/ #3,13,18,19,22
12.4/ #7,15,21,23,27,33,35,45
09/09 3 12.5 Lines and Planes in Space
12.6 Cylinders and Quadric Surfaces		 12.5/ #6,6,9,23,27,31,37,41, 47, 57
12.6/ #1-12, 13, 15, 21, 25
09/13 4 13.1 Curves in Space and Their Tangents 13.1/ #1,15,19,23, 31
09/16 5 13.2 Integrals of Vector-Valued Functions, Projectile Motion 13.2/ #3,5,8,11,15,19
09/20 6 13.3 Arc Length in Space 13.3/ #5,9,13,15
09/23 7 14.1 Functions of Several Variables
14.2 Limits and Continuity in Higher Dimensions		 14.1/ #6,6,9,15-18,27,31,41,58,59
14.2/ #11,15,20-22,31,47,48,53,59
09/27 8 14.3 Partial Derivatives
14.4 The Chain Rule		 14.3/ #9,14-18,27,3046,67
14.4/ #7,28,29,33,39,44
09/30 9 14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials		 14.5/ #3-6,9,10,21,28,29,31
14.6/ #5,9,13,19,21,31
10/04 10 14.7 Extreme Values and Saddle Points 14.7/ #13,19,29,33,35,43,45,62
10/07 11 14.8 Lagrange Multipliers 14.8/ #1,5,9,13,17,21,29
10/11 12 15.1 Double and Iterated Integrals Over Rectangles
15.2 Double Integrals over General Regions		 15.1/ #7,11,13,18,23,27,29,36
15.2/ #1-8,12,15,18,23,29,35,38,43,53
10/14 13 15.3 Area by Double Integration
15.4 Double Integrals in Polar Form		 15.3/ #6-8,16,18,21
15.4/ #1-6,9,11,16,23,25,28,35
10/18 14 15.5 Triple Integrals in Rectangular Coordinates 15.5/ #3,6,17,21,27,28,37,45
10/21 15 15.7 Triple Integrals in Cylindrical and Spherical Coordinates
10/25 16 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7/ #3-7,13-17,25,31,38,47,59,65
10/28 17 15.8 Substitution in Multiple Integrals 15.8/ #1,3,6,7,9
11/01 18 16.1 Line Integrals of Scalar Functions 16.1/ #1-9,14,15,25,26,29,35,36
11/04 19 16.2 Vector Fields & Line Integrals: Work, Circulation, Flux 16.2/ #3,7,11,14,15,18,25,27,29,30,35,39,40,57,59
11/08 20 16.3 Path Independence, Conservative Fields, Potentials 16.3/ #3,5,9,11,19,22,25,29,31
11/11 21 16.4 Green's Theorem in the Plane 16.4/ #2,5,9,13,16,17,21,29,31,37
11/15 22 16.5 Surfaces and Area 6.5/ #1,7,11,13,15,27,41,43
11/18 23 16.5 Surfaces and Area, start 16.6 16.5/ #1,7,11,13,15,27,41,43
11/22 24 16.6 Surface Integrals 16.6/#3,5,6,17,23,26,28,43
12/02 25 16.7 Stokes' Theorem 16.7/ #5,7,11,19,23,28
12/06 26 16.8 The Divergence Theorem & A Unified Theory 16.8/ #9,11,13,15,27,28
12/09 27 Catch up & Review  
12/13 28 Catch up & Review